AI Data Trainer/annotator

Retrieval-augmented generation

Retrieval-augmented generation (RAG) is a technique that enables large language models (LLMs) to retrieve and incorporate new information from external data sources. With RAG, LLMs first refer to a specified set of documents, then respond to user queries. These documents supplement information from the LLM's pre-existing training data. This allows LLMs to use domain-specific and/or updated information that is not available in the training data. For example, this enables LLM-based chatbots to access internal company data or generate responses based on authoritative sources. RAG improves LLMs by incorporating information retrieval before generating responses. Unlike LLMs that rely on static training data, RAG pulls relevant text from databases, uploaded documents, or web sources. According to Ars Technica, "RAG is a way of improving LLM performance, in essence by blending the LLM process with a web search or other document look-up process to help LLMs stick to the facts." This method helps reduce AI hallucinations, which have caused chatbots to describe policies that don't exist, or recommend nonexistent legal cases to lawyers that are looking for citations to support their arguments. RAG also reduces the need to retrain LLMs with new data, saving on computational and financial costs. Beyond efficiency gains, RAG also allows LLMs to include sources in their responses, so users can verify the cited sources. This provides greater transparency, as users can cross-check retrieved content to ensure accuracy and relevance. The term retrieval-augmented generation (RAG) was introduced in a 2020 paper that described combining a parametric language model with a non-parametric external memory accessed through retrieval at inference time. == RAG and LLM limitations == LLMs can provide incorrect information. For example, when Google first demonstrated its LLM tool "Google Bard" (later re-branded to Gemini), the LLM provided incorrect information about the James Webb Space Telescope. This error contributed to a $100 billion decline in Google's stock value. RAG is used to prevent these errors, but it does not solve all the problems. For example, LLMs can generate misinformation even when pulling from factually correct sources if they misinterpret the context. MIT Technology Review gives the example of an AI-generated response stating, "The United States has had one Muslim president, Barack Hussein Obama." The model retrieved this from an academic book rhetorically titled Barack Hussein Obama: America's First Muslim President? The LLM did not "know" or "understand" the context of the title, generating a false statement. LLMs with RAG are programmed to prioritize new information. This technique has been called "prompt stuffing." Without prompt stuffing, the LLM's input is generated by a user; with prompt stuffing, additional relevant context is added to this input to guide the model's response. This approach provides the LLM with key information early in the prompt, encouraging it to prioritize the supplied data over pre-existing training knowledge. == Process == Retrieval-augmented generation (RAG) enhances large language models (LLMs) by incorporating an information-retrieval mechanism that allows models to access and utilize additional data beyond their original training set. Ars Technica notes that "when new information becomes available, rather than having to retrain the model, all that's needed is to augment the model's external knowledge base with the updated information" ("augmentation"). IBM states that "in the generative phase, the LLM draws from the augmented prompt and its internal representation of its training data to synthesize" an answer. === RAG key stages === Typically, the data to be referenced is converted into LLM embeddings, numerical representations in the form of a large vector space. RAG can be used on unstructured (usually text), semi-structured, or structured data (for example knowledge graphs). These embeddings are then stored in a vector database to allow for document retrieval. Given a user query, a document retriever is first called to select the most relevant documents that will be used to augment the query. This comparison can be done using a variety of methods, which depend in part on the type of indexing used. The model feeds this relevant retrieved information into the LLM via prompt engineering of the user's original query. Newer implementations (as of 2023) can also incorporate specific augmentation modules with abilities such as expanding queries into multiple domains and using memory and self-improvement to learn from previous retrievals. Finally, the LLM can generate output based on both the query and the retrieved documents. Some models incorporate extra steps to improve output, such as the re-ranking of retrieved information, context selection, and fine-tuning. == Applications == Retrieval-augmented generation is used in applications where generated responses need to be grounded in external or frequently updated information. Commonly cited use cases include search engines, question-answering systems, customer support chatbots, enterprise knowledge assistants, content generation, recommendation systems, retail and e-commerce, and industrial or manufacturing workflows. In healthcare, RAG has been studied as a way to ground large language model outputs in external medical knowledge sources, although reviews have noted continuing challenges around evaluation, ethics, and clinical reliability. == Improvements == Improvements to the basic process above can be applied at different stages in the RAG flow. === Encoder === These methods focus on the encoding of text as either dense or sparse vectors. Sparse vectors, which encode the identity of a word, are typically dictionary-length and contain mostly zeros. Dense vectors, which encode meaning, are more compact and contain fewer zeros. Various enhancements can improve the way similarities are calculated in the vector stores (databases). Performance improves by optimizing how vector similarities are calculated. Dot products enhance similarity scoring, while approximate nearest neighbor (ANN) searches improve retrieval efficiency over K-nearest neighbors (KNN) searches. Accuracy may be improved with Late Interactions, which allow the system to compare words more precisely after retrieval. This helps refine document ranking and improve search relevance. Hybrid vector approaches may be used to combine dense vector representations with sparse one-hot vectors, taking advantage of the computational efficiency of sparse dot products over dense vector operations. Other retrieval techniques focus on improving accuracy by refining how documents are selected. Some retrieval methods combine sparse representations, such as SPLADE, with query expansion strategies to improve search accuracy and recall. === Retriever-centric methods === These methods aim to enhance the quality of document retrieval in vector databases: Pre-training the retriever using the Inverse Cloze Task (ICT), a technique that helps the model learn retrieval patterns by predicting masked text within documents. Supervised retriever optimization aligns retrieval probabilities with the generator model's likelihood distribution. This involves retrieving the top-k vectors for a given prompt, scoring the generated response's perplexity, and minimizing KL divergence between the retriever's selections and the model's likelihoods to refine retrieval. Reranking techniques can refine retriever performance by prioritizing the most relevant retrieved documents during training. === Language model === By redesigning the language model with the retriever in mind, a 25-time smaller network can get comparable perplexity as its much larger counterparts. Because it is trained from scratch, this method (Retro) incurs the high cost of training runs that the original RAG scheme avoided. The hypothesis is that by giving domain knowledge during training, Retro needs less focus on the domain and can devote its smaller weight resources only to language semantics. The redesigned language model is shown here. It has been reported that Retro is not reproducible, so modifications were made to make it so. The more reproducible version is called Retro++ and includes in-context RAG. === Chunking === Chunking involves various strategies for breaking up the data into vectors so the retriever can find details in it. Three types of chunking strategies are: Fixed length with overlap. This is fast and easy. Overlapping consecutive chunks helps to maintain semantic context across chunks. Syntax-based chunks can break the document up into sentences. Libraries such as spaCy or NLTK can also help. File format-based chunking. Certain file types have natural chunks built in, and it's best to respect them. For example, code files are best chunked and vectorized as whole functions or classes. HTML files should leave

