a set of intersecting classes, as shown below.
4. Create a «recognition committee» – a logical expert system that concludes based on the sum of recognitions for different classes and images. Thus, it reproduces what a person does by looking closely at the object.
2.4.4. Indexing Number Sequences in BCF
Indexing for quick retrieval of information.
Today, search indexing is widely used in computer science. Index files make it easier to find information and are ten times smaller than the original files. However, indexing is more difficult for different types of files (for example, graphics), and search does not always work adequately. PANN allows for a more organized and standardized approach to indexing and searching.
Using Progress Binary Comparison Format (BCF), you can build standard and universal search indices, i.e., identifiers for any numerical sequence as linear convolutions of a digital array. These indices are a sequence of matrix sums with matching row and column numbers obtained by vector multiplying a given digital array by its transposition. And they can be much smaller in volume than with conventional indexing.
At the same time, the index search process takes place in parallel, which ensures that it is accelerated many times. For example, an image is described as a matrix |X| with a number of pixels n = 1024 and a number of weight levels k = 10.
Let us define the vector product of the matrix |X| on its transposition |X|T as index I. I = |X| × |X|T = |Σ| = Σ00, Σ11, Σ22, Σ33, Σ44, … Σ99:
Fig. 9. Formation of search images
The length of the resulting index is equal to the number of weight levels and does not depend on the number of pixels in the images. Thus, if you set the standard number of weights to 10 (which is convenient because it corresponds to the accepted decimal system), these indices will be standard for all libraries, allowing them to be used universally.
Each image in the recognition libraries must be provided with an index. The recognition of each new image should begin with forming its index, allowing for quick recognition against the prepared libraries.
For example, suppose we use a decimal system (10 weight levels from 0 to 9); even if we limit ourselves to only the first significant digit of each sum, the index will be a combination of 10 single digits; the probability of random coincidences of indices will not exceed 10—10 (1/10 billion).
2.4.5. Similarity Patterns and Other Ways of Comparison and Indexing in BCF
Identifying patterns to understand and manage events is one of the most essential applications of neural networks.
Two images can be similar or appear similar to us for many reasons. Most often, similarity is determined by the common origin or manufacture of different objects or by the fact that different objects change and develop according to some general patterns, such as the laws of nature. Patterns in painting or music may be laws of composition, and the construction of machines may be formulas of material resistance science, customs, legal laws in society, etc.
An analogue of an object is another object with a high degree of similarity to this object. Analogy (similarity) can be general or particular, for a specific parameter, static or dynamic, complete or partial, etc. Any object can have a significant number of different analogues.
We described the recognition of images and the formation of search indices using similarity coefficients obtained through the vector product of image matrices. But that’s not the only option available with PANN. We have also tested other features, in particular, recognition through:
1. Matrix products of the input and comparison arrays on the array representing the «comparison standard» [Xst] and CoS calculations through the difference of the resulting matrix sums.
2. Characteristic sums of two arrays and calculation of CoS through the difference in the power spectra of the input and compared arrays.
3. Fourier transformation of the amplitude-frequency spectra of the input with compared arrays, and calculation of CoS through the difference or ratio of the BCF format harmonics lines of the same name.
Different types of recognition can be used together to improve the accuracy and reliability of the conclusion.
2.5. COMPARISON OF LIBRARIES AS A BASIS FOR RECOGNITION
Recognition on PANN networks is similar to recognition in the living brain.
Human memory is a vast library containing many objects and information related to these objects. At the same time, many objects are directly or indirectly connected by associative connections. When we see an object, we compare it with images in our memory and thus recognize it, for example, as a dog, a house, or a car. When we recognize an object and recall its closest analogues, we can transfer information from analogues to this object. In this way, we gain additional knowledge about the object, realize the possibilities of using this object or protecting ourselves from it, and so on.
PANN networks work similarly. Comparison libraries are formed in the computer’s memory, and recognition operates by comparing the received information with the information in these libraries according to the degree of similarity determined by similarity coefficients.
PANN comparison libraries consist of «memory units» whereby:
1. Each «memory unit» is a numerical sequence that can be written in graphical or text formats or a BCF format explicitly designed for PANN.
2. Each «memory unit» can be provided with its indices (public and private, in different details) so that the PANN network can quickly search libraries for information.
3. Each «memory unit» has a complex structure and contains data on different parameters and properties of the object. For example, when one of us says «airplane,» many airplanes come to mind, seen in real life or pictures, as well as knowledge about their design and application and the problems we have solved for Boeing and other companies.
4. Each «memory unit» has associative, programmatic, hypertextual, etc., connections with many other «memory units.» For example, I associate an airplane with a rubber-engine model that I built as a child, with the time I almost got into an air accident, with the terrorist attacks of September 11, 2001, etc.
5. Also, the «memory unit» can store crucial additional information, including information leading to understanding the process, emotional attitude, assessment of its usefulness, harmfulness, risks, etc.
Fig. 10. Associative memory unit
The memory library provides the identification of a particular object and, on its basis, the identification of close analogues or antagonist objects and the possibility of transferring information related to the found analogues to the identified object.
Each newly identified «memory unit» can be included in the comparison libraries, allowing the PANN to be continuously
