Information Mandala: Statistical Distance Matrix with Clustering
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.
Code (0)
등록된 구현이 없습니다.
Tasks
ClusteringObject RecognitionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Chronological Analysis of Rigvedic Mandalas using Social Networks
Establishing the chronology of the Vedas has interested scholars for the last two centuries. The oldest among them is Rig-Veda which has ten Mandalas, each composed separately. In this paper, we look at deciphering plaus…
Superclustering by finding statistically significant separable groups of optimal gaussian clusters
The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical se…
ClusteringClustering in Hilbert simplex geometry
Clustering categorical distributions in the finite-dimensional probability simplex is a fundamental task met in many applications dealing with normalized histograms. Traditionally, the differential-geometric structures o…
ClusteringMeasuring Spatial Clustering via Metropolis-Hastings Diffusion Distance
We propose a novel measure of the discrepancy between two probability distributions $f$ and $g$ on a graph - which we call the diffusion distance - that measures the rate of convergence of $f$ to $g$ under a graph-constr…
Multi-view Banded Spectral Clustering with Application to ICD9 Clustering
Despite recent development in methodology, community detection remains a challenging problem. Existing literature largely focuses on the standard setting where a network is learned using an observed adjacency matrix from…
ClusteringCommunity DetectionStochastic Block Model