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Topic: Classifier (mathematics)

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Naive Bayes classifier

	Classifier Systems Abstracts
		A classifier system (sometimes referred to as adaptive agents) is a specialized application of genetic algorithms.
		A classifier system has the ability to categorize its environment and create rules dynamically, thus making it able to adapt to differing circumstances on the fly.
		The classifier system works by selecting and applying rules to the different categories, constantly recombining those rules so they give better and better results on an individual basis.
	subsimple.com /classifier.asp (1513 words)

	Encyclopedia topic: Classifier (mathematics) (Site not responding. Last check: 2007-10-16)
		In mathematics (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement), a classifier is a mapping from a (discrete or continuous) feature space X to a discrete set of labels Y.
		Classifiers may either be fixed classifiers or learning classifiers (additional info and facts about learning classifiers), and learning classifiers may in turn be divided into supervised (additional info and facts about supervised) and unsupervised learning (additional info and facts about unsupervised learning) classifiers.
		For a list of classifier applications and classifier technologies, please see Pattern recognition (additional info and facts about Pattern recognition).
	www.absoluteastronomy.com /encyclopedia/c/cl/classifier_(mathematics).htm (156 words)

	Encyclopedia: Classifier (mathematics) (Site not responding. Last check: 2007-10-16)
		In mathematics, a classifier is a mapping from a (discrete or continuous) feature space X to a discrete set of labels Y.
		Mathematics is often defined as the study of topics such as quantity, structure, space, and change.
		A linear classifier is a classifier that uses a linear function of its inputs to base its decision on.
	www.nationmaster.com /encyclopedia/Classifier-%28mathematics%29 (254 words)

	Naive Bayes classifier - Wikipedia, the free encyclopedia
		Naive Bayes classifiers are based on probability models that incorporate strong independence assumptions which often have no bearing in reality, hence are (deliberately) naive.
		The naive Bayes classifier has several properties that make it surprisingly useful in practice, despite the fact that the far-reaching independence assumptions are often violated.
		Like all probabilistic classifiers under the MAP decision rule, it arrives at the correct classification as long as the correct class is more probable than any other class; class probabilities do not have to be estimated very well.
	en.wikipedia.org /wiki/Naive_Bayesian_classification (1118 words)

	Subobject classifier - RecipeFacts (Site not responding. Last check: 2007-10-16)
		In category theory, a subobject classifier is a special object Ω of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Ω.
		As an example, the set Ω = {0,1} is a subobject classifier in the category of sets and functions: to every subset U of X we can assign the function from X to Ω that maps precisely the elements of U to 1 (see characteristic function).
		Then π is a local homeomorphism, and the sheaf corresponding is the required subobject classifier (in other words the construction of Ω is by means of its espace étalé).
	www.recipeland.com /encyclopaedia/index.php/Subobject_classifier (305 words)

	Encyclopedia: Naive Bayes classifier (Site not responding. Last check: 2007-10-16)
		NaÃ¯ve Bayes classifiers are based on probability models that incorporate strong independence assumptions which often have no bearing in reality, hence are (deliberately) naÃ¯ve.
		In mathematics, a classifier is a mapping from a (discrete or continuous) feature space X to a discrete set of labels Y. Classifiers may either be fixed classifiers or learning classifiers, and learning classifiers may in turn be divided into supervised and unsupervised learning classifiers.
		Consider the problem of classifying documents by their content, for example into (A canned meat made largely from pork) spam and non-spam ((computer science) a system of world-wide electronic communication in which a computer user can compose a message at one terminal that is generated at the recipient's terminal when he logs in) E-mails.
	www.nationmaster.com /encyclopedia/Naive-Bayes-classifier (630 words)

