LemonStand was a Canadian e-commerce company headquartered in Vancouver, British Columbia, that developed cloud-based computer software for online retailers. LemonStand was shut down on June 5, 2019. == History == LemonStand Version 1 was launched on July 28, 2001. It is written in the PHP programming language. Version 1 was released as an on-premises proprietary licensed software, and the commercial license was not free. However, there was a free trial license available. June 2012, LemonStand raised seed funding from the BDC Venture Capital, and a group of angel investors. December 20, 2013, a cloud-based SaaS version of the LemonStand eCommerce platform was released publicly. May 9, 2014, LemonStand and Payfirma, a payments processing company, partnered to provide integrated services for online retailers. May 3, 2016, LemonStand raised funding from BDC Venture Capital and Silicon Valley–based angel investors. March 5, 2019, LemonStand announced their intention to shut down on June 5, 2019. LemonStand was quietly acquired by Mailchimp at the end of February. == Pricing == LemonStand offered three levels of service plans. LemonStand did not charge any transaction fees.
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.
Multi expression programming
Multi Expression Programming (MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is a Genetic Programming variant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have been tested). In the simplest variant, MEP chromosomes are linear strings of instructions. This representation was inspired by Three-address code. MEP strength consists in the ability to encode multiple solutions, of a problem, in the same chromosome. In this way, one can explore larger zones of the search space. For most of the problems this advantage comes with no running-time penalty compared with genetic programming variants encoding a single solution in a chromosome. == Representation == MEP chromosomes are arrays of instructions represented in Three-address code format. Each instruction contains a variable, a constant, or a function. If the instruction is a function, then the arguments (given as instruction's addresses) are also present. === Example of MEP program === Here is a simple MEP chromosome (labels on the left side are not a part of the chromosome): 1: a 2: b 3: + 1, 2 4: c 5: d 6: + 4, 5 7: 3, 5 == Fitness computation == When the chromosome is evaluated it is unclear which instruction will provide the output of the program. In many cases, a set of programs is obtained, some of them being completely unrelated (they do not have common instructions). For the above chromosome, here is the list of possible programs obtained during decoding: E1 = a, E2 = b, E4 = c, E5 = d, E3 = a + b. E6 = c + d. E7 = (a + b) d. Each instruction is evaluated as a possible output of the program. The fitness (or error) is computed in a standard manner. For instance, in the case of symbolic regression, the fitness is the sum of differences (in absolute value) between the expected output (called target) and the actual output. == Fitness assignment process == Which expression will represent the chromosome? Which one will give the fitness of the chromosome? In MEP, the best of them (which has the lowest error) will represent the chromosome. This is different from other GP techniques: In Linear genetic programming the last instruction will give the output. In Cartesian Genetic Programming the gene providing the output is evolved like all other genes. Note that, for many problems, this evaluation has the same complexity as in the case of encoding a single solution in each chromosome. Thus, there is no penalty in running time compared to other techniques. == Software == === MEPX === MEPX is a cross-platform (Windows, macOS, and Linux Ubuntu) free software for the automatic generation of computer programs. It can be used for data analysis, particularly for solving symbolic regression, statistical classification and time-series problems. === libmep === Libmep is a free and open source library implementing Multi Expression Programming technique. It is written in C++. === hmep === hmep is a new open source library implementing Multi Expression Programming technique in Haskell programming language.