or base64 encoded elements

Brill tagger

The Brill tagger is an inductive method for part-of-speech tagging. It was described and invented by Eric Brill in his 1993 PhD thesis. It can be summarized as an "error-driven transformation-based tagger". It is: a form of supervised learning, which aims to minimize error; and, a transformation-based process, in the sense that a tag is assigned to each word and changed using a set of predefined rules. In the transformation process, if the word is known, it first assigns the most frequent tag, or if the word is unknown, it naively assigns the tag "noun" to it. High accuracy is eventually achieved by applying these rules iteratively and changing the incorrect tags. This approach ensures that valuable information such as the morphosyntactic construction of words is employed in an automatic tagging process. == Algorithm == The algorithm starts with initialization, which is the assignment of tags based on their probability for each word (for example, "dog" is more often a noun than a verb). Then "patches" are determined via rules that correct (probable) tagging errors made in the initialization phase: Initialization: Known words (in vocabulary): assigning the most frequent tag associated to a form of the word Unknown word == Rules and processing == The input text is first tokenized, or broken into words. Typically in natural language processing, contractions such as "'s", "n't", and the like are considered separate word tokens, as are punctuation marks. A dictionary and some morphological rules then provide an initial tag for each word token. For example, a simple lookup would reveal that "dog" may be a noun or a verb (the most frequent tag is simply chosen), while an unknown word will be assigned some tag(s) based on capitalization, various prefix or suffix strings, etc. (such morphological analyses, which Brill calls Lexical Rules, may vary between implementations). After all word tokens have (provisional) tags, contextual rules apply iteratively, to correct the tags by examining small amounts of context. This is where the Brill method differs from other part of speech tagging methods such as those using Hidden Markov Models. Rules are reapplied repeatedly, until a threshold is reached, or no more rules can apply. Brill rules are of the general form: tag1 → tag2 IF Condition where the Condition tests the preceding and/or following word tokens, or their tags (the notation for such rules differs between implementations). For example, in Brill's notation: IN NN WDPREVTAG DT while would change the tag of a word from IN (preposition) to NN (common noun), if the preceding word's tag is DT (determiner) and the word itself is "while". This covers cases like "all the while" or "in a while", where "while" should be tagged as a noun rather than its more common use as a conjunction (many rules are more general). Rules should only operate if the tag being changed is also known to be permissible, for the word in question or in principle (for example, most adjectives in English can also be used as nouns). Rules of this kind can be implemented by simple Finite-state machines. See Part of speech tagging for more general information including descriptions of the Penn Treebank and other sets of tags. Typical Brill taggers use a few hundred rules, which may be developed by linguistic intuition or by machine learning on a pre-tagged corpus. == Code == Brill's code pages at Johns Hopkins University are no longer on the web. An archived version of a mirror of the Brill tagger at its latest version as it was available at Plymouth Tech can be found on Archive.org. The software uses the MIT License.

