The ACL Data Collection Initiative (ACL/DCI) was a project established in 1989 by the Association for Computational Linguistics (ACL) to create and distribute large text and speech corpora for computational linguistics research. The initiative aimed to address the growing need for substantial text databases that could support research in areas such as natural language processing, speech recognition, and computational linguistics. By 1993, the initiative’s activities had effectively ceased, with its functions and datasets absorbed by the Linguistic Data Consortium (LDC), which was founded in 1992. == Objectives == The ACL/DCI had several key objectives: To acquire a large and diverse text corpus from various sources To transform the collected texts into a common format based on the Standard Generalized Markup Language (SGML) To make the corpus available for scientific research at low cost with minimal restrictions To provide a common database that would allow researchers to replicate or extend published results To reduce duplication of effort among researchers in obtaining and preparing text data These objectives were designed to address the growing demand for very large amounts of text arising from applications in recognition and analysis of text and speech. Its core objective was to "oversee the acquisition and preparation of a large text corpus to be made available for scientific research at cost and without royalties". == History == By the late 1980s, researchers in computational linguistics and speech recognition faced a significant problem: the lack of large-scale, accessible text corpora for developing statistical models and testing algorithms. Existing generally available text databases were too small to meet the needs of developing applications in text and speech recognition. The initiative was formed to meet this need by collecting, standardizing, and distributing large quantities of text data with minimal restrictions for scientific research. As stated by Liberman (1990), "research workers have been severely hampered by the lack of appropriate materials, and specially by the lack of a large enough body of text on which published results can be replicated or extended by others." The ACL/DCI committee was established in February 1989. The committee included members from academic and industrial research laboratories in the United States and Europe. The initiative was chaired by Mark Liberman from the University of Pennsylvania (formerly of AT&T Bell Laboratories). Other committee members included representatives from organizations such as Bellcore, IBM T.J. Watson Research Center, Cambridge University, Virginia Polytechnic Institute & State University, Northeastern University, University of Pennsylvania, SRI International, MCC, Xerox PARC, ISSCO, and University of Pisa. The project operated initially without dedicated funding, relying on volunteer efforts from committee members and their affiliated institutions. Key supporters included AT&T Bell Labs, Bellcore, IBM, Xerox, and the University of Pennsylvania, which allowed the use of their computing facilities for ACL/DCI-related work. Previously running on volunteer effort pro bono, in 1991, it obtained funding from General Electric and the National Science Foundation (IRI-9113530). == Data == As of 1990, the ACL/DCI had collected hundreds of millions of words of diverse text. The collection included: Wall Street Journal articles (25 to 50 million words); Canadian Hansard (parliamentary records) in parallel English and French versions: cleaned-up English Hansard donated by the IBM alignment models group (100 million words), and original Bilingual Hansard (from a different time period) obtained directly (200 million words). Collins English Dictionary (1979 edition), both as fulltext (3 million words) and as various "database" versions, constructed using "typographers' tape" donated by Collins, which were computer tapes containing the structured digital data used to typeset and print the 1979 edition of the dictionary; Emails from ARPANET newsletters for the ACM Special Interest Group on Information Retrieval Forum (IRLIST) and AIList Digest issues distributed over the ARPANET (AILIST) (5 million words), both collected by Edward A. Fox at VIPSU; Articles on networking (2 million words); U.S. Department of Agriculture Extension Service Fact Sheets (>1 million words); 200,000 scientific abstracts of about 1,500 words each from the Department of Energy (25 million words); Archives of the Challenger Investigation Commission, including transcripts of depositions and hearings (2.5 million words); Books from the Library of America, including works by Mark Twain, Eugene O'Neill, Ralph Waldo Emerson, Herman Melville, W.E.B. DuBois, Willa Cather, and Benjamin Franklin (130 books, 20 million words); Public domain books like the King James Bible, Tristram Shandy, The Federalist Papers; Several million words of transcribed radiologists' reports, donated by Francis Ganong at Kurzweil Applied Intelligence Inc (about 5 million words); The Child Language Data Exchange corpus of child language acquisition transcripts; U.S. Department of Justice Justice Retrieval and Inquiry System (JURIS) materials; The Swiss Civil Code in parallel German, French and Italian; Economic reports from the Union Bank of Switzerland, in parallel English, German, French and Italian; About 12K words of administrative policy manuals and 14K words of administrative memos, contributed by Geoff Pullum of U.C.S.C.; Material from various ACM journals and the ACL journal Computational Linguistics; The CSLI publications series: 50-100 reports (8K words each) and 5-10 books (80K words each). The initiative started with North American English text but expanded to include Canadian French and planned to include Japanese, Chinese, and other Asian languages. At least 5 million words from the collection were tagged under the Penn Treebank project, and those tags were distributed by DCI as well. After DCI was absorbed by the LDC, the datasets were curated under LDC. == Format == The ACL/DCI corpus was coded in a standard form based on SGML (Standard Generalized Markup Language, ISO 8879), consistent with the recommendations of the Text Encoding Initiative (TEI), of which the DCI was an affiliated project. The TEI was a joint project of the ACL, the Association for Computers and the Humanities, and the Association for Literary and Linguistic Computing, aiming to provide a common interchange format for literary and linguistic data. The initiative planned to add annotations reflecting consensually approved linguistic features like part of speech and various aspects of syntactic and semantic structure over time. == Examples == As an example of the use of ACL/DCI, consider the Wall Street Journal (WSJ) corpus for speech recognition research. The WSJ corpus was used as the basis for the DARPA Spoken Language System (SLS) community's Continuous Speech Recognition (CSR) Corpus. The WSJ corpus became a standard benchmark for evaluating speech recognition systems and has been used in numerous research papers. The WSJ CSR Corpus provided DARPA with its first general-purpose English, large vocabulary, natural language, high perplexity corpus containing speech (400 hours) and text (47 million words) during 1987–89. The text corpus was 313 MB in size. The text was preprocessed to remove ambiguity in the word sequence that a reader might choose, ensuring that the unread text used to train language models was representative of the spoken test material. The preprocessing included converting numbers into orthographics, expanding abbreviations, resolving apostrophes and quotation marks, and marking punctuation. As another example, the Yarowsky algorithm used bitext data from DCI to train a simple word-sense disambiguation model that was competitive with advanced models trained on smaller datasets. == Distribution == Materials from the ACL/DCI collection were distributed to research groups on a non-commercial basis. By 1990, about 25 research groups and individual researchers had received tapes containing various portions of the collected material. To obtain the data, researchers had to sign an agreement not to redistribute the data or make direct commercial use of it. However, commercial application of "analytical materials" derived from the text, such as statistical tables or grammar rules, was explicitly permitted. The initiative first distributed data via 12-inch reels of 9-track tape, then via CD-ROMs. Each such tape could contain 30 million words compressed via the Lempel-Ziv algorithms. The first CD-ROM distribution was in 1991, funded by Dragon Systems Inc. It contained Collins English Dictionary, WSJ, scientific abstracts provided by the U.S. Department of Energy, and the Penn Treebank.
Automatic taxonomy construction
Automatic taxonomy construction (ATC) is the use of software programs to generate taxonomical classifications from a body of texts called a corpus. ATC is a branch of natural language processing, which in turn is a branch of artificial intelligence. A taxonomy (or taxonomical classification) is a scheme of classification, especially, a hierarchical classification, in which things are organized into groups or types. Among other things, a taxonomy can be used to organize and index knowledge (stored as documents, articles, videos, etc.), such as in the form of a library classification system, or a search engine taxonomy, so that users can more easily find the information they are searching for. Many taxonomies are hierarchies (and thus, have an intrinsic tree structure), but not all are. Manually developing and maintaining a taxonomy is a labor-intensive task requiring significant time and resources, including familiarity of or expertise in the taxonomy's domain (scope, subject, or field), which drives the costs and limits the scope of such projects. Also, domain modelers have their own points of view which inevitably, even if unintentionally, work their way into the taxonomy. ATC uses artificial intelligence techniques to quickly automatically generate a taxonomy for a domain in order to avoid these problems and remove limitations. == Approaches == There are several approaches to ATC. One approach is to use rules to detect patterns in the corpus and use those patterns to infer relations such as hyponymy. Other approaches use machine learning techniques such as Bayesian inferencing and Artificial Neural Networks. === Keyword extraction === One approach to building a taxonomy is to automatically gather the keywords from a domain using keyword extraction, then analyze the relationships between them (see Hyponymy, below), and then arrange them as a taxonomy based on those relationships. === Hyponymy and "is-a" relations === In ATC programs, one of the most important tasks is the discovery of hypernym and hyponym relations among words. One way to do that from a body of text is to search for certain phrases like "is a" and "such as". In linguistics, is-a relations are called hyponymy. Words that describe categories are called hypernyms and words that are examples of categories are hyponyms. For example, dog is a hypernym and Fido is one of its hyponyms. A word can be both a hyponym and a hypernym. So, dog is a hyponym of mammal and also a hypernym of Fido. Taxonomies are often represented as is-a hierarchies where each level is more specific than (in mathematical language "a subset of") the level above it. For example, a basic biology taxonomy would have concepts such as mammal, which is a subset of animal, and dogs and cats, which are subsets of mammal. This kind of taxonomy is called an is-a model because the specific objects are considered instances of a concept. For example, Fido is-a instance of the concept dog and Fluffy is-a cat. == Applications == ATC can be used to build taxonomies for search engines, to improve search results. ATC systems are a key component of ontology learning (also known as automatic ontology construction), and have been used to automatically generate large ontologies for domains such as insurance and finance. They have also been used to enhance existing large networks such as Wordnet to make them more complete and consistent. == ATC software == == Other names == Other names for automatic taxonomy construction include: Automated outline building Automated outline construction Automated outline creation Automated outline extraction Automated outline generation Automated outline induction Automated outline learning Automated outlining Automated taxonomy building Automated taxonomy construction Automated taxonomy creation Automated taxonomy extraction Automated taxonomy generation Automated taxonomy induction Automated taxonomy learning Automatic outline building Automatic outline construction Automatic outline creation Automatic outline extraction Automatic outline generation Automatic outline induction Automatic outline learning Automatic taxonomy building Automatic taxonomy creation Automatic taxonomy extraction Automatic taxonomy generation Automatic taxonomy induction Automatic taxonomy learning Outline automation Outline building Outline construction Outline creation Outline extraction Outline generation Outline induction Outline learning Semantic taxonomy building Semantic taxonomy construction Semantic taxonomy creation Semantic taxonomy extraction Semantic taxonomy generation Semantic taxonomy induction Semantic taxonomy learning Taxonomy automation Taxonomy building Taxonomy construction Taxonomy creation Taxonomy extraction Taxonomy generation Taxonomy induction Taxonomy learning
Automatic taxonomy construction
Automatic taxonomy construction (ATC) is the use of software programs to generate taxonomical classifications from a body of texts called a corpus. ATC is a branch of natural language processing, which in turn is a branch of artificial intelligence. A taxonomy (or taxonomical classification) is a scheme of classification, especially, a hierarchical classification, in which things are organized into groups or types. Among other things, a taxonomy can be used to organize and index knowledge (stored as documents, articles, videos, etc.), such as in the form of a library classification system, or a search engine taxonomy, so that users can more easily find the information they are searching for. Many taxonomies are hierarchies (and thus, have an intrinsic tree structure), but not all are. Manually developing and maintaining a taxonomy is a labor-intensive task requiring significant time and resources, including familiarity of or expertise in the taxonomy's domain (scope, subject, or field), which drives the costs and limits the scope of such projects. Also, domain modelers have their own points of view which inevitably, even if unintentionally, work their way into the taxonomy. ATC uses artificial intelligence techniques to quickly automatically generate a taxonomy for a domain in order to avoid these problems and remove limitations. == Approaches == There are several approaches to ATC. One approach is to use rules to detect patterns in the corpus and use those patterns to infer relations such as hyponymy. Other approaches use machine learning techniques such as Bayesian inferencing and Artificial Neural Networks. === Keyword extraction === One approach to building a taxonomy is to automatically gather the keywords from a domain using keyword extraction, then analyze the relationships between them (see Hyponymy, below), and then arrange them as a taxonomy based on those relationships. === Hyponymy and "is-a" relations === In ATC programs, one of the most important tasks is the discovery of hypernym and hyponym relations among words. One way to do that from a body of text is to search for certain phrases like "is a" and "such as". In linguistics, is-a relations are called hyponymy. Words that describe categories are called hypernyms and words that are examples of categories are hyponyms. For example, dog is a hypernym and Fido is one of its hyponyms. A word can be both a hyponym and a hypernym. So, dog is a hyponym of mammal and also a hypernym of Fido. Taxonomies are often represented as is-a hierarchies where each level is more specific than (in mathematical language "a subset of") the level above it. For example, a basic biology taxonomy would have concepts such as mammal, which is a subset of animal, and dogs and cats, which are subsets of mammal. This kind of taxonomy is called an is-a model because the specific objects are considered instances of a concept. For example, Fido is-a instance of the concept dog and Fluffy is-a cat. == Applications == ATC can be used to build taxonomies for search engines, to improve search results. ATC systems are a key component of ontology learning (also known as automatic ontology construction), and have been used to automatically generate large ontologies for domains such as insurance and finance. They have also been used to enhance existing large networks such as Wordnet to make them more complete and consistent. == ATC software == == Other names == Other names for automatic taxonomy construction include: Automated outline building Automated outline construction Automated outline creation Automated outline extraction Automated outline generation Automated outline induction Automated outline learning Automated outlining Automated taxonomy building Automated taxonomy construction Automated taxonomy creation Automated taxonomy extraction Automated taxonomy generation Automated taxonomy induction Automated taxonomy learning Automatic outline building Automatic outline construction Automatic outline creation Automatic outline extraction Automatic outline generation Automatic outline induction Automatic outline learning Automatic taxonomy building Automatic taxonomy creation Automatic taxonomy extraction Automatic taxonomy generation Automatic taxonomy induction Automatic taxonomy learning Outline automation Outline building Outline construction Outline creation Outline extraction Outline generation Outline induction Outline learning Semantic taxonomy building Semantic taxonomy construction Semantic taxonomy creation Semantic taxonomy extraction Semantic taxonomy generation Semantic taxonomy induction Semantic taxonomy learning Taxonomy automation Taxonomy building Taxonomy construction Taxonomy creation Taxonomy extraction Taxonomy generation Taxonomy induction Taxonomy learning
Ontology learning