Mating pool
Mating pool is a concept used in evolutionary algorithms and means a population of parents for the next population. The mating pool is formed by candidate solutions that the selection operators deem to have the highest fitness in the current population. Solutions that are included in the mating pool are referred to as parents. Individual solutions can be repeatedly included in the mating pool, with individuals of higher fitness values having a higher chance of being included multiple times. Crossover operators are then applied to the parents, resulting in recombination of genes recognized as superior. Lastly, random changes in the genes are introduced through mutation operators, increasing the genetic variation in the gene pool. Those two operators improve the chance of creating new, superior solutions. A new generation of solutions is thereby created, the children, who will constitute the next population. Depending on the selection method, the total number of parents in the mating pool can be different to the size of the initial population, resulting in a new population that’s smaller. To continue the algorithm with an equally sized population, random individuals from the old populations can be chosen and added to the new population. At this point, the fitness value of the new solutions is evaluated. If the termination conditions are fulfilled, processes come to an end. Otherwise, they are repeated. The repetition of the steps result in candidate solutions that evolve towards the most optimal solution over time. The genes will become increasingly uniform towards the most optimal gene, a process called convergence. If 95% of the population share the same version of a gene, the gene has converged. When all the individual fitness values have reached the value of the best individual, i.e. all the genes have converged, population convergence is achieved. == Mating pool creation == Several methods can be applied to create a mating pool. All of these processes involve the selective breeding of a particular number of individuals within a population. There are multiple criteria that can be employed to determine which individuals make it into the mating pool and which are left behind. The selection methods can be split into three general types: fitness proportionate selection, ordinal based selection and threshold based selection. === Fitness proportionate selection === In the case of fitness proportionate selection, random individuals are selected to enter the pool. However, the ones with a higher level of fitness are more likely to be picked and therefore have a greater chance of passing on their features to the next generation. One of the techniques used in this type of parental selection is the roulette wheel selection. This approach divides a hypothetical circular wheel into different slots, the size of which is equal to the fitness values of each potential candidate. Afterwards, the wheel is rotated and a fixed point determines which individual gets picked. The greater the fitness value of an individual, the higher the probability of being chosen as a parent by the random spin of the wheel. Alternatively, stochastic universal sampling can be implemented. This selection method is also based on the rotation of a spinning wheel. However, in this case there is more than one fixed point and as a result all of the mating pool members will be selected simultaneously. === Ordinal based selection === The ordinal based selection methods include the tournament and ranking selection. Tournament selection involves the random selection of individuals of a population and the subsequent comparison of their fitness levels. The winners of these “tournaments” are the ones with the highest values and will be put into the mating pool as parents. In ranking selection all the individuals are sorted based on their fitness values. Then, the selection of the parents is made according to the rank of the candidates. Every individual has a chance of being chosen, but higher ranked ones are favored === Threshold based selection === The last type of selection method is referred to as the threshold based method. This includes the truncation selection method, which sorts individuals based on their phenotypic values on a specific trait and later selects the proportion of them that are within a certain threshold as parents.
List of text mining software
Text mining computer programs are available from many commercial and open source companies and sources. == Commercial == Angoss – Angoss Text Analytics provides entity and theme extraction, topic categorization, sentiment analysis and document summarization capabilities via the embedded AUTINDEX – is a commercial text mining software package based on sophisticated linguistics by IAI (Institute for Applied Information Sciences), Saarbrücken. DigitalMR – social media listening & text+image analytics tool for market research. FICO Score – leading provider of analytics. General Sentiment – Social Intelligence platform that uses natural language processing to discover affinities between the fans of brands with the fans of traditional television shows in social media. Stand alone text analytics to capture social knowledge base on billions of topics stored to 2004. IBM LanguageWare – the IBM suite for text analytics (tools and Runtime). IBM SPSS – provider of Modeler Premium (previously called IBM SPSS Modeler and IBM SPSS Text Analytics), which contains advanced NLP-based text analysis capabilities (multi-lingual