Viola–Jones object detection framework

The Viola–Jones object detection framework is a machine learning object detection framework proposed in 2001 by Paul Viola and Michael Jones. It was motivated primarily by the problem of face detection, although it can be adapted to the detection of other object classes. In short, it consists of a sequence of classifiers. Each classifier is a single perceptron with several binary masks (Haar features). To detect faces in an image, a sliding window is computed over the image. For each image, the classifiers are applied. If at any point, a classifier outputs "no face detected", then the window is considered to contain no face. Otherwise, if all classifiers output "face detected", then the window is considered to contain a face. The algorithm is efficient for its time, able to detect faces in 384 by 288 pixel images at 15 frames per second on a conventional 700 MHz Intel Pentium III. It is also robust, achieving high precision and recall. While it has lower accuracy than more modern methods such as convolutional neural network, its efficiency and compact size (only around 50k parameters, compared to millions of parameters for typical CNN like DeepFace) means it is still used in cases with limited computational power. For example, in the original paper, they reported that this face detector could run on the Compaq iPAQ at 2 fps (this device has a low power StrongARM without floating point hardware). == Problem description == Face detection is a binary classification problem combined with a localization problem: given a picture, decide whether it contains faces, and construct bounding boxes for the faces. To make the task more manageable, the Viola–Jones algorithm only detects full view (no occlusion), frontal (no head-turning), upright (no rotation), well-lit, full-sized (occupying most of the frame) faces in fixed-resolution images. The restrictions are not as severe as they appear, as one can normalize the picture to bring it closer to the requirements for Viola-Jones. any image can be scaled to a fixed resolution for a general picture with a face of unknown size and orientation, one can perform blob detection to discover potential faces, then scale and rotate them into the upright, full-sized position. the brightness of the image can be corrected by white balancing. the bounding boxes can be found by sliding a window across the entire picture, and marking down every window that contains a face. This would generally detect the same face multiple times, for which duplication removal methods, such as non-maximal suppression, can be used. The "frontal" requirement is non-negotiable, as there is no simple transformation on the image that can turn a face from a side view to a frontal view. However, one can train multiple Viola-Jones classifiers, one for each angle: one for frontal view, one for 3/4 view, one for profile view, a few more for the angles in-between them. Then one can at run time execute all these classifiers in parallel to detect faces at different view angles. The "full-view" requirement is also non-negotiable, and cannot be simply dealt with by training more Viola-Jones classifiers, since there are too many possible ways to occlude a face. == Components of the framework == A full presentation of the algorithm is in. Consider an image I ( x , y ) {\displaystyle I(x,y)} of fixed resolution ( M , N ) {\displaystyle (M,N)} . Our task is to make a binary decision: whether it is a photo of a standardized face (frontal, well-lit, etc) or not. Viola–Jones is essentially a boosted feature learning algorithm, trained by running a modified AdaBoost algorithm on Haar feature classifiers to find a sequence of classifiers f 1 , f 2 , . . . , f k {\displaystyle f_{1},f_{2},...,f_{k}} . Haar feature classifiers are crude, but allows very fast computation, and the modified AdaBoost constructs a strong classifier out of many weak ones. At run time, a given image I {\displaystyle I} is tested on f 1 ( I ) , f 2 ( I ) , . . . f k ( I ) {\displaystyle f_{1}(I),f_{2}(I),...f_{k}(I)} sequentially. If at any point, f i ( I ) = 0 {\displaystyle f_{i}(I)=0} , the algorithm immediately returns "no face detected". If all classifiers return 1, then the algorithm returns "face detected". For this reason, the Viola-Jones classifier is also called "Haar cascade classifier". === Haar feature classifiers === Consider a perceptron f w , b {\displaystyle f_{w,b}} defined by two variables w ( x , y ) , b {\displaystyle w(x,y),b} . It takes in an image I ( x , y ) {\displaystyle I(x,y)} of fixed resolution, and returns f w , b ( I ) = { 1 , if ∑ x , y w ( x , y ) I ( x , y ) + b > 0 0 , else {\displaystyle f_{w,b}(I)={\begin{cases}1,\quad {\text{if }}\sum _{x,y}w(x,y)I(x,y)+b>0\\0,\quad {\text{else}}\end{cases}}} A Haar feature classifier is a perceptron f w , b {\displaystyle f_{w,b}} with a very special kind of w {\displaystyle w} that makes it extremely cheap to calculate. Namely, if we write out the matrix w ( x , y ) {\displaystyle w(x,y)} , we find that it takes only three possible values { + 1 , − 1 , 0 } {\displaystyle \{+1,-1,0\}} , and if we color the matrix with white on + 1 {\displaystyle +1} , black on − 1 {\displaystyle -1} , and transparent on 0 {\displaystyle 0} , the matrix is in one of the 5 possible patterns shown on the right. Each pattern must also be symmetric to x-reflection and y-reflection (ignoring the color change), so for example, for the horizontal white-black feature, the two rectangles must be of the same width. For the vertical white-black-white feature, the white rectangles must be of the same height, but there is no restriction on the black rectangle's height. ==== Rationale for Haar features ==== The Haar features used in the Viola-Jones algorithm are a subset of the more general Haar basis functions, which have been used previously in the realm of image-based object detection. While crude compared to alternatives such as steerable filters, Haar features are sufficiently complex to match features of typical human faces. For example: The eye region is darker than the upper-cheeks. The nose bridge region is brighter than the eyes. Composition of properties forming matchable facial features: Location and size: eyes, mouth, bridge of nose Value: oriented gradients of pixel intensities Further, the design of Haar features allows for efficient computation of f w , b ( I ) {\displaystyle f_{w,b}(I)} using only constant number of additions and subtractions, regardless of the size of the rectangular features, using the summed-area table. === Learning and using a Viola–Jones classifier === Choose a resolution ( M , N ) {\displaystyle (M,N)} for the images to be classified. In the original paper, they recommended ( M , N ) = ( 24 , 24 ) {\displaystyle (M,N)=(24,24)} . ==== Learning ==== Collect a training set, with some containing faces, and others not containing faces. Perform a certain modified AdaBoost training on the set of all Haar feature classifiers of dimension ( M , N ) {\displaystyle (M,N)} , until a desired level of precision and recall is reached. The modified AdaBoost algorithm would output a sequence of Haar feature classifiers f 1 , f 2 , . . . , f k {\displaystyle f_{1},f_{2},...,f_{k}} . The details of the modified AdaBoost algorithm is detailed below. ==== Using ==== To use a Viola-Jones classifier with f 1 , f 2 , . . . , f k {\displaystyle f_{1},f_{2},...,f_{k}} on an image I {\displaystyle I} , compute f 1 ( I ) , f 2 ( I ) , . . . f k ( I ) {\displaystyle f_{1}(I),f_{2}(I),...f_{k}(I)} sequentially. If at any point, f i ( I ) = 0 {\displaystyle f_{i}(I)=0} , the algorithm immediately returns "no face detected". If all classifiers return 1, then the algorithm returns "face detected". === Learning algorithm === The speed with which features may be evaluated does not adequately compensate for their number, however. For example, in a standard 24x24 pixel sub-window, there are a total of M = 162336 possible features, and it would be prohibitively expensive to evaluate them all when testing an image. Thus, the object detection framework employs a variant of the learning algorithm AdaBoost to both select the best features and to train classifiers that use them. This algorithm constructs a "strong" classifier as a linear combination of weighted simple “weak” classifiers. h ( x ) = sgn ⁡ ( ∑ j = 1 M α j h j ( x ) ) {\displaystyle h(\mathbf {x} )=\operatorname {sgn} \left(\sum _{j=1}^{M}\alpha _{j}h_{j}(\mathbf {x} )\right)} Each weak classifier is a threshold function based on the feature f j {\displaystyle f_{j}} . h j ( x ) = { − s j if f j < θ j s j otherwise {\displaystyle h_{j}(\mathbf {x} )={\begin{cases}-s_{j}&{\text{if }}f_{j}<\theta _{j}\\s_{j}&{\text{otherwise}}\end{cases}}} The threshold value θ j {\displaystyle \theta _{j}} and the polarity s j ∈ ± 1 {\displaystyle s_{j}\in \pm 1} are determined in the training, as well as the coefficients α j {\displaystyle \alpha _{j}} . Here a simplified version of the lea

Ghana Post GPS

GhanaPostGPS is a web and smartphone application, sponsored by the government of Ghana and developed by Vokacom, to provide a digital addresses and postal codes for every 5 squared meter location in Ghana. The digital address is a composite of the postcode (region, district & area code) plus a unique address. GhanaPostGPS is the first digital addressing system created by the government of Ghana. GhanaPost GPS is a mandatory requirement for obtaining the National Identification Card and other services.

Luminance HDR

Luminance HDR, formerly Qtpfsgui, is graphics software used for the creation and manipulation of high-dynamic-range images. Released under the terms of the GPL, it is available for Linux, Microsoft Windows, and Mac OS X (Intel only). Luminance HDR supports several High Dynamic Range (HDR) as well as Low Dynamic Range (LDR) file formats. == Functionality == Prerequisite of HDR photography are several narrow-range digital images with different exposures. Luminance HDR combines these images and calculates a high-contrast image. In order to view this image on a regular computer monitor, Luminance HDR can convert it into a displayable LDR image format using a variety of methods, such as tone mapping. Currently fifteen different tone mapping operators (algorithms) are available, each one with its tunable parameters. Different image processing techniques can be applied to the generated HDR images, such as resizing, cropping, rotating and a number of projective transformations. The software also provides batch processing functionality for creating HDR images and for tone mapping them in a non-interactive way. A module for copying Exif data among sets of images is also provided. For users who prefers the command line, a non-GUI, non-graphical interface is also available on all supported platforms. A common problem with HDR photography is that images need to be aligned exactly. If the subject is static, this can be achieved using a tripod or a stable surface on which the camera is placed. In the case of image data that does not align exactly, an automatic alignment can be performed using a tool provided by the Hugin project. If this automation doesn't provide the desired result, the user may improve it manually. == Supported formats == HDR images are images with a high dynamic range and, using Luminance HDR, they can be created as well as edited. The following HDR graphic formats are supported: OpenEXR Radiance HDR Tag Image File Format (TIFF) Format: 16 Bit, 32 Bit (Float) and LogLuv Raw PFS native Luminance HDR can create an HDR image from several LDR images and tonemap an HDR into an LDR. The following LDR formats are supported: JPG PNG Portable Pixmap (PPM) Portable Bitmap (PBM) TIFF (8 Bit)

