  In machine learning, observation features are measured in a metric space to
obtain their distance function for optimization. Given similar features that
are statistically sufficient as a population, a statistical distance between
two probability distributions can be calculated for more precise learning.
Provided the observed features are multi-valued, the statistical distance
function is still efficient. However, 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, called a statistical distance matrix. In experiments, the proposed
approach performs well in object recognition tasks and clearly and intuitively
represents the dissimilarities between cat and dog images in the CIFAR dataset,
even when directly calculated using the image pixels. By using the hierarchical
clustering of the statistical distance matrix, the image pixels can be
separated into several clusters that are geometrically arranged around a center
like a Mandala pattern. The statistical distance matrix with clustering, called
the Information Mandala, is beyond ordinary saliency maps and can help to
understand the basic principles of the convolution neural network.