	I_worked_on (Site not responding. Last check: 2007-10-16)
		Without knowing about complex mathematical techniques to find a probability that a value of a linear discriminant function of a sample based Euclidean distance classifier is negative I approximated an unknown distribution of the discriminant function by a Gaussian law.
		While classifying objects characterized by the categorical (discrete) variables, or while constructing a decision rule for making a unifying decision according to decisions of single modules in a cooperative neural network design (a classifiers' fusion rule), we can use a multinomial classifier.
		We concluded that one from the two classical statistical classifiers - the standard linear discriminant function or the PW classifier - most often appears to be the best one (or is very close to the best one) in a pool of the statistical classifiers.
	www.science.mii.lt /mii/raudys/i_worked_on.html (2238 words)

	SIAM News
		A classifier provides a list of genes whose products, or more specifically the amounts of whose products, are indicative of important differences in cell state, such as the presence of a particular type of cancer.
		Moreover, sufficient information must be vested in sets of genes small enough to serve either as convenient diagnostic panels or as candidates for the very expensive and time-consuming analysis required to determine their use as targets for therapy.
		In addition, given a feature set, two issues must be addressed: (1) design of a close-to-optimal classifier from the sample data and (2) estimation of the error of the classifier.
	www.siam.org /siamnews/05-02/genes.htm (875 words)

	Extending Reynolds
		Now if B contains the subobject classifier as a subobject, we can carry out a version of Cantor's diagonal argument in the internal logic of the topos E to conclude that it is degenerate.
		In SET, the subobject classifier coincides with the coproduct, 1+1, of the terminal object with itself; but in a general topos these two objects are very different.
		Note that the "modest sets" model of polymorphism [Hy] shows that even though P(0) cannot have a subobject classifier, it can have many of the properties which are consequences of being a topos (such as being locally cartesian closed, having a natural number object and being finitely cocomplete).
	www.seas.upenn.edu /~sweirich/types/archive/1988/msg00065.html (827 words)

	[No title]
		In this thesis we focused on Bayesian classification.
		A Bayesian classifier is a statistical classifier, which uses the Bayes theorem to predict class membership as a conditional probability that a given data sample falls into a particular class.
		The former is called eager classifier and the later is called ‘lazy classifier.’ 2.2.3 Clustering Clustering is a process of grouping the similar type of data sample together.
	www.cs.ndsu.nodak.edu /~mhossain/thesis.doc (6556 words)

	Automatical Classification of Road Signs (Site not responding. Last check: 2007-10-16)
		The advantages of such approach (compared to the monolithical classifier) are fast classifier responses, better results (error rates) and also existence of partial results (class estimates) during the classification process.
		From many experiments, undertaken for the construction of the most effective road signs classifier, follows, that colour information may be fruitful for the task decomposition but is not required on principle.
		The theoretical part of the work (kernel classifier and novel approach for its optimization) may be utilized in many different pattern recognition applications.
	euler.fd.cvut.cz /~paclik/thesis.html (891 words)

	CBofN - Glossary - C
		Classifier A rule that is part of a classifier system and has a condition that must be matched before its message (or action) can be posted (or effected).
		The strength of a classifier determines the likelihood that it can outbid other classifiers if more than one condition is matched.
		The strengths of the classifiers are modified by the bucket brigade algorithm, and new rules can be introduced via a genetic algorithm.
	mitpress.mit.edu /books/FLAOH/cbnhtml/glossary-C.html (829 words)

	Laird Breyer's Free software (Site not responding. Last check: 2007-10-16)
		Cross-validation is a method which is widely used to compare the quality of classification and learning algorithms, and as such permits rudimentary comparisons between those classifiers which make use of dbacl(1) and bayesol(1), and other competing classifiers.
		For each subset, the filter (by default, dbacl(1)) is used to classify each message within this subset, based upon having learned the categories from the remaining subsets.
		Since classifiers have widely varying interfaces, this is only possible by wrapping those interfaces individually into a standard form which can be used by mailcross testsuite.
	www.lbreyer.com /mailcrossman.html (1358 words)

	CBofN - Glossary
		Detector A sensor that translates the state of a classifier's environment into a message that is suitable for posting to the message list of the classifier system.
		For example, classifying many images of letters to one of the twenty-six letters of the alphabet is a pattern classification task.
		Self-Organized Criticality (SOC) A mathematical theory that describes how systems composed of many interacting parts can tune themselves toward dynamical behavior that is critical in the sense that it is neither stable nor unstable but at a region near a phase transition.
	mitpress.mit.edu /books/FLAOH/cbnhtml/glossary.html (8347 words)

