1. Deterministic methods for solving recognition problems. Building decision rules. The method of building standards.

Those methods that have both deterministic and statistical interpretation will be considered twice in the relevant sections of the course. This concerns, in particular, the method of potential functions, the methods of the nearest neighbor and nearest neighbors and others.

To build decision rules, a training sample is needed. A training sample is a set of objects specified by the values ​​of attributes and which belong to a particular class is reliably known to the “teacher” and is communicated by the teacher to the “learning” system. According to the training set, the system builds decision rules. The quality of decision rules is assessed by a control (examination) sample, which includes objects specified by the values ​​of attributes and whose belonging to a particular image is known only to the teacher. By providing the learning system for test recognition objects of an examination sample, the teacher is able to assess the likelihood of recognition errors, that is, to assess the quality of learning. Certain requirements are imposed on the training and control samples. For example, it is important that the test sample objects are not included in the training sample (sometimes, however, this requirement is violated if the total sample size is small and it is either impossible to increase or extremely difficult).

Training and examination samples must adequately represent the general population (a hypothetical set of all possible objects of each image). For example, when training a medical diagnostic system in a training and control sample, patients of different age and gender groups with different anatomical and physiological features, associated diseases, etc. should be represented. In case of sociological research, this is called representativeness of the sample.

So, to build the decision rules, the system presents the objects included in the training sample.

For each class, a benchmark is constructed according to the training sample;

,

Where = ,

- the number of objects of this image in the training sample,

- feature number.

Essentially, the standard is the abstract object averaged over the training sample (Fig. 2). We call it abstract because it may not coincide not only with one object of the training sample, but also with one object of the general population.

Recognition is as follows. The object enters the system input , whose belonging to this or that image is unknown to the system. From this object, the distances to the standards of all images are measured, and The system refers to the image, the distance to the standard of which is minimal. The distance is measured in the metric that is entered to solve a specific recognition problem.

Fig. 2. Decision rule "Minimum distance
up to the standard of class ":