Pattern recognition
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Machine learning and data mining 

Pattern recognition is a branch of machine learning that focuses on the recognition of patterns and regularities in data, although it is in some cases considered to be nearly synonymous with machine learning.^{[1]} Pattern recognition systems are in many cases trained from labeled "training" data (supervised learning), but when no labeled data are available other algorithms can be used to discover previously unknown patterns (unsupervised learning).
The terms pattern recognition, machine learning, data mining and knowledge discovery in databases (KDD) are hard to separate, as they largely overlap in their scope. Machine learning is the common term for supervised learning methods^{[dubious – discuss]} and originates from artificial intelligence, whereas KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition has its origins in engineering, and the term is popular in the context of computer vision: a leading computer vision conference is named Conference on Computer Vision and Pattern Recognition. In pattern recognition, there may be a higher interest to formalize, explain and visualize the pattern, while machine learning traditionally focuses on maximizing the recognition rates. Yet, all of these domains have evolved substantially from their roots in artificial intelligence, engineering and statistics, and they've become increasingly similar by integrating developments and ideas from each other.
In machine learning, pattern recognition is the assignment of a label to a given input value. In statistics, discriminant analysis was introduced for this same purpose in 1936. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes (for example, determine whether a given email is "spam" or "nonspam"). However, pattern recognition is a more general problem that encompasses other types of output as well. Other examples are regression, which assigns a realvalued output to each input; sequence labeling, which assigns a class to each member of a sequence of values (for example, part of speech tagging, which assigns a part of speech to each word in an input sentence); and parsing, which assigns a parse tree to an input sentence, describing the syntactic structure of the sentence.^{[citation needed]}
Pattern recognition algorithms generally aim to provide a reasonable answer for all possible inputs and to perform "most likely" matching of the inputs, taking into account their statistical variation. This is opposed to pattern matching algorithms, which look for exact matches in the input with preexisting patterns. A common example of a patternmatching algorithm is regular expression matching, which looks for patterns of a given sort in textual data and is included in the search capabilities of many text editors and word processors. In contrast to pattern recognition, pattern matching is generally a type of machine learning, although patternmatching algorithms (especially with fairly general, carefully tailored patterns) can sometimes succeed in providing similarquality output of the sort provided by patternrecognition algorithms.
Contents
 1 Overview
 2 Problem statement (supervised version)
 3 Uses

4 Algorithms
 4.1 Classification algorithms (supervised algorithms predicting categorical labels)
 4.2 Clustering algorithms (unsupervised algorithms predicting categorical labels)
 4.3 Ensemble learning algorithms (supervised metaalgorithms for combining multiple learning algorithms together)
 4.4 General algorithms for predicting arbitrarilystructured (sets of) labels
 4.5 Multilinear subspace learning algorithms (predicting labels of multidimensional data using tensor representations)
 4.6 Realvalued sequence labeling algorithms (predicting sequences of realvalued labels)
 4.7 Regression algorithms (predicting realvalued labels)
 4.8 Sequence labeling algorithms (predicting sequences of categorical labels)
 5 See also
 6 References
 7 Further reading
 8 External links
Overview
Pattern recognition is generally categorized according to the type of learning procedure used to generate the output value. Supervised learning assumes that a set of training data (the training set) has been provided, consisting of a set of instances that have been properly labeled by hand with the correct output. A learning procedure then generates a model that attempts to meet two sometimes conflicting objectives: Perform as well as possible on the training data, and generalize as well as possible to new data (usually, this means being as simple as possible, for some technical definition of "simple", in accordance with Occam's Razor, discussed below). Unsupervised learning, on the other hand, assumes training data that has not been handlabeled, and attempts to find inherent patterns in the data that can then be used to determine the correct output value for new data instances.^{[2]} A combination of the two that has recently been explored is semisupervised learning, which uses a combination of labeled and unlabeled data (typically a small set of labeled data combined with a large amount of unlabeled data). Note that in cases of unsupervised learning, there may be no training data at all to speak of; in other words,and the data to be labeled is the training data.
