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We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…

In machine learning, the performance of a classifier depends on both the classifier model and the dataset. For a specific neural network classifier, the training process varies with the training set used; some training data make training…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…

In this paper, we present novel variations of an earlier approach called homogeneous clustering algorithm for reducing dataset size. The intuition behