Information Mandala: Statistical Distance Matrix with Its Clustering
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In machine learning, observation features are measured in a metric space to get their distance function for optimization. Given the similar features are many enough as a population in statistics, a statistical distance between two probability distributions can be calculated for more precise learning than before. Moreover, the statistical distance is still efficient enough, provided the observed features are multi-valued, but due to its scalar output it cannot be applied to represent detailed distances between feature elements. To resolve this problem, this paper extends the traditional statistical distance to a matrix form, referred as to statistical distance matrix, to achieve distance refinement. In experiments, the proposed statistical distance matrix performs so well in object recognition as to clearly and intuitively represent the differences between cat and dog images in the CIFAR dataset, even if it is directly calculated using the image pixels. By using the hierarchical clustering of the statistical distance matrix, the image pixels can be separated into several classes that are geometrically arranged around a center, like a Mandala pattern. The statistical distance matrix with its clustering called Information Mandala is beyond ordinary saliency map and helps to understand the basic principles of the convolution neural network.
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