Note that sometimes different terms are used to describe the corresponding supervised and unsupervised learning procedures for the same type of output. For example, the unsupervised equivalent of classification is normally known as clustering, based on the common perception of the task as involving no training data to speak of, and of grouping the input data into clusters based on some inherent similarity measure (e.g. the distance between instances, considered as vectors in a multidimensional vector space), rather than assigning each input instance into one of a set of predefined classes. Note also that in some fields, the terminology is different: For example, in community ecology, the term "classification" is used to refer to what is commonly known as "clustering".
The piece of input data for which an output value is generated is formally termed an instance. The instance is formally described by a vector of features, which together constitute a description of all known characteristics of the instance. (These feature vectors can be seen as defining points in an appropriate multidimensional space, and methods for manipulating vectors in vector spaces can be correspondingly applied to them, such as computing the dot product or the angle between two vectors.) Typically, features are either categorical (also known as nominal, i.e., consisting of one of a set of unordered items, such as a gender of "male" or "female", or a blood type of "A", "B", "AB" or "O"), ordinal (consisting of one of a set of ordered items, e.g., "large", "medium" or "small"), integervalued (e.g., a count of the number of occurrences of a particular word in an email) or realvalued (e.g., a measurement of blood pressure). Often, categorical and ordinal data are grouped together; likewise for integervalued and realvalued data. Furthermore, many algorithms work only in terms of categorical data and require that realvalued or integervalued data be discretized into groups (e.g., less than 5, between 5 and 10, or greater than 10).
Probabilistic classifiers
It has been suggested that portions of this section be split out into another article titled Probabilistic classifier. (Discuss) (May 2014)

Many common pattern recognition algorithms are probabilistic in nature, in that they use statistical inference to find the best label for a given instance. Unlike other algorithms, which simply output a "best" label, often probabilistic algorithms also output a probability of the instance being described by the given label. In addition, many probabilistic algorithms output a list of the Nbest labels with associated probabilities, for some value of N, instead of simply a single best label. When the number of possible labels is fairly small (e.g., in the case of classification), N may be set so that the probability of all possible labels is output. Probabilistic algorithms have many advantages over nonprobabilistic algorithms:
 They output a confidence value associated with their choice. (Note that some other algorithms may also output confidence values, but in general, only for probabilistic algorithms is this value mathematically grounded in probability theory. Nonprobabilistic confidence values can in general not be given any specific meaning, and only used to compare against other confidence values output by the same algorithm.)
 Correspondingly, they can abstain when the confidence of choosing any particular output is too low.
 Because of the probabilities output, probabilistic patternrecognition algorithms can be more effectively incorporated into larger machinelearning tasks, in a way that partially or completely avoids the problem of error propagation.
Number of important feature variables
Feature selection algorithms attempt to directly prune out redundant or irrelevant features. A general introduction to feature selection which summarizes approaches and challenges, has been given.^{[3]} The complexity of featureselection is, because of its nonmonotonous character, an optimization problem where given a total of features the powerset consisting of all subsets of features need to be explored. The BranchandBound algorithm^{[4]} does reduce this complexity but is intractable for medium to large values of the number of available features . For a largescale comparison of featureselection algorithms see .^{[5]}
Techniques to transform the raw feature vectors (feature extraction) are sometimes used prior to application of the patternmatching algorithm. For example, feature extraction algorithms attempt to reduce a largedimensionality feature vector into a smallerdimensionality vector that is easier to work with and encodes less redundancy, using mathematical techniques such as principal components analysis (PCA). The distinction between feature selection and feature extraction is that the resulting features after feature extraction has taken place are of a different sort than the original features and may not easily be interpretable, while the features left after feature selection are simply a subset of the original features.