Ontology learning (ontology extraction, ontology augmentation generation, ontology generation, or ontology acquisition) is the automatic or semi-automatic creation of ontologies, including extracting the corresponding domain's terms and the relationships between the concepts that these terms represent from a corpus of natural language text, and encoding them with an ontology language for easy retrieval. As building ontologies manually is extremely labor-intensive and time-consuming, there is great motivation to automate the process. Typically, the process starts by extracting terms and concepts or noun phrases from plain text using linguistic processors such as part-of-speech tagging and phrase chunking. Then statistical or symbolic techniques are used to extract relation signatures, often based on pattern-based or definition-based hypernym extraction techniques. == Procedure == Ontology learning (OL) is used to (semi-)automatically extract whole ontologies from natural language text. The process is usually split into the following eight tasks, which are not all necessarily applied in every ontology learning system. === Domain terminology extraction === During the domain terminology extraction step, domain-specific terms are extracted, which are used in the following step (concept discovery) to derive concepts. Relevant terms can be determined, e.g., by calculation of the TF/IDF values or by application of the C-value / NC-value method. The resulting list of terms has to be filtered by a domain expert. In the subsequent step, similarly to coreference resolution in information extraction, the OL system determines synonyms, because they share the same meaning and therefore correspond to the same concept. The most common methods therefore are clustering and the application of statistical similarity measures. === Concept discovery === In the concept discovery step, terms are grouped to meaning bearing units, which correspond to an abstraction of the world and therefore to concepts. The grouped terms are these domain-specific terms and their synonyms, which were identified in the domain terminology extraction step. === Concept hierarchy derivation === In the concept hierarchy derivation step, the OL system tries to arrange the extracted concepts in a taxonomic structure. This is mostly achieved with unsupervised hierarchical clustering methods. Because the result of such methods is often noisy, a supervision step, e.g., user evaluation, is added. A further method for the derivation of a concept hierarchy exists in the usage of several patterns that should indicate a sub- or supersumption relationship. Patterns like “X, that is a Y” or “X is a Y” indicate that X is a subclass of Y. Such pattern can be analyzed efficiently, but they often occur too infrequently to extract enough sub- or supersumption relationships. Instead, bootstrapping methods are developed, which learn these patterns automatically and therefore ensure broader coverage. === Learning of non-taxonomic relations === In the learning of non-taxonomic relations step, relationships are extracted that do not express any sub- or supersumption. Such relationships are, e.g., works-for or located-in. There are two common approaches to solve this subtask. The first is based upon the extraction of anonymous associations, which are named appropriately in a second step. The second approach extracts verbs, which indicate a relationship between entities, represented by the surrounding words. The result of both approaches need to be evaluated by an ontologist to ensure accuracy. === Rule discovery === During rule discovery, axioms (formal description of concepts) are generated for the extracted concepts. This can be achieved, e.g., by analyzing the syntactic structure of a natural language definition and the application of transformation rules on the resulting dependency tree. The result of this process is a list of axioms, which, afterwards, is comprehended to a concept description. This output is then evaluated by an ontologist. === Ontology population === At this step, the ontology is augmented with instances of concepts and properties. For the augmentation with instances of concepts, methods based on the matching of lexico-syntactic patterns are used. Instances of properties are added through the application of bootstrapping methods, which collect relation tuples. === Concept hierarchy extension === In this step, the OL system tries to extend the taxonomic structure of an existing ontology with further concepts. This can be performed in a supervised manner with a trained classifier or in an unsupervised manner via the application of similarity measures. === Frame and Event detection === During frame/event detection, the OL system tries to extract complex relationships from text, e.g., who departed from where to what place and when. Approaches range from applying SVM with kernel methods to semantic role labeling (SRL) to deep semantic parsing techniques. == Tools == Dog4Dag (Dresden Ontology Generator for Directed Acyclic Graphs) is an ontology generation plugin for Protégé 4.1 and OBOEdit 2.1. It allows for term generation, sibling generation, definition generation, and relationship induction. Integrated into Protégé 4.1 and OBO-Edit 2.1, DOG4DAG allows ontology extension for all common ontology formats (e.g., OWL and OBO). Limited largely to EBI and Bio Portal lookup service extensions.
