pattern recognition

the scientific field concerned with the development of principles and construction of systems used in determining the membership of a given object in one of several previously selected classes of objects. The objects in pattern recognition may be various phenomena, processes, situations, signals, or physical objects. Every object is described by a set of basic features (attributes, properties) X = (x₁ …, x_i …, x_n), where the ith coordinate of the vector X determines the values of the ith feature, and by an additional feature S that indicates the membership of the object in some class (pattern). A set of previously classified objects—that is, objects for which the features of X and S are known—is used to detect regular relationships between the values of these features and is therefore called the training sample. Those objects for which the feature S is unknown form the control sample. Individual objects in the learning and control samples are called realizations.

One of the basic tasks of pattern recognition is to select a rule, or decision function, D in accordance with which, depending on the value of the control realization X, the membership of the realization in one of the classes is established—that is, the “most plausible” values of the feature S are indicated for the given X. The selection of the decision function D must be made so as to minimize the cost of the recognition device, the device’s operating costs, and the losses owing to recognition errors. An example of a problem of this type of pattern recognition is the distinguishing of oil-bearing and water-bearing strata through the use of indirect geophysical data. On the basis of such features, fluid-saturated strata can be detected relatively easily. It is much more difficult to determine whether the strata contain oil or water. A rule must be found for the use of the information contained in the geophysical features in order to place each fluid-saturated stratum in one of the two classes—waterbearing or oil-bearing. In solving this problem, the geophysical data on developed strata are included in the training sample.

Success in solving the problem of pattern recognition depends largely on how well the features of X are selected. The initial set of features is often very large. An acceptable rule, however, must be based on the use of a moderate number of features that are of great importance for the distinguishing of one pattern from another. Thus, in problems of medical diagnostics it is important to determine what symptoms and syndromes should be used in formulating a diagnosis of a given disease. The selection of informative features is therefore an important part of the problem of pattern recognition.

The problem of pattern recognition is closely connected with the problem of preliminary classification, or taxonomy.

In the fundamental for pattern recognition task of constructing decision functions D, use is made of those regular relationships between the features of X and S that are observable in the training sample and of some additional a priori assumptions. Examples of such assumptions are the following hypotheses: the features of X for realizations of patterns are random samples of parent populations with a normal distribution, the realizations of one pattern are arranged compactly (in some sense), and the features in the set X are independent.

Pattern recognition makes considerable use of the ideas and results of many other fields, such as mathematics, cybernetics and psychology.

Automatic recognition systems found extensive application in the 1960’s because of the development of electronic technology, particularly electronic computers. Recognition systems are usually complexes of equipment designed to solve the problems described above. Pattern recognition techniques are used in the machine diagnosis of various diseases, in predicting the location of minerals in geology, in analyzing economic and social processes, and in such areas as psychology, criminalistics, linguistics, oceanography, chemistry, nuclear physics, space physics, and automated control systems. Their use is warranted practically everywhere that the classification of experimental data must be dealt with. (See alsoCYBERNETICS; CYBERNETICS, ENGINEERING; and AUTOMATIC LEARNING SYSTEM.)

Pattern recognition in mathematical statistics is the class of problems associated with determining the membership of a given observation in one of several parent populations (with unknown distributions) that are represented only by finite samples. A set of observations (a sample) from one of the represented parent populations may also serve as a given observation. Each observation is a number or vector. The indicated class of problems is often called discriminatory analysis or classification.

Suppose there are known n₁ observations from a parent population A₁, n₂ observations from a parent population A₂, …, and n_m observations from a parent population A_m, m ≥ 2. The sample z = (z₁, …, z_n) is also given. The problem of pattern recognition is to determine to which of the parent populations A_j(j = 1, 2,…, m) the sample z belongs. The assumption usually is made here that the distributions P_j (•) of the populations A_j belong to some family {P (θ, •)} of distributions dependent on the vector θ, so that P_j (•) = P(θ_j, •), where the θ_j are unknown.

Suppose L_ij is given, where L_ij is the losses the observer incurs on classifying the sample z with population (pattern) A_j when the sample actually belongs to A_i. The problem formulated above may then be considered and solved by means of the methods of the theory of statistical games. The natural strategy here is the set (θ₁,…, θ_m, j), where j indicates the number of the population in which z is placed. It is possible to seek optimal decision functions that in some sense minimize the observer’s losses.

The problems of pattern recognition are extremely difficult and as of 1978 had been investigated only for some special cases. With respect to the general problem, if certain additional assumptions are made, it is possible to indicate asymptotically optimal rules that give losses approaching the minimum when the numbers n_j increase without bound.

The problems stated above are one of the most natural mathematical models, or formalizations, for the problems of pattern recognition.

The biological aspect of pattern recognition is closely connected with the organization of the behavior of animals. Under natural conditions, animals generally perceive external objects simultaneously with different sense organs; the patterns of real objects therefore combine, for example, visual, tactile, and taste features. For convenience of investigation, the processes associated with the perception and recognition of optical, acoustical, and other properties of objects are usually separated. The term “pattern” is used more often in connection with visual and auditory perception. The recognition of visual patterns has been studied in the greatest detail.

The surrounding world visually perceived by animals and man is a three-dimensional space with three-dimensional objects of relatively constant shape and color. The objects generally are non-self-luminous and are contained in a transparent medium, such as air or water. Because of the mobility of animals and some external objects, to every object, even an unchanging one, there corresponds a number of different images of the object on the retina of the eye. These images are plane projections of objects on the surface of the retinal photosensitive receptors. An important function of the visual system is the reconstruction of the three-dimensional world on the basis of these plane images. This reconstruction is necessary for the organization of the active behavior of animals. The constancy of the perception by man and animal of the size, shape, and color of objects is a result of the operation of the mechanisms that perform the reconstruction. A no less important function of the visual system is the classification of objects according to the objects’ biological significance to the animal (what is usually meant by recognition). Depending on the species of the animal and the level of organization of its visual system, recognition occurs in different ways: animals differ both in their ability to perceive certain optical properties of objects—such as the visible region of the spectrum, color, and the polarization of light—and in the degree of complexity of their processing of visual information. Lower animals have specialized, detector nerve cells in the retina that single out biologically important features of objects directly from the retinal image; an example is the dark spot detector in the frog’s eye. In higher animals, great importance is had by the visual centers of the brain, where specialized nerve cells with extremely complex properties are also found. Not only innate mechanisms of pattern recognition but individual experience (learning) and one of its distinctive forms—imprinting—are of great importance in the operation of the visual system, as well as other receptor systems.

Despite the tremendous diversity of animals and the differences in the visual apparatus, the methods by which animals of different species process visual information have much in common. This is evidenced, in particular, by the common character of the means of visual camouflage and the means of attracting and repelling other animals widely used in the animal world. A number of the characteristics of perception and pattern recognition that have been best studied for the visual process are of general consequence. Thus, the problem of the stable perception (correctness of recognition) of auditory patterns under variable conditions—a problem solved by the auditory system—is analogous to the problem of the constant recognition of color. (See alsoPERCEPTION and .)