	SPHINcsX: Section 1.3 (Site not responding. Last check: 2007-10-16)
		The classifier system can potentially overcome many of the limitations of current methods due to its generality, thereby not depending on the problem to be optimized possessing certain properties (as is the case in many present approaches).
		Although classifier systems and their underlying genetic algorithm are not common in the mechanical engineering field, genetic algorithms have already proven their worth in other real world applications.
		As a mathematician with no knowledge of engineering is likely to perform sub-par to an engineer in the application of mathematics to engineering problems, one needs engineering acumen to successfully apply and interface classifier systems to engineering shape improvement or any other engineering problem.
	www.stanford.edu /~buc/SPHINcsX/bkhm043.htm (934 words)

	ei (Site not responding. Last check: 2007-10-16)
		By mathematical inductive method, we have proved that a generalized Hopfield network with non negative weights is strictly stable, that is, the network evolves to a simple hole - stable state with probability one when it starts at any initial state.
		The non-Gaussian AR model of PCG signals (phonocardiogram) is used to detect quadratic nonlinear interactions and to classify the two patterns of phonocardiograms in terms of the parametric bispectral estimate.
		By mathematical inductive method, we have proved that a generalized Hopfield network with non-negative weights is strictly stable, that is, the network evolves to a simple hole-a stable state with probability one when it starts at any initial state.
	www.lib.stu.edu.cn /html/info/issue/ei.htm (6853 words)

	Pattern Recognition Preprints 1999
		The first GA version selects disjoint feature subsets to be used by the individual classifiers, whereas the second version selects (possibly) overlapping feature subsets and also the types of the individual classifiers.
		The multiple classifier systems designed with the two GAs were compared against classifiers using: (a) all features; (b) the best feature subset found by the sequential backward selection (SBS) method; and (c), the best feature subset found by a GA (individual classifier!).
		We found that: (1) the multiple classifier system derived through the GA, Version 2, yielded the smallest training error rate in all experiments; (2) with Satimage and Forensic glasses data it also produced the smallest test error rate.
	www.informatics.bangor.ac.uk /public/mathematics/research/preprints/99/patrec99.html (1402 words)

	Marrying Statistics and Neural Networks to Design Classification Algorithms (Site not responding. Last check: 2007-10-16)
		The statistical parametric classifiers are based on parameterization of the multivariate distribution densities, while in the non-parametric (neural net) approach, one makes assumptions about a structure of the classification rule and then estimates unknown coefficients of the decision rule directly from the training data.
		We present an overview of main multivariate density parameterization methods useful in the classifier design and express a gain from the parameterization in terms of decrease in a generalization error or the training set size.
		If certain conditions are satisfied then after the first gradient descent training iteration we obtain a classifier equivalent to the statistical classifier which could be obtained by utilizing "the learning set based information" directly.
	www.cvc.uab.es /icpr2000/homepage/techprogram/tutorials/descriptions/desc7.htm (926 words)

	Classifying Gene Expression Profiles from Pairwise mRNA Comparisons
		In contrast, the TSP classifier provides decision rules which i) involve very few genes and only relative expression values (e.g., comparing the mRNA counts within a single pair of genes); ii) are both accurate and transparent; and iii) provide specific hypotheses for follow-up studies.
		In particular, the TSP classifier achieves prediction rates with standard cancer data that are as high as those of previous studies which use considerably more genes and complex procedures.
		Finally, the TSP classifier is parameter-free, thus avoiding the type of over-fitting and inflated estimates of performance that result when all aspects of learning a predictor are not properly cross-validated.
	www.bepress.com /sagmb/vol3/iss1/art19 (378 words)