Problem statement (supervised version)
Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function (the ground truth) that maps input instances to output labels , along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping . (For example, if the problem is filtering spam, then is some representation of an email and is either "spam" or "nonspam"). In order for this to be a welldefined problem, "approximates as closely as possible" needs to be defined rigorously. In decision theory, this is defined by specifying a loss function or cost function that assigns a specific value to "loss" resulting from producing an incorrect label. The goal then is to minimize the expected loss, with the expectation taken over the probability distribution of . In practice, neither the distribution of nor the ground truth function are known exactly, but can be computed only empirically by collecting a large number of samples of and handlabeling them using the correct value of (a timeconsuming process, which is typically the limiting factor in the amount of data of this sort that can be collected). The particular loss function depends on the type of label being predicted. For example, in the case of classification, the simple zeroone loss function is often sufficient. This corresponds simply to assigning a loss of 1 to any incorrect labeling and implies that the optimal classifier minimizes the error rate on independent test data (i.e. counting up the fraction of instances that the learned function labels wrongly, which is equivalent to maximizing the number of correctly classified instances). The goal of the learning procedure is then to minimize the error rate (maximize the correctness) on a "typical" test set.
For a probabilistic pattern recognizer, the problem is instead to estimate the probability of each possible output label given a particular input instance, i.e., to estimate a function of the form
where the feature vector input is , and the function f is typically parameterized by some parameters .^{[6]} In a discriminative approach to the problem, f is estimated directly. In a generative approach, however, the inverse probability is instead estimated and combined with the prior probability using Bayes' rule, as follows:
When the labels are continuously distributed (e.g., in regression analysis), the denominator involves integration rather than summation:
The value of is typically learned using maximum a posteriori (MAP) estimation. This finds the best value that simultaneously meets two conflicting objects: To perform as well as possible on the training data (smallest errorrate) and to find the simplest possible model. Essentially, this combines maximum likelihood estimation with a regularization procedure that favors simpler models over more complex models. In a Bayesian context, the regularization procedure can be viewed as placing a prior probability on different values of . Mathematically:
where is the value used for in the subsequent evaluation procedure, and , the posterior probability of , is given by
In the Bayesian approach to this problem, instead of choosing a single parameter vector , the probability of a given label for a new instance is computed by integrating over all possible values of , weighted according to the posterior probability:
Frequentist or Bayesian approach to pattern recognition
The first pattern classifier – the linear discriminant presented by Fisher – was developed in the frequentist tradition. The frequentist approach entails that the model parameters are considered unknown, but objective. The parameters are then computed (estimated) from the collected data. For the linear discriminant, these parameters are precisely the mean vectors and the covariance matrix. Also the probability of each class is estimated from the collected dataset. Note that the usage of 'Bayes rule' in a pattern classifier does not make the classification approach Bayesian.
Bayesian statistics has its origin in Greek philosophy where a distinction was already made between the 'a priori' and the 'a posteriori' knowledge. Later Kant defined his distinction between what is a priori known – before observation – and the empirical knowledge gained from observations. In a Bayesian pattern classifier, the class probabilities can be chosen by the user, which are then a priori. Moreover, experience quantified as a priori parameter values can be weighted with empirical observations – using e.g., the Beta (conjugate prior) and Dirichletdistributions. The Bayesian approach facilitates a seamless intermixing between expert knowledge in the form of subjective probabilities, and objective observations.
Probabilistic pattern classifiers can be used according to a frequentist or a Bayesian approach.
Uses
Within medical science, pattern recognition is the basis for computeraided diagnosis (CAD) systems. CAD describes a procedure that supports the doctor's interpretations and findings. Other typical applications of pattern recognition techniques are automatic speech recognition, classification of text into several categories (e.g., spam/nonspam email messages), the automatic recognition of handwritten postal codes on postal envelopes, automatic recognition of images of human faces, or handwriting image extraction from medical forms.^{[7]} The last two examples form the subtopic image analysis of pattern recognition that deals with digital images as input to pattern recognition systems.^{[8]}^{[9]}
Optical character recognition is a classic example of the application of a pattern classifier, see OCRexample. The method of signing one's name was captured with stylus and overlay starting in 1990.^{[citation needed]} The strokes, speed, relative min, relative max, acceleration and pressure is used to uniquely identify and confirm identity. Banks were first offered this technology, but were content to collect from the FDIC for any bank fraud and did not want to inconvenience customers..^{[citation needed]}
Artificial neural networks (neural net classifiers) and deep learning have many realworld applications in image processing, a few examples:
 identification and authentication: e.g., license plate recognition,^{[10]} fingerprint analysis and face detection/verification;^{[11]}
 medical diagnosis: e.g., screening for cervical cancer (Papnet)^{[12]} or breast tumors;
 defence: various navigation and guidance systems, target recognition systems, shape recognition technology etc.