Common data model

A common data model (CDM) can refer to any standardised data model which allows for data and information exchange between different applications and data sources. Common data models aim to standardise logical infrastructure so that related applications can "operate on and share the same data", and can be seen as a way to "organize data from many sources that are in different formats into a standard structure". A common data model has been described as one of the components of a "strong information system". A standardised common data model has also been described as a typical component of a well designed agile application besides a common communication protocol. Providing a single common data model within an organisation is one of the typical tasks of a data warehouse. == Examples of common data models == === Border crossings === X-trans.eu was a cross-border pilot project between the Free State of Bavaria (Germany) and Upper Austria with the aim of developing a faster procedure for the application and approval of cross-border large-capacity transports. The portal was based on a common data model that contained all the information required for approval. === Climate data === The Climate Data Store Common Data Model is a common data model set up by the Copernicus Climate Change Service for harmonising essential climate variables from different sources and data providers. === General information technology === Within service-oriented architecture, S-RAMP is a specification released by HP, IBM, Software AG, TIBCO, and Red Hat which defines a common data model for SOA repositories as well as an interaction protocol to facilitate the use of common tooling and sharing of data. Content Management Interoperability Services (CMIS) is an open standard for inter-operation of different content management systems over the internet, and provides a common data model for typed files and folders used with version control. The NetCDF software libraries for array-oriented scientific data implements a common data model called the NetCDF Java common data model, which consists of three layers built on top of each other to add successively richer semantics. === Health === Within genomic and medical data, the Observational Medical Outcomes Partnership (OMOP) research program established under the U.S. National Institutes of Health has created a common data model for claims and electronic health records which can accommodate data from different sources around the world. PCORnet, which was developed by the Patient-Centered Outcomes Research Institute, is another common data model for health data including electronic health records and patient claims. The Sentinel Common Data Model was initially started as Mini-Sentinel in 2008. It is used by the Sentinel Initiative of the USA's Food and Drug Administration. The Generalized Data Model was first published in 2019. It was designed to be a stand-alone data model as well as to allow for further transformation into other data models (e.g., OMOP, PCORNet, Sentinel). It has a hierarchical structure to flexibly capture relationships among data elements. The JANUS clinical trial data repository also provides a common data model which is based on the SDTM standard to represent clinical data submitted to regulatory agencies, such as tabulation datasets, patient profiles, listings, etc. === Logistics === SX000i is a specification developed jointly by the Aerospace and Defence Industries Association of Europe (ASD) and the American Aerospace Industries Association (AIA) to provide information, guidance and instructions to ensure compatibility and the commonality. The associated SX002D specification contains a common data model. === Microsoft Common Data Model === The Microsoft Common Data Model is a collection of many standardised extensible data schemas with entities, attributes, semantic metadata, and relationships, which represent commonly used concepts and activities in various businesses areas. It is maintained by Microsoft and its partners, and is published on GitHub. Microsoft's Common Data Model is used amongst others in Microsoft Dataverse and with various Microsoft Power Platform and Microsoft Dynamics 365 services. === Rail transport === RailTopoModel is a common data model for the railway sector. === Other === There are many more examples of various common data models for different uses published by different sources.

CMU Pronouncing Dictionary

The CMU Pronouncing Dictionary (also known as CMUdict) is an open-source pronouncing dictionary originally created by the Speech Group at Carnegie Mellon University (CMU) for use in speech recognition research. CMUdict provides a mapping orthographic/phonetic for English words in their North American pronunciations. It is commonly used to generate representations for speech recognition (ASR), e.g. the CMU Sphinx system, and speech synthesis (TTS), e.g. the Festival system. CMUdict can be used as a training corpus for building statistical grapheme-to-phoneme (g2p) models that will generate pronunciations for words not yet included in the dictionary. The most recent release is 0.7b; it contains over 134,000 entries. An interactive lookup version is available. == Database format == The database is distributed as a plain text file with one entry to a line in the format "WORD " with a two-space separator between the parts. If multiple pronunciations are available for a word, variants are identified using numbered versions (e.g. WORD(1)). The pronunciation is encoded using a modified form of the ARPABET system, with the addition of stress marks on vowels of levels 0, 1, and 2. A line-initial ;;; token indicates a comment. A derived format, directly suitable for speech recognition engines is also available as part of the distribution; this format collapses stress distinctions (typically not used in ASR). The following is a table of phonemes used by CMU Pronouncing Dictionary. == History == == Applications == The Unifon converter is based on the CMU Pronouncing Dictionary. The Natural Language Toolkit contains an interface to the CMU Pronouncing Dictionary. The Carnegie Mellon Logios tool incorporates the CMU Pronouncing Dictionary. PronunDict, a pronunciation dictionary of American English, uses the CMU Pronouncing Dictionary as its data source. Pronunciation is transcribed in IPA symbols. This dictionary also supports searching by pronunciation. Some singing voice synthesizer software like CeVIO Creative Studio and Synthesizer V uses modified version of CMU Pronouncing Dictionary for synthesizing English singing voices. Transcriber, a tool for the full text phonetic transcription, uses the CMU Pronouncing Dictionary 15.ai, a real-time text-to-speech tool using artificial intelligence, uses the CMU Pronouncing Dictionary

Textual case-based reasoning

Textual case-based reasoning (TCBR) is a subtopic of case-based reasoning, in short CBR, a popular area in artificial intelligence. CBR suggests the ways to use past experiences to solve future similar problems, requiring that past experiences be structured in a form similar to attribute-value pairs. This leads to the investigation of textual descriptions for knowledge exploration whose output will be, in turn, used to solve similar problems. == Subareas == Textual case-base reasoning research has focused on: measuring similarity between textual cases mapping texts into structured case representations adapting textual cases for reuse automatically generating representations.