sentiment, event and fact extraction), that can be used in conjunction with Predictive Modeling. Text Analytics for Surveys provides the ability to categorize survey responses using NLP-based capabilities for further analysis or reporting. Inxight – provider of text analytics, search, and unstructured visualization technologies. (Inxight was bought by Business Objects that was bought by SAP AG in 2008). Language Computer Corporation – text extraction and analysis tools, available in multiple languages. Lexalytics – provider of a text analytics engine used in Social Media Monitoring, Voice of Customer, Survey Analysis, and other applications. Salience Engine. The software provides the unique capability of merging the output of unstructured, text-based analysis with structured data to provide additional predictive variables for improved predictive models and association analysis. Linguamatics – provider of natural language processing (NLP) based enterprise text mining and text analytics software, I2E, for high-value knowledge discovery and decision support. Mathematica – provides built in tools for text alignment, pattern matching, clustering and semantic analysis. See Wolfram Language, the programming language of Mathematica. MATLAB offers Text Analytics Toolbox for importing text data, converting it to numeric form for use in machine and deep learning, sentiment analysis and classification tasks. Medallia – offers one system of record for survey, social, text, written and online feedback. NetMiner – software for network analysis and text mining. Supports social media and bibliographic data collection, NLP for english and chinese, sentiment analysis, work co-occurrence network(text network analysis) and visualization. NetOwl – suite of multilingual text and entity analytics products, including entity extraction, link and event extraction, sentiment analysis, geotagging, name translation, name matching, and identity resolution, among others. PolyAnalyst - text analytics environment. PoolParty Semantic Suite - graph-based text mining platform. RapidMiner with its Text Processing Extension – data and text mining software. SAS – SAS Text Miner and Teragram; commercial text analytics, natural language processing, and taxonomy software used for Information Management. Sketch Engine – a corpus manager and analysis software which providing creating text corpora from uploaded texts or the Web including part-of-speech tagging and lemmatization or detecting a particular website. Sysomos – provider social media analytics software platform, including text analytics and sentiment analysis on online consumer conversations. WordStat – Content analysis and text mining add-on module of QDA Miner for analyzing large amounts of text data. == Open source == Carrot2 – text and search results clustering framework. GATE – general Architecture for Text Engineering, an open-source toolbox for natural language processing and language engineering. Gensim – large-scale topic modelling and extraction of semantic information from unstructured text (Python). KH Coder – for Quantitative Content Analysis or Text Mining The KNIME Text Processing extension. Natural Language Toolkit (NLTK) – a suite of libraries and programs for symbolic and statistical natural language processing (NLP) for the Python programming language. OpenNLP – natural language processing. Orange with its text mining add-on. The PLOS Text Mining Collection. The programming language R provides a framework for text mining applications in the package tm. The Natural Language Processing task view contains tm and other text mining library packages. spaCy – open-source Natural Language Processing library for Python Stanbol – an open source text mining engine targeted at semantic content management. Voyant Tools – a web-based text analysis environment, created as a scholarly project.
DesktopTwo
Desktoptwo was a free Webtop (whose URL was desktoptwo.com and which is now a parked domain) developed by Sapotek (whose URL was sapotek.com, which also is now a parked domain). It's also been called a WebOS although Sapotek stated on its website that the term is premature and presumptuous. It mimics the look, feel and functionality of the desktop environment of an operating system. The software only reached beta stage. It had a Spanish version called Computadora.de. Desktoptwo was web-based and required Adobe Flash Player to operate. The web applications' found on Desktoptwo were built on PHP in the back end. Features included drag-and-drop functionality. Sapotek had liberated all the web applications found on Desktoptwo through Sapodesk on an AGPL license. Desktoptwo belonged to a category of services that intended to turn the Web into a full-fledged platform by using web services as a foundation along with presentation technologies that replicated the experience of desktop applications for users. In a "Cloud OS" the functionality of a server was granularized and abstracted as Web services that Web developers used to create composite applications similar to how desktop software developers use several APIs of the OS to create their applications. Sites like Facebook attempt to create a similar effect by exposing their APIs and allowing developers to create applications upon these. Some of the features found on Desktoptwo were: File sharing, Webmail, Blog creator, Instant messenger, Address book, Calendar, RSS Reader and Office productivity applications. Desktoptwo.com and the Sapotek website no longer operate.