For a discussion of the aforementioned applications of neural networks in image processing, see e.g.^{[13]}
In psychology, pattern recognition (making sense of and identifying objects) is closely related to perception, which explains how the sensory inputs humans receive are made meaningful. Pattern recognition can be thought of in two different ways: the first being template matching and the second being feature detection. A template is a pattern used to produce items of the same proportions. The templatematching hypothesis suggests that incoming stimuli are compared with templates in the long term memory. If there is a match, the stimulus is identified. Feature detection models, such as the Pandemonium system for classifying letters (Selfridge, 1959), suggest that the stimuli are broken down into their component parts for identification. For example, a capital E has three horizontal lines and one vertical line.^{[14]}
Algorithms
Algorithms for pattern recognition depend on the type of label output, on whether learning is supervised or unsupervised, and on whether the algorithm is statistical or nonstatistical in nature. Statistical algorithms can further be categorized as generative or discriminative.
This article contains embedded lists that may be poorly defined, unverified or indiscriminate. (May 2014)

Classification algorithms (supervised algorithms predicting categorical labels)
Parametric:^{[15]}
 Linear discriminant analysis
 Quadratic discriminant analysis
 Maximum entropy classifier (aka logistic regression, multinomial logistic regression): Note that logistic regression is an algorithm for classification, despite its name. (The name comes from the fact that logistic regression uses an extension of a linear regression model to model the probability of an input being in a particular class.)
Nonparametric:^{[16]}
 Decision trees, decision lists
 Kernel estimation and Knearestneighbor algorithms
 Naive Bayes classifier
 Neural networks (multilayer perceptrons)
 Perceptrons
 Support vector machines
 Gene expression programming
Clustering algorithms (unsupervised algorithms predicting categorical labels)
 Categorical mixture models
 Deep learning methods^{[citation needed]}
 Hierarchical clustering (agglomerative or divisive)
 Kmeans clustering
 Correlation clustering
 Kernel principal component analysis (Kernel PCA)
Ensemble learning algorithms (supervised metaalgorithms for combining multiple learning algorithms together)
 Boosting (metaalgorithm)
 Bootstrap aggregating ("bagging")
 Ensemble averaging
 Mixture of experts, hierarchical mixture of experts
General algorithms for predicting arbitrarilystructured (sets of) labels
Multilinear subspace learning algorithms (predicting labels of multidimensional data using tensor representations)
Unsupervised:
Realvalued sequence labeling algorithms (predicting sequences of realvalued labels)
Supervised (?):
Regression algorithms (predicting realvalued labels)
Supervised:
 Gaussian process regression (kriging)
 Linear regression and extensions
 Neural networks and Deep learning methods
Unsupervised:
Sequence labeling algorithms (predicting sequences of categorical labels)
Supervised:
 Conditional random fields (CRFs)
 Hidden Markov models (HMMs)
 Maximum entropy Markov models (MEMMs)
 Recurrent neural networks
Unsupervised:
 Hidden Markov models (HMMs)
See also
 Adaptive resonance theory
 Black box
 Cache language model
 Compound term processing
 Computeraided diagnosis
 Data mining
 Deep Learning
 List of numerical analysis software
 List of numerical libraries
 Machine learning
 Multilinear subspace learning
 Neocognitron
 Perception
 Perceptual learning
 Predictive analytics
 Prior knowledge for pattern recognition
 Sequence mining
 Template matching
 Contextual image classification
 List of datasets for machine learning research
References
This article is based on material taken from the Free Online Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

^ Bishop, Christopher M. (2006). Pattern Recognition and Machine Learning (PDF). Springer. p. vii.
Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years.
 ^ Carvalko, J.R., Preston K. (1972). "On Determining Optimum Simple Golay Marking Transforms for Binary Image Processing". IEEE Transactions on Computers. 21: 1430–33. doi:10.1109/TC.1972.223519. .