SemEval

SemEval (Semantic Evaluation) is an ongoing series of evaluations of computational semantic analysis systems; it evolved from the Senseval word sense evaluation series. The evaluations are intended to explore the nature of meaning in language. While meaning is intuitive to humans, transferring those intuitions to computational analysis has proved elusive. This series of evaluations provides a mechanism to characterize in more precise terms exactly what is necessary to compute in meaning. As such, the evaluations provide an emergent mechanism to identify the problems and solutions for computations with meaning. These exercises have evolved to articulate more of the dimensions that are involved in our use of language. They began with apparently simple attempts to identify word senses computationally. They have evolved to investigate the interrelationships among the elements in a sentence (e.g., semantic role labeling), relations between sentences (e.g., coreference), and the nature of what we are saying (semantic relations and sentiment analysis). The purpose of the SemEval and Senseval exercises is to evaluate semantic analysis systems. "Semantic Analysis" refers to a formal analysis of meaning, and "computational" refer to approaches that in principle support effective implementation. The first three evaluations, Senseval-1 through Senseval-3, were focused on word sense disambiguation (WSD), each time growing in the number of languages offered in the tasks and in the number of participating teams. Beginning with the fourth workshop, SemEval-2007 (SemEval-1), the nature of the tasks evolved to include semantic analysis tasks outside of word sense disambiguation. Triggered by the conception of the SEM conference, the SemEval community had decided to hold the evaluation workshops yearly in association with the SEM conference. It was also the decision that not every evaluation task will be run every year, e.g. none of the WSD tasks were included in the SemEval-2012 workshop. == History == === Early evaluation of algorithms for word sense disambiguation === From the earliest days, assessing the quality of word sense disambiguation algorithms had been primarily a matter of intrinsic evaluation, and “almost no attempts had been made to evaluate embedded WSD components”. Only very recently (2006) had extrinsic evaluations begun to provide some evidence for the value of WSD in end-user applications. Until 1990 or so, discussions of the sense disambiguation task focused mainly on illustrative examples rather than comprehensive evaluation. The early 1990s saw the beginnings of more systematic and rigorous intrinsic evaluations, including more formal experimentation on small sets of ambiguous words. === Senseval to SemEval === In April 1997, Martha Palmer and Marc Light organized a workshop entitled Tagging with Lexical Semantics: Why, What, and How? in conjunction with the Conference on Applied Natural Language Processing. At the time, there was a clear recognition that manually annotated corpora had revolutionized other areas of NLP, such as part-of-speech tagging and parsing, and that corpus-driven approaches had the potential to revolutionize automatic semantic analysis as well. Kilgarriff recalled that there was "a high degree of consensus that the field needed evaluation", and several practical proposals by Resnik and Yarowsky kicked off a discussion that led to the creation of the Senseval evaluation exercises. === SemEval's 3, 2 or 1 year(s) cycle === After SemEval-2010, many participants feel that the 3-year cycle is a long wait. Many other shared tasks such as Conference on Natural Language Learning (CoNLL) and Recognizing Textual Entailments (RTE) run annually. For this reason, the SemEval coordinators gave the opportunity for task organizers to choose between a 2-year or a 3-year cycle. The SemEval community favored the 3-year cycle. Although the votes within the SemEval community favored a 3-year cycle, organizers and coordinators had settled to split the SemEval task into 2 evaluation workshops. This was triggered by the introduction of the new SEM conference. The SemEval organizers thought it would be appropriate to associate our event with the SEM conference and collocate the SemEval workshop with the SEM conference. The organizers got very positive responses (from the task coordinators/organizers and participants) about the association with the yearly SEM, and 8 tasks were willing to switch to 2012. Thus was born SemEval-2012 and SemEval-2013. The current plan is to switch to a yearly SemEval schedule to associate it with the SEM conference but not every task needs to run every year. ==== List of Senseval and SemEval Workshops ==== Senseval-1 took place in the summer of 1998 for English, French, and Italian, culminating in a workshop held at Herstmonceux Castle, Sussex, England on September 2–4. Senseval-2 took place in the summer of 2001, and was followed by a workshop held in July 2001 in Toulouse, in conjunction with ACL 2001. Senseval-2 included tasks for Basque, Chinese, Czech, Danish, Dutch, English, Estonian, Italian, Japanese, Korean, Spanish and Swedish. Senseval-3 took place in March–April 2004, followed by a workshop held in July 2004 in Barcelona, in conjunction with ACL 2004. Senseval-3 included 14 different tasks for core word sense disambiguation, as well as identification of semantic roles, multilingual annotations, logic forms, subcategorization acquisition. SemEval-2007 (Senseval-4) took place in 2007, followed by a workshop held in conjunction with ACL in Prague. SemEval-2007 included 18 different tasks targeting the evaluation of systems for the semantic analysis of text. A special issue of Language Resources and Evaluation is devoted to the result. SemEval-2010 took place in 2010, followed by a workshop held in conjunction with ACL in Uppsala. SemEval-2010 included 18 different tasks targeting the evaluation of semantic analysis systems. SemEval-2012 took place in 2012; it was associated with the new SEM, First Joint Conference on Lexical and Computational Semantics, and co-located with NAACL, Montreal, Canada. SemEval-2012 included 8 different tasks targeting at evaluating computational semantic systems. However, there was no WSD task involved in SemEval-2012, the WSD related tasks were scheduled in the upcoming SemEval-2013. SemEval-2013 was associated with NAACL 2013, North American Association of Computational Linguistics, Georgia, USA and took place in 2013. It included 13 different tasks targeting at evaluating computational semantic systems. SemEval-2014 took place in 2014. It was co-located with COLING 2014, 25th International Conference on Computational Linguistics and SEM 2014, Second Joint Conference on Lexical and Computational Semantics, Dublin, Ireland. There were 10 different tasks in SemEval-2014 evaluating various computational semantic systems. SemEval-2015 took place in 2015. It was co-located with NAACL-HLT 2015, 2015 Conference of the North American Chapter of the Association for Computational Linguistics – Human Language Technologies and SEM 2015, Third Joint Conference on Lexical and Computational Semantics, Denver, USA. There were 17 different tasks in SemEval-2015 evaluating various computational semantic systems. == SemEval Workshop framework == The framework of the SemEval/Senseval evaluation workshops emulates the Message Understanding Conferences (MUCs) and other evaluation workshops ran by ARPA (Advanced Research Projects Agency, renamed the Defense Advanced Research Projects Agency (DARPA)). Stages of SemEval/Senseval evaluation workshops Firstly, all likely participants were invited to express their interest and participate in the exercise design. A timetable towards a final workshop was worked out. A plan for selecting evaluation materials was agreed. 'Gold standards' for the individual tasks were acquired, often human annotators were considered as a gold standard to measure precision and recall scores of computer systems. These 'gold standards' are what the computational systems strive towards. In WSD tasks, human annotators were set on the task of generating a set of correct WSD answers (i.e. the correct sense for a given word in a given context) The gold standard materials, without answers, were released to participants, who then had a short time to run their programs over them and return their sets of answers to the organizers. The organizers then scored the answers and the scores were announced and discussed at a workshop. == Semantic evaluation tasks == Senseval-1 & Senseval-2 focused on evaluation WSD systems on major languages that were available corpus and computerized dictionary. Senseval-3 looked beyond the lexemes and started to evaluate systems that looked into wider areas of semantics, such as Semantic Roles (technically known as Theta roles in formal semantics), Logic Form Transformation (commonly semantics of phrases, clauses or sentences were represented

Sparrow (chatbot)