Radial basis function kernel
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification. The RBF kernel on two samples x , x ′ ∈ R k {\displaystyle \mathbf {x} ,\mathbf {x'} \in \mathbb {R} ^{k}} , represented as feature vectors in some input space, is defined as K ( x , x ′ ) = exp ( − ‖ x − x ′ ‖ 2 2 σ 2 ) {\displaystyle K(\mathbf {x} ,\mathbf {x'} )=\exp \left(-{\frac {\|\mathbf {x} -\mathbf {x'} \|^{2}}{2\sigma ^{2}}}\right)} ‖ x − x ′ ‖ 2 {\displaystyle \textstyle \|\mathbf {x} -\mathbf {x'} \|^{2}} may be recognized as the squared Euclidean distance between the two feature vectors. σ {\displaystyle \sigma } is a free parameter. An equivalent definition involves a parameter γ = 1 2 σ 2 {\displaystyle \textstyle \gamma ={\tfrac {1}{2\sigma ^{2}}}} : K ( x , x ′ ) = exp ( − γ ‖ x − x ′ ‖ 2 ) {\displaystyle K(\mathbf {x} ,\mathbf {x'} )=\exp(-\gamma \|\mathbf {x} -\mathbf {x'} \|^{2})} Since the value of the RBF kernel decreases with distance and ranges between zero (in the infinite-distance limit) and one (when x = x'), it has a ready interpretation as a similarity measure. The feature space of the kernel has an infinite number of dimensions; for σ = 1 {\displaystyle \sigma =1} , its expansion using the multinomial theorem is: exp ( − 1 2 ‖ x − x ′ ‖ 2 ) = exp ( 2 2 x ⊤ x ′ − 1 2 ‖ x ‖ 2 − 1 2 ‖ x ′ ‖ 2 ) = exp ( x ⊤ x ′ ) exp ( − 1 2 ‖ x ‖ 2 ) exp ( − 1 2 ‖ x ′ ‖ 2 ) = ∑ j = 0 ∞ ( x ⊤ x ′ ) j j ! exp ( − 1 2 ‖ x ‖ 2 ) exp ( − 1 2 ‖ x ′ ‖ 2 ) = ∑ j = 0 ∞ ∑ n 1 + n 2 + ⋯ + n k = j exp ( − 1 2 ‖ x ‖ 2 ) x 1 n 1 ⋯ x k n k n 1 ! ⋯ n k ! exp ( − 1 2 ‖ x ′ ‖ 2 ) x ′ 1 n 1 ⋯ x ′ k n k n 1 ! ⋯ n k ! = ⟨ φ ( x ) , φ ( x ′ ) ⟩ {\displaystyle {\begin{alignedat}{2}\exp \left(-{\frac {1}{2}}\|\mathbf {x} -\mathbf {x'} \|^{2}\right)&=\exp \left({\frac {2}{2}}\mathbf {x} ^{\top }\mathbf {x'} -{\frac {1}{2}}\|\mathbf {x} \|^{2}-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right)\\[5pt]&=\exp \left(\mathbf {x} ^{\top }\mathbf {x'} \right)\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right)\exp \left(-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right)\\[5pt]&=\sum _{j=0}^{\infty }{\frac {(\mathbf {x} ^{\top }\mathbf {x'} )^{j}}{j!}}\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right)\exp \left(-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right)\\[5pt]&=\sum _{j=0}^{\infty }\quad \sum _{n_{1}+n_{2}+\dots +n_{k}=j}\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right){\frac {x_{1}^{n_{1}}\cdots x_{k}^{n_{k}}}{\sqrt {n_{1}!\cdots n_{k}!}}}\exp \left(-{\frac {1}{2}}\|\mathbf {x'} \|^{2}\right){\frac {{x'}_{1}^{n_{1}}\cdots {x'}_{k}^{n_{k}}}{\sqrt {n_{1}!\cdots n_{k}!