 ^ Isabelle Guyon Clopinet, André Elisseeff (2003). An Introduction to Variable and Feature Selection. The Journal of Machine Learning Research, Vol. 3, 11571182. Link
 ^ Iman Foroutan; Jack Sklansky (1987). "Feature Selection for Automatic Classification of NonGaussian Data". IEEE Transactions on Systems, Man and Cybernetics. 17 (2): 187–198. doi:10.1109/TSMC.1987.4309029..
 ^ Mineichi Kudo; Jack Sklansky (2000). "Comparison of algorithms that select features for pattern classifiers". Pattern Recognition. 33 (1): 25–41. doi:10.1016/S00313203(99)000412..
 ^ For linear discriminant analysis the parameter vector consists of the two mean vectors and and the common covariance matrix .
 ^ Milewski, Robert; Govindaraju, Venu (31 March 2008). "Binarization and cleanup of handwritten text from carbon copy medical form images". Pattern Recognition. 41 (4): 1308–1315. doi:10.1016/j.patcog.2007.08.018.
 ^ Richard O. Duda, Peter E. Hart, David G. Stork (2001). Pattern classification (2nd ed.). Wiley, New York. ISBN 0471056693.
 ^ R. Brunelli, Template Matching Techniques in Computer Vision: Theory and Practice, Wiley, ISBN 9780470517062, 2009
 ^ THE AUTOMATIC NUMBER PLATE RECOGNITION TUTORIAL http://anprtutorial.com/
 ^ Neural Networks for Face Recognition Companion to Chapter 4 of the textbook Machine Learning.
 ^ PAPNET For Cervical Screening Archived 20120708 at Archive.is "Archived copy". Archived from the original on 20120708. Retrieved 20120506.
 ^ EgmontPetersen, M., de Ridder, D., Handels, H. (2002). "Image processing with neural networks  a review". Pattern Recognition. 35 (10): 2279–2301. doi:10.1016/S00313203(01)001789.
 ^ "Alevel Psychology Attention Revision  Pattern recognition  Scool, the revision website". Scool.co.uk. Retrieved 20120917.
 ^ Assuming known distributional shape of feature distributions per class, such as the Gaussian shape.
 ^ No distributional assumption regarding shape of feature distributions per class.
Further reading
 Fukunaga, Keinosuke (1990). Introduction to Statistical Pattern Recognition (2nd ed.). Boston: Academic Press. ISBN 0122698517.
 Hornegger, Joachim; Paulus, Dietrich W. R. (1999). Applied Pattern Recognition: A Practical Introduction to Image and Speech Processing in C++ (2nd ed.). San Francisco: Morgan Kaufmann Publishers. ISBN 3528155582.
 Schuermann, Juergen (1996). Pattern Classification: A Unified View of Statistical and Neural Approaches. New York: Wiley. ISBN 0471135348.
 Godfried T. Toussaint, ed. (1988). Computational Morphology. Amsterdam: NorthHolland Publishing Company.
 Kulikowski, Casimir A.; Weiss, Sholom M. (1991). Computer Systems That Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems. Machine Learning. San Francisco: Morgan Kaufmann Publishers. ISBN 1558600655.
 Jain, Anil.K.; Duin, Robert.P.W.; Mao, Jianchang (2000). "Statistical pattern recognition: a review". IEEE Transactions on Pattern Analysis and Machine Intelligence. 22 (1): 4–37. doi:10.1109/34.824819.
 An introductory tutorial to classifiers (introducing the basic terms, with numeric example)
External links
 The International Association for Pattern Recognition
 List of Pattern Recognition web sites
 Journal of Pattern Recognition Research
 Pattern Recognition Info
 Pattern Recognition (Journal of the Pattern Recognition Society)
 International Journal of Pattern Recognition and Artificial Intelligence
 International Journal of Applied Pattern Recognition
 Open Pattern Recognition Project, intended to be an open source platform for sharing algorithms of pattern recognition
 Improved Fast Pattern Matching Improved Fast Pattern Matching