Sparrow is a chatbot developed by the artificial intelligence research lab DeepMind, a subsidiary of Alphabet Inc. It is designed to answer users' questions correctly, while reducing the risk of unsafe and inappropriate answers. One motivation behind Sparrow is to address the problem of language models producing incorrect, biased or potentially harmful outputs. Sparrow is trained using human judgements, in order to be more “Helpful, Correct and Harmless” compared to baseline pre-trained language models. The development of Sparrow involved asking paid study participants to interact with Sparrow, and collecting their preferences to train a model of how useful an answer is. To improve accuracy and help avoid the problem of hallucinating incorrect answers, Sparrow has the ability to search the Internet using Google Search in order to find and cite evidence for any factual claims it makes. To make the model safer, its behaviour is constrained by a set of rules, for example "don't make threatening statements" and "don't make hateful or insulting comments", as well as rules about possibly harmful advice, and not claiming to be a person. During development study participants were asked to converse with the system and try to trick it into breaking these rules. A 'rule model' was trained on judgements from these participants, which was used for further training. Sparrow was introduced in a paper in September 2022, titled "Improving alignment of dialogue agents via targeted human judgements"; however, the bot was not released publicly. DeepMind CEO Demis Hassabis said DeepMind is considering releasing Sparrow for a "private beta" some time in 2023. == Training == Sparrow is a deep neural network based on the transformer machine learning model architecture. It is fine-tuned from DeepMind's Chinchilla AI pre-trained large language model (LLM), which has 70 Billion parameters. Sparrow is trained using reinforcement learning from human feedback (RLHF), although some supervised fine-tuning techniques are also used. The RLHF training utilizes two reward models to capture human judgements: a “preference model” that predicts what a human study participant would prefer and a “rule model” that predicts if the model has broken one of the rules. == Limitations == Sparrow's training data corpus is mainly in English, meaning it performs worse in other languages. When adversarially probed by study participants it breaks the rules 8% of the time; however, this is still three times lower than the baseline prompted pre-trained model (Chinchilla).

Automatic summarization

Automatic summarization is the process of shortening a set of data computationally, to create a subset (a summary) that represents the most important or relevant information within the original content. Artificial intelligence (AI) algorithms are commonly developed and employed to achieve this, specialized for different types of data. Text summarization is usually implemented by natural language processing methods, designed to locate the most informative sentences in a given document. On the other hand, visual content can be summarized using computer vision algorithms. Image summarization is the subject of ongoing research; existing approaches typically attempt to display the most representative images from a given image collection, or generate a video that only includes the most important content from the entire collection. Video summarization algorithms identify and extract from the original video content the most important frames (key-frames), and/or the most important video segments (key-shots), normally in a temporally ordered fashion. Video summaries simply retain a carefully selected subset of the original video frames and, therefore, are not identical to the output of video synopsis algorithms, where new video frames are being synthesized based on the original video content. == Commercial products == In 2022 Google Docs released an automatic summarization feature. == Approaches == There are two general approaches to automatic summarization: extraction and abstraction. === Extraction-based summarization === Here, content is extracted from the original data, but the extracted content is not modified in any way. Examples of extracted content include key-phrases that can be used to "tag" or index a text document, or key sentences (including headings) that collectively comprise an abstract, and representative images or video segments, as stated above. For text, extraction is analogous to the process of skimming, where the summary (if available), headings and subheadings, figures, the first and last paragraphs of a section, and optionally the first and last sentences in a paragraph are read before one chooses to read the entire document in detail. Other examples of extraction that include key sequences of text in terms of clinical relevance (including patient/problem, intervention, and outcome). === Abstractive-based summarization === Abstractive summarization methods generate new text that did not exist in the original text. This has been applied mainly for text. Abstractive methods build an internal semantic representation of the original content (often called a language model), and then use this representation to create a summary that is closer to what a human might express. Abstraction may transform the extracted content by paraphrasing sections of the source document, to condense a text more strongly than extraction. Such transformation, however, is computationally much more challenging than extraction, involving both natural language processing and often a deep understanding of the domain of the original text in cases where the original document relates to a special field of knowledge. "Paraphrasing" is even more difficult to apply to images and videos, which is why most summarization systems are extractive. === Aided summarization === Approaches aimed at higher summarization quality rely on combined software and human effort. In Machine Aided Human Summarization, extractive techniques highlight candidate passages for inclusion (to which the human adds or removes text). In Human Aided Machine Summarization, a human post-processes software output, in the same way that one edits the output of automatic translation by Google Translate. == Applications and systems for summarization == There are broadly two types of extractive summarization tasks depending on what the summarization program focuses on. The first is generic summarization, which focuses on obtaining a generic summary or abstract of the collection (whether documents, or sets of images, or videos, news stories etc.). The second is query relevant summarization, sometimes called query-based summarization, which summarizes objects specific to a query. Summarization systems are able to create both query relevant text summaries and generic machine-generated summaries depending on what the user needs. An example of a summarization problem is document summarization, which attempts to automatically produce an abstract from a given document. Sometimes one might be interested in generating a summary from a single source document, while others can use multiple source documents (for example, a cluster of articles on the same topic). This problem is called multi-document summarization. A related application is summarizing news articles. Imagine a system, which automatically pulls together news articles on a given topic (from the web), and concisely represents the latest news as a summary. Image collection summarization is another application example of automatic summarization. It consists in selecting a representative set of images from a larger set of images. A summary in this context is useful to show the most representative images of results in an image collection exploration system. Video summarization is a related domain, where the system automatically creates a trailer of a long video. This also has applications in consumer or personal videos, where one might want to skip the boring or repetitive actions. Similarly, in surveillance videos, one would want to extract important and suspicious activity, while ignoring all the boring and redundant frames captured. At a very high level, summarization algorithms try to find subsets of objects (like set of sentences, or a set of images), which cover information of the entire set. This is also called the core-set. These algorithms model notions like diversity, coverage, information and representativeness of the summary. Query based summarization techniques, additionally model for relevance of the summary with the query. Some techniques and algorithms which naturally model summarization problems are TextRank and PageRank, Submodular set function, Determinantal point process, maximal marginal relevance (MMR) etc. === Keyphrase extraction === The task is the following. You are given a piece of text, such as a journal article, and you must produce a list of keywords or key[phrase]s that capture the primary topics discussed in the text. In the case of research articles, many authors provide manually assigned keywords, but most text lacks pre-existing keyphrases. For example, news articles rarely have keyphrases attached, but it would be useful to be able to automatically do so for a number of applications discussed below. Consider the example text from a news article: "The Army Corps of Engineers, rushing to meet President Bush's promise to protect New Orleans by the start of the 2006 hurricane season, installed defective flood-control pumps last year despite warnings from its own expert that the equipment would fail during a storm, according to documents obtained by The Associated Press". A keyphrase extractor might select "Army Corps of Engineers", "President Bush", "New Orleans", and "defective flood-control pumps" as keyphrases. These are pulled directly from the text. In contrast, an abstractive keyphrase system would somehow internalize the content and generate keyphrases that do not appear in the text, but more closely resemble what a human might produce, such as "political negligence" or "inadequate protection from floods". Abstraction requires a deep understanding of the text, which makes it difficult for a computer system. Keyphrases have many applications. They can enable document browsing by providing a short summary, improve information retrieval (if documents have keyphrases assigned, a user could search by keyphrase to produce more reliable hits than a full-text search), and be employed in generating index entries for a large text corpus. Depending on the different literature and the definition of key terms, words or phrases, keyword extraction is a highly related theme. ==== Supervised learning approaches ==== Beginning with the work of Turney, many researchers have approached keyphrase extraction as a supervised machine learning problem. Given a document, we construct an example for each unigram, bigram, and trigram found in the text (though other text units are also possible, as discussed below). We then compute various features describing each example (e.g., does the phrase begin with an upper-case letter?). We assume there are known keyphrases available for a set of training documents. Using the known keyphrases, we can assign positive or negative labels to the examples. Then we learn a classifier that can discriminate between positive and negative examples as a function of the features. Some classifiers make a binary classification for a test example, while others assign a probability of being a keyphrase. For ins