}}}\\[5pt]&=\langle \varphi (\mathbf {x} ),\varphi (\mathbf {x'} )\rangle \end{alignedat}}} φ ( x ) = exp ( − 1 2 ‖ x ‖ 2 ) ( a ℓ 0 ( 0 ) , a 1 ( 1 ) , … , a ℓ 1 ( 1 ) , … , a 1 ( j ) , … , a ℓ j ( j ) , … ) {\displaystyle \varphi (\mathbf {x} )=\exp \left(-{\frac {1}{2}}\|\mathbf {x} \|^{2}\right)\left(a_{\ell _{0}}^{(0)},a_{1}^{(1)},\dots ,a_{\ell _{1}}^{(1)},\dots ,a_{1}^{(j)},\dots ,a_{\ell _{j}}^{(j)},\dots \right)} where ℓ j = ( k + j − 1 j ) {\displaystyle \ell _{j}={\tbinom {k+j-1}{j}}} , a ℓ ( j ) = x 1 n 1 ⋯ x k n k n 1 ! ⋯ n k ! | n 1 + n 2 + ⋯ + n k = j ∧ 1 ≤ ℓ ≤ ℓ j {\displaystyle a_{\ell }^{(j)}={\frac {x_{1}^{n_{1}}\cdots x_{k}^{n_{k}}}{\sqrt {n_{1}!\cdots n_{k}!}}}\quad |\quad n_{1}+n_{2}+\dots +n_{k}=j\wedge 1\leq \ell \leq \ell _{j}} == Approximations == Because support vector machines and other models employing the kernel trick do not scale well to large numbers of training samples or large numbers of features in the input space, several approximations to the RBF kernel (and similar kernels) have been introduced. Typically, these take the form of a function z that maps a single vector to a vector of higher dimensionality, approximating the kernel: ⟨ z ( x ) , z ( x ′ ) ⟩ ≈ ⟨ φ ( x ) , φ ( x ′ ) ⟩ = K ( x , x ′ ) {\displaystyle \langle z(\mathbf {x} ),z(\mathbf {x'} )\rangle \approx \langle \varphi (\mathbf {x} ),\varphi (\mathbf {x'} )\rangle =K(\mathbf {x} ,\mathbf {x'} )} where φ {\displaystyle \textstyle \varphi } is the implicit mapping embedded in the RBF kernel. === Fourier random features === One way to construct such a z is to randomly sample from the Fourier transformation of the kernel φ ( x ) = 1 D [ cos ⟨ w 1 , x ⟩ , sin ⟨ w 1 , x ⟩ , … , cos ⟨ w D , x ⟩ , sin ⟨ w D , x ⟩ ] T {\displaystyle \varphi (x)={\frac {1}{\sqrt {D}}}[\cos \langle w_{1},x\rangle ,\sin \langle w_{1},x\rangle ,\ldots ,\cos \langle w_{D},x\rangle ,\sin \langle w_{D},x\rangle ]^{T}} where w 1 , . . . , w D {\displaystyle w_{1},...,w_{D}} are independent samples from the normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Theorem: E [ ⟨ φ ( x ) , φ ( y ) ⟩ ] = e ‖ x − y ‖ 2 / ( 2 σ 2 ) . {\displaystyle \operatorname {E} [\langle \varphi (x),\varphi (y)\rangle ]=e^{\|x-y\|^{2}/(2\sigma ^{2})}.} Proof: It suffices to prove the case of D = 1 {\displaystyle D=1} . Use the trigonometric identity cos ( a − b ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b ) {\displaystyle \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)} , the spherical symmetry of Gaussian distribution, then evaluate the integral ∫ − ∞ ∞ cos ( k x ) e − x 2 / 2 2 π d x = e − k 2 / 2 . {\displaystyle \int _{-\infty }^{\infty }{\frac {\cos(kx)e^{-x^{2}/2}}{\sqrt {2\pi }}}dx=e^{-k^{2}/2}.} Theorem: Var [ ⟨ φ ( x ) , φ ( y ) ⟩ ] = O ( D − 1 ) {\displaystyle \operatorname {Var} [\langle \varphi (x),\varphi (y)\rangle ]=O(D^{-1})} . (Appendix A.2). === Nyström method === Another approach uses the Nyström method to approximate the eigendecomposition of the Gram matrix K, using only a random sample of the training set.