Euratlas
Euratlas is a Switzerland-based software company dedicated to elaborate digital history maps of Europe. Founded in 2001, Euratlas has created a collection of history maps of Europe from year 1 AD to year 2000 AD that present the evolution of every country from the Roman Empire to present times. The evolution includes sovereign states and their administrative subdivisions, but also unorganized peoples and dependent territories. The maps show European country borders at regular intervals of 100 years, but not year by year. This leaves out many important turning points in history. Euratlas is considered a digital humanities company, and a scholar research software used in the field of historic cartography. It is broadly known among American and European universities, who mainly use Euratlas as a research tool and as a digital library atlas. == Sequential mapping policy == This concept was first designed by the German scholar Christian Kruse (1753–1827). Kruse, well aware that historical accounts are often biased for geographical, philosophical or political reasons, created a set of sequential maps in order to give a global vision of the successive political situations. Nowadays, the majority of atlases don't use this approach, but are event-based, like the well-known Penguin Atlas of History. The sequential approach intends to make the sequence of maps more neutral and suitable for students, historians and professionals of several fields. Although, this approach has been discussed as it leaves out many important history events that are not reflected on any of the maps because of the century interval. == Geo-referenced historical data == Initially, the European maps by century were developed as vector maps. From 2006 on, they have been converted to a geographic information system (GIS) database, enabling geo-referenced data capabilities. The map information is distributed in several layers: physical (geography information layer); political information layer (supranational entities, sovereign states, administrative divisions, dependent states and autonomous peoples); and special layers for cities and uncertain borders. The software database also contains much non-geographical information about political relationships between the various kinds of territories. == Map projection == Euratlas History Maps uses a Mercator projection, with the center in Europe. The maps include the North-African coast and the Near-East, offering a complete view of the Mediterranean Basin. The European Russia plains are shown, but not Scandinavia, specially Finland, which is cropped off the map view.
Bazaart
Bazaart is an AI-powered design platform with image and video editing capabilities for iOS, Android, MacOS, and the web. == History == Bazaart was founded in 2012 in Israel. In April 2012, Bazaart launched a Facebook app called Pinvolve, which converts Facebook Pages into Pinterest pinboards. From June to August 2012, it participated in the DreamIt startup accelerator in New York and raised $25,000 from the accelerator. In July 2012, it launched its first version as an iPad app connected to Pinterest. In December 2013, it pivoted and launched a major version of its app, a "social" photoshop that allowed users to edit images which could be pulled in from the camera roll, social networks, and other sources. In July 2014, Bazaart reached one million downloads and in December was selected by Apple as Best of 2014. In 2015, Bazaart added Photoshop integration in a partnership with Adobe. In September 2020, Bazaart launched an Android app. In December 2020, Bazaart was selected by Google as Best of 2020. In January 2022, Bazaart added video editing capabilities. In 2023, the platform added AI-powered backgrounds and video background removal features.
Ugly duckling theorem
The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969. == Mathematical formula == Suppose there are n things in the universe, and one wants to put them into classes or categories. One has no preconceived ideas or biases about what sorts of categories are "natural" or "normal" and what are not. So one has to consider all the possible classes that could be, all the possible ways of making a set out of the n objects. There are 2 n {\displaystyle 2^{n}} such ways, the size of the power set of n objects. One can use that to measure the similarity between two objects, and one would see how many sets they have in common. However, one cannot. Any two objects have exactly the same number of classes in common if we can form any possible class, namely 2 n − 1 {\displaystyle 2^{n-1}} (half the total number of classes there are). To see this is so, one may imagine each class is represented by an n-bit string (or binary encoded integer), with a zero for each element not in the class and a one for each element in the class. As one finds, there are 2 n {\displaystyle 2^{n}} such strings. As all possible choices of zeros and ones are there, any two bit-positions will agree exactly half the time. One may pick two elements and reorder the bits so they are the first two, and imagine the numbers sorted lexicographically. The first 2 n / 2 {\displaystyle 2^{n}/2} numbers will have bit #1 set to zero, and the second 2 n / 2 {\displaystyle 2^{n}/2} will have it set to one. Within each of those blocks, the top 2 n / 4 {\displaystyle 2^{n}/4} will have bit #2 set to zero and the other 2 n / 4 {\displaystyle 2^{n}/4} will have it as one, so they