Language resource

In linguistics and language technology, a language resource is a "[composition] of linguistic material used in the construction, improvement and/or evaluation of language processing applications, (...) in language and language-mediated research studies and applications." According to Bird & Simons (2003), this includes data, i.e. "any information that documents or describes a language, such as a published monograph, a computer data file, or even a shoebox full of handwritten index cards. The information could range in content from unanalyzed sound recordings to fully transcribed and annotated texts to a complete descriptive grammar", tools, i.e., "computational resources that facilitate creating, viewing, querying, or otherwise using language data", and advice, i.e., "any information about what data sources are reliable, what tools are appropriate in a given situation, what practices to follow when creating new data". The latter aspect is usually referred to as "best practices" or "(community) standards". In a narrower sense, language resource is specifically applied to resources that are available in digital form, and then, "encompassing (a) data sets (textual, multimodal/multimedia and lexical data, grammars, language models, etc.) in machine readable form, and (b) tools/technologies/services used for their processing and management". == Typology == As of May 2020, no widely used standard typology of language resources has been established (current proposals include the LREMap, METASHARE, and, for data, the LLOD classification). Important classes of language resources include data lexical resources, e.g., machine-readable dictionaries, linguistic corpora, i.e., digital collections of natural language data, linguistic data bases such as the Cross-Linguistic Linked Data collection, tools linguistic annotations and tools for creating such annotations in a manual or semiautomated fashion (e.g., tools for annotating interlinear glossed text such as Toolbox and FLEx, or other language documentation tools), applications for search and retrieval over such data (corpus management systems), for automated annotation (part-of-speech tagging, syntactic parsing, semantic parsing, etc.), metadata and vocabularies vocabularies, repositories of linguistic terminology and language metadata, e.g., MetaShare (for language resource metadata), the ISO 12620 data category registry (for linguistic features, data structures and annotations within a language resource), or the Glottolog database (identifiers for language varieties and bibliographical database). == Language resource publication, dissemination and creation == A major concern of the language resource community has been to develop infrastructures and platforms to present, discuss and disseminate language resources. Selected contributions in this regard include: a series of International Conferences on Language Resources and Evaluation (LREC), the European Language Resources Association (ELRA, EU-based), and the Linguistic Data Consortium (LDC, US-based), which represent commercial hosting and dissemination platforms for language resources, the Open Languages Archives Community (OLAC), which provides and aggregates language resource metadata, the Language Resources and Evaluation Journal (LREJ), the European Language Grid is a European platform for language technologies (eg services), data and resources. As for the development of standards and best practices for language resources, these are subject of several community groups and standardization efforts, including ISO Technical Committee 37: Terminology and other language and content resources (ISO/TC 37), developing standards for all aspects of language resources, W3C Community Group Best Practices for Multilingual Linked Open Data (BPMLOD), working on best practice recommendations for publishing language resources as Linked Data or in RDF, W3C Community Group Linked Data for Language Technology (LD4LT), working on linguistic annotations on the web and language resource metadata, W3C Community Group Ontology-Lexica (OntoLex), working on lexical resources, the Open Linguistics working group of the Open Knowledge Foundation, working on conventions for publishing and linking open language resources, developing the Linguistic Linked Open Data cloud, the Text Encoding Initiative (TEI), working on XML-based specifications for language resources and digitally edited text.

Jive (software)

Jive (formerly known as Clearspace, then Jive SBS, then Jive Engage) is a commercial Java EE-based Enterprise 2.0 collaboration and knowledge management tool produced by Jive Software. It was first released as "Clearspace" in 2006, then renamed SBS (for "Social Business Software") in March 2009, then renamed "Jive Engage" in 2011, and renamed simply to "Jive" in 2012. Jive integrates the functionality of online communities, microblogging, social networking, discussion forums, blogs, wikis, and IM under one unified user interface. Content placed into any of the systems (blog, wiki, documentation, etc.) can be found through a common search interface. Other features include RSS capability, email integration, a reputation and reward system for participation, personal user profiles, JAX-WS web service interoperability, and integration with the Spring Framework. The product is a pure-Java server-side web application and will run on any platform where Java (JDK 1.5 or higher) is installed. It does not require a dedicated server - users have reported successful deployment in both shared environments and multiple machine clusters. As of Jive 8, released March 30, 2015, there is a Jive-n version which is for internal use (hosted by the consumer or hosted by Jive as a service) and a Jive-x version which is an external version hosted as a service. Jive no longer supports wiki markup language. == Server requirements for Jive 8-n == The following are the server requirements for Jive 8-n Operating systems: RHEL version 6 or 7 for x86_64, CentOS version 6 or 7 for x86_64 or SuSE Enterprise Linux Server (SLES) 11 and 12 for x86_64 Application Servers: Jive ships with its own embedded Apache HTTPD and Tomcat servers as part of the install package. It is not possible to deploy the application onto other appservers. Databases: MySQL (5.1, 5.5, 5.6) Oracle (11gR2, 12c) Postgres (9.0, 9.1, 9.2, 9.3, 9.4 - 9.2 or higher recommended) Microsoft SQL Server (2008R2, 2012, 2014) Environment: Jive recommends a server with at least 4GB of RAM and a dual-core 2 GHz processor with x86_64 architecture The product integrates with an LDAP repository or Active Directory For optimal deployment with a large community Jive Software recommends: using dedicated cache and document-conversion servers hosting the application and database servers separately == Releases == Jive 8, released on March 30, 2015 Jive 7, released in October 2013 Jive 9.0.x, released in November 2016 Jive 9, released in November 2016, supported now