	Ethnomathematics Digital Library (EDL) (Site not responding. Last check: 2007-10-16)
		He examines the presence and use of morphemes in numeral prefixes and numeral classifiers with examples and a diagram of the construction of numeral classifiers using three morphemes.
		Their system was based on an accumulation of knowledge obtained through “observing their environment and structuring their island society.” The different methods of Mwoakillese mathematics covered include time and linear measurements, counting, and enumeration.
		This case study, a school course overview of navigational knowledge, includes a discussion of how the Micronesian system of hatag is used to keep track of position at sea, seen possibly as a kind of mental geometry.
	www.ethnomath.org /search/browseResources.asp?type=country&id=308 (971 words)

	Ethnomathematics Digital Library (EDL) (Site not responding. Last check: 2007-10-16)
		The premise is that mathematical concepts are contained in the language, culture, worldview, and subsistence activities.
		For example, “numeral classifier for an arm length: -paiu”; ”numeral classifier for forearm lengths, from elbow to the end of forefinger: -mwaliu”; numeral classifier for lines, processions, layers: -tal”; and so on.
		The Ethnomathematics Digital Library is a component of the National Science, Technology, Engineering and Mathematics Education Digital Library (NSDL), funded by the National Science Foundation.
	www.ethnomath.org /search/browseResources.asp?type=subject&id=279 (421 words)

	Epsilon-Delta
		Ideally, the trained machine will be able to classify new e-mail messages as spam or not spam, using what it has learned already about the character of spam.
		It works so well because the classifier can compute correlations between word occurrence, which is a fairly good indicator of semantic meaning.
		An offline classifier is the sort of classifier I have been talking about - you gather your training data, train the classifier, then use it to classify new instances.
	epsilondelta.net (2358 words)

	On the Finite Sample Performance of the Nearest Neighbor Classifier -- from Mathematica Information Center
		The finite sample performance of a nearest neighbor classifier is analyzed for a two-class pattern recognition problem.
		An exact integral expression is derived for the m-sample risk Rm given that a reference m-sample of labeled points is available to the classifier.
		The statistical setup assumes that the pattern classes arise in nature with fixed a priori probabilities and that points representing the classes are drawn from Euclidean n-space according to fixed class-conditional probability distributions.
	library.wolfram.com /infocenter/Articles/2871 (228 words)

	What's New (Site not responding. Last check: 2007-10-16)
		Abstract: An approach to cancer class prediction from gene expression profiling is devised, based on an enhancement of the simple nearest prototype (centroid) classifier.
		A classifier is obtained via shrinking of the prototypes, it turned out often to be more accurate than competing methods.
		To demonstrate the effectiveness of the method, the authors show that the method was highly efficient in finding genes for classifying small round blue cell tumors and leukemias.
	www.uncfsu.edu /Macsc/News/Seminars.htm (388 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		The method constructs an accurate classifier by combining a large number of very weak discriminators that are generated essentially at random.
		In this tutorial we explain these concepts via a simple numerical example, with a focus on a fundamental symmetry in point set covering that is the key observation leading to the foundation of the SD theory.
		In response to this, I propose that further exploration of the methodology be guided by detailed descriptions of geometrical characteristics of data and classifier models.
	cm.bell-labs.com /who/tkh/talks.html (815 words)

	General Mathematics Colloquium Leiden: Archive (Site not responding. Last check: 2007-10-16)
		A classifier is a subset G of X.
		The optimal classifier is Bayes rule, which is to predict the most likely label given X.
		Roughly speaking, the idea is to find the classifier which minimizes the number of errors in the training data among a certain collection of classifiers G.
	www.math.leidenuniv.nl /~evertse/colloquium-vdgeer.shtml (282 words)

	main
		For classifier with identical structure of the stages we proved in [1], that the degree of fractional extraction is
		be a function giving the total number of separation acts (including the initial position), during which acts the particle remains in the classifier before its output to the fine or coarse product.
		, and hence, using (16) and (17) we obtain the expectation and variance of the total number of separation acts during which the particle is in the classifier.
	www.it.lut.fi /mat/EcmiNL/ecmi37/case4.html (506 words)

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