PANN: A New Artificial Intelligence Technology. Tutorial. Boris Zlotin
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Название: PANN: A New Artificial Intelligence Technology. Tutorial
Автор: Boris Zlotin
Издательство: Издательские решения
isbn: 9785006423817
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• In each column of the matrix, one unit corresponds to the value of this figure, and all other values in this column are equal to 0.
• The sum of all units in the array matrix is equal to the length N of the array; for example, for an array of 20 digits, it is 20.
• The total number of zeros and ones in the matrix of each array is equal to the product of the length N of this array and the value of the base of the number system used.
Example: BCF notation of an array of 20 decimal digits [1, 9, 3, 6, 4, 5, 4, 9, 8, 7, 7, 1, 0, 7, 8, 0, 9, 8, 0,2].
Fig. 6. BCF image as a sparse binary matrix
A feature of the PANN network is that the image training of neurons typical of neural networks can be replaced by reformatting files that carry numerical dependencies to the BCF format or simply loading files in this format to the network.
Type X arrays in BCF format are denoted as matrices |X|.
2.4.2. Comparing Numeric Arrays
Comparing objects or determining similarities and differences
Determining the similarity of particular objects by comparing them plays an enormous role in thinking, making it possible to identify analogies and differences between different objects – beings, objects, processes, ideas, etc. In various branches of science, primarily in the Theory of Similarity, dimensionless similarity coefficients or similarity criteria (Similarity Coefficient or CoS) are used, sometimes called the «measure of similarity,» the «measure of association,» and so on.
Comparison functions in PANN are implemented through mathematical operations on matrices of numeric arrays. Let’s consider the most straightforward comparison algorithm, which uses the vector product of image neuron matrices.
Two arrays are given for comparison in the form of matrices |X1| and |X2|.
|X1| × |X2|T is the vector product of the matrix |X1| on a transposed matrix |X2|. Moreover, the value of this product is proportional to the number of units in |X1| and |X2|.
|X1| × |X2|T = N only if |X1| = |X2|;
|X1| × |X2|T <N if |X1| ≠ |X2|;
|X1| × |X2|T = 0 if none of the pixels of these matrices match.
Consider the relationship:
Here, the CoS (Similarity Coefficient) between the numerical vectors X1 and X2 determines the degree of closeness of these vectors and the images described by these vectors.
Examples:
Fig. 7. Multiplying matrices to compare numerical arrays
Fig. 8. Comparison of decimal numerical arrays |A| and |B|
Classical neural networks only determine which class a recognizable object is most similar to. At the same time, they cannot specify how similar it is. Because of this, recognition is sometimes unstable – there are well-known examples where a change in a pixel in an image was enough to change its recognition. Thus, recognition in classical networks is highly dependent on random noise.
In PANN, the situation is different – the similarity coefficient value very clearly shows how significant the difference between the images is. A similarity difference of one hundredth in the format of 32 × 32 pixels corresponds to a change of about 10 pixels. And this is already enough to distinguish the images from each other confidently. The one-tenth difference indicates a profound difference and high recognition stability – low dependence of recognition on noise.
In contrast to classical neural networks, PANN networks allow you to improve the quality of recognition dramatically by:
• Statistical processing of recognition by classes and by images.
• Combining class-based recognition and image-based recognition. Moreover, combined recognition by classes and images allows us to solve one of the most unpleasant problems that limit the use of neural networks in medicine and many other applications – the problem of transparency and explainability of the network results. We will discuss this in l in the «4.6. Recognition on the PANN Network» section.
2.4.3. Assessment of the validity and accuracy of recognition
The validity and accuracy of image recognition by neural networks are essential for their use.
The accuracy and reliability of recognition of a classical neural network are determined by testing several dozens, hundreds, or thousands of images and counting the number of correct and incorrect recognitions. This test is very controversial. Due to the opacity of classical networks, recognition is highly dependent on random training features:
• Sometimes, training outcomes are poorly reproduced; the same network trained on the same images will recognize better in some cases than worse in others.
• There are no ways to assess each image’s accuracy and recognition reliability adequately.
• Impact of test image selection. Sometimes, they are selected specifically to ensure the desired result.
Recognition by PANN networks is evaluated by the numerical similarity coefficient of the image under consideration:
1. With any set of individual images loaded to the network.
2. With all classes that this network is trained in.
At the same time, both classes and individual images are ranked according to the degree of similarity, which allows for an accurate assessment of the magnitude of the differences between all the compared classes and, thereby, assessment of the accuracy and reliability of recognition.
Of course, formally correct recognition (from the point of view of a machine) is possible, but it is not satisfactory. People often recognize others not by their main features but by secondary ones. For example, we can evaluate similarity not by facial features but depending on clothes. It happens that when recognizing human faces, the features of the lighting are more significant than the facial features.
Problems of this kind can be solved in PANN in several ways, in particular:
1. Equalization of illumination by known graphical or mathematical means.
2. СКАЧАТЬ