Common data model

Scale space

Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter t {\displaystyle t} in this family is referred to as the scale parameter, with the interpretation that image structures of spatial size smaller than about t {\displaystyle {\sqrt {t}}} have largely been smoothed away in the scale-space level at scale t {\displaystyle t} . The main type of scale space is the linear (Gaussian) scale space, which has wide applicability as well as the attractive property of being possible to derive from a small set of scale-space axioms. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made scale invariant, which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances. == Definition == The notion of scale space applies to signals of arbitrary numbers of variables. The most common case in the literature applies to two-dimensional images, which is what is presented here. Consider a given image f {\displaystyle f} where f ( x , y ) {\displaystyle f(x,y)} is the greyscale value of the pixel at position ( x , y ) {\displaystyle (x,y)} . The linear (Gaussian) scale-space representation of f {\displaystyle f} is a family of derived signals L ( x , y ; t ) {\displaystyle L(x,y;t)} defined by the convolution of f ( x , y ) {\displaystyle f(x,y)} with the two-dimensional Gaussian kernel g ( x , y ; t ) = 1 2 π t e − ( x 2 + y 2 ) / 2 t {\displaystyle g(x,y;t)={\frac {1}{2\pi t}}e^{-(x^{2}+y^{2})/2t}\,} such that L ( ⋅ , ⋅ ; t ) = g ( ⋅ , ⋅ ; t ) ∗ f ( ⋅ , ⋅ ) , {\displaystyle L(\cdot ,\cdot ;t)\ =g(\cdot ,\cdot ;t)f(\cdot ,\cdot ),} where the semicolon in the argument of L {\displaystyle L} implies that the convolution is performed only over the variables x , y {\displaystyle x,y} , while the scale parameter t {\displaystyle t} after the semicolon just indicates which scale level is being defined. This definition of L {\displaystyle L} works for a continuum of scales t ≥ 0 {\displaystyle t\geq 0} , but typically only a finite discrete set of levels in the scale-space representation would be actually considered. The scale parameter t = σ 2 {\displaystyle t=\sigma ^{2}} is the variance of the Gaussian filter and as a limit for t = 0 {\displaystyle t=0} the filter g {\displaystyle g} becomes an impulse function such that L ( x , y ; 0 ) = f ( x , y ) , {\displaystyle L(x,y;0)=f(x,y),} that is, the scale-space representation at scale level t = 0 {\displaystyle t=0} is the image f {\displaystyle f} itself. As t {\displaystyle t} increases, L {\displaystyle L} is the result of smoothing f {\displaystyle f} with a larger and larger filter, thereby removing more and more of the details that the image contains. Since the standard deviation of the filter is σ = t {\displaystyle \sigma ={\sqrt {t}}} , details that are significantly smaller than this value are to a large extent removed from the image at scale parameter t {\displaystyle t} , see the following figures and for graphical illustrations. === Why a Gaussian filter? === When faced with the task of generating a multi-scale representation one may ask: could any filter g of low-pass type and with a parameter t which determines its width be used to generate a scale space? The answer is no, as it is of crucial importance that the smoothing filter does not introduce new spurious structures at coarse scales that do not correspond to simplifications of corresponding structures at finer scales. In the scale-space literature, a number of different ways have been expressed to formulate this criterion in precise mathematical terms. The conclusion from several different axiomatic derivations that have been presented is that the Gaussian scale space constitutes the canonical way to generate a linear scale space, based on the essential requirement that new structures must not be created when going from a fine scale to any coarser scale. Conditions, referred to as scale-space axioms, that have been used for deriving the uniqueness of the Gaussian kernel include linearity, shift invariance, semi-group structure, non-enhancement of local extrema, scale invariance and rotational invariance. In the works, the uniqueness claimed in the arguments based on scale invariance has been criticized, and alternative self-similar scale-space kernels have been proposed. The Gaussian kernel is, however, a unique choice according to the scale-space axiomatics based on causality or non-enhancement of local extrema. === Alternative definition === Equivalently, the scale-space family can be defined as the solution of the diffusion equation (for example in terms of the heat equation), ∂ t L = 1 2 ∇ 2 L , {\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L,} with initial condition L ( x , y ; 0 ) = f ( x , y ) {\displaystyle L(x,y;0)=f(x,y)} . This formulation of the scale-space representation L means that it is possible to interpret the intensity values of the image f as a "temperature distribution" in the image plane and that the process that generates the scale-space representation as a function of t corresponds to heat diffusion in the image plane over time t (assuming the thermal conductivity of the material equal to the arbitrarily chosen constant ⁠1/2⁠). Although this connection may appear superficial for a reader not familiar with differential equations, it is indeed the case that the main scale-space formulation in terms of non-enhancement of local extrema is expressed in terms of a sign condition on partial derivatives in the 2+1-D volume generated by the scale space, thus within the framework of partial differential equations. Furthermore, a detailed analysis of the discrete case shows that the diffusion equation provides a unifying link between continuous and discrete scale spaces, which also generalizes to nonlinear scale spaces, for example, using anisotropic diffusion. Hence, one may say that the primary way to generate a scale space is by the diffusion equation, and that the Gaussian kernel arises as the Green's function of this specific partial differential equation. == Motivations == The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects are composed of different structures at different scales. This implies that real-world objects, in contrast to idealized mathematical entities such as points or lines, may appear in different ways depending on the scale of observation. For example, the concept of a "tree" is appropriate at the scale of meters, while concepts such as leaves and molecules are more appropriate at finer scales. For a computer vision system analysing an unknown scene, there is no way to know a priori what scales are appropriate for describing the interesting structures in the image data. Hence, the only reasonable approach is to consider descriptions at multiple scales in order to be able to capture the unknown scale variations that may occur. Taken to the limit, a scale-space representation considers representations at all scales. Another motivation to the scale-space concept originates from the process of performing a physical measurement on real-world data. In order to extract any information from a measurement process, one has to apply operators of non-infinitesimal size to the data. In many branches of computer science and applied mathematics, the size of the measurement operator is disregarded in the theoretical modelling of a problem. The scale-space theory on the other hand explicitly incorporates the need for a non-infinitesimal size of the image operators as an integral part of any measurement as well as any other operation that depends on a real-world measurement. There is a close link between scale-space theory and biological vision. Many scale-space operations show a high degree of similarity with receptive field profiles recorded from the mammalian retina and the first stages in the visual cortex. In these respects, the scale-space framework can be seen as a theoretically well-founded paradigm for early vision, which in addition has been thoroughly tested by algorithms and experiments. == Gaussian derivatives == At any scale in scale space, we c