Information Mandala: Statistical Distance Matrix With Clustering

• Published in: IEEE access Vol. 9; pp. 56563 - 56577
• Main Author: Lu, Xin
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.01.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cluster analysis; Clustering; Clustering algorithms; Extraterrestrial measurements; hierarchical clustering; Jacobian matrices; Machine learning; Mandala; Mathematical analysis; Measurement; Metric space; Object recognition; Optimization; Pixels; Random variables; Statistical analysis; Statistical distance matrix; Support vector machines
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2021.3072237

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. 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 is called the Information Mandala.