agree on two blocks of 2 n / 4 {\displaystyle 2^{n}/4} or on half of all the cases, no matter which two elements one picks. So if we have no preconceived bias about which categories are better, everything is then equally similar (or equally dissimilar). The number of predicates simultaneously satisfied by two non-identical elements is constant over all such pairs. Thus, some kind of inductive bias is needed to make judgements to prefer certain categories over others. === Boolean functions === Let x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} be a set of vectors of k {\displaystyle k} booleans each. The ugly duckling is the vector which is least like the others. Given the booleans, this can be computed using Hamming distance. However, the choice of boolean features to consider could have been somewhat arbitrary. Perhaps there were features derivable from the original features that were important for identifying the ugly duckling. The set of booleans in the vector can be extended with new features computed as boolean functions of the k {\displaystyle k} original features. The only canonical way to do this is to extend it with all possible Boolean functions. The resulting completed vectors have 2 k {\displaystyle 2^{k}} features. The ugly duckling theorem states that there is no ugly duckling because any two completed vectors will either be equal or differ in exactly half of the features. Proof. Let x and y be two vectors. If they are the same, then their completed vectors must also be the same because any Boolean function of x will agree with the same Boolean function of y. If x and y are different, then there exists a coordinate i {\displaystyle i} where the i {\displaystyle i} -th coordinate of x {\displaystyle x} differs from the i {\displaystyle i} -th coordinate of y {\displaystyle y} . Now the completed features contain every Boolean function on k {\displaystyle k} Boolean variables, with each one exactly once. Viewing these Boolean functions as polynomials in k {\displaystyle k} variables over GF(2), segregate the functions into pairs ( f , g ) {\displaystyle (f,g)} where f {\displaystyle f} contains the i {\displaystyle i} -th coordinate as a linear term and g {\displaystyle g} is f {\displaystyle f} without that linear term. Now, for every such pair ( f , g ) {\displaystyle (f,g)} , x {\displaystyle x} and y {\displaystyle y} will agree on exactly one of the two functions. If they agree on one, they must disagree on the other and vice versa. (This proof is believed to be due to Watanabe.) == Discussion == A possible way around the ugly duckling theorem would be to introduce a constraint on how similarity is measured by limiting the properties involved in classification, for instance, between A and B. However Medin et al. (1993) point out that this does not actually resolve the arbitrariness or bias problem since in what respects A is similar to B: "varies with the stimulus context and task, so that there is no unique answer, to the question of how similar is one object to another". For example, "a barberpole and a zebra would be more similar than a horse and a zebra if the feature striped had sufficient weight. Of course, if these feature weights were fixed, then these similarity relations would be constrained". Yet the property "striped" as a weight 'fix' or constraint is arbitrary itself, meaning: "unless one can specify such criteria, then the claim that categorization is based on attribute matching is almost entirely vacuous". Stamos (2003) remarked that some judgments of overall similarity are non-arbitrary in the sense they are useful: "Presumably, people's perceptual and conceptual processes have evolved that information that matters to human needs and goals can be roughly approximated by a similarity heuristic... If you are in the jungle and you see a tiger but you decide not to stereotype (perhaps because you believe that similarity is a false friend), then you will probably be eaten. In other words, in the biological world stereotyping based on veridical judgments of overall similarity statistically results in greater survival and reproductive success." Unless some properties are considered more salient, or 'weighted' more important than others, everything will appear equally similar, hence Watanabe (1986) wrote: "any objects, in so far as they are distinguishable, are equally similar". In a weaker setting that assumes infinitely many properties, Murphy and Medin (1985) give an example of two putative classified things, plums and lawnmowers: "Suppose that one is to list the attributes that plums and lawnmowers have in common in order to judge their similarity. It is easy to see that the list could be infinite: Both weigh less than 10,000 kg (and less than 10,001 kg), both did not exist 10,000,000 years ago (and 10,000,001 years ago), both cannot hear well, both can be dropped, both take up space, and so on. Likewise, the list of differences could be infinite… any two entities can be arbitrarily similar or dissimilar by changing the criterion of what counts as a relevant attribute." According to Woodward, the ugly duckling theorem is related to Schaffer's Conservation Law for Generalization Performance, which states that all algorithms for learning of boolean functions from input/output examples have the same overall generalization performance as random guessing. The latter result is generalized by Woodward to functions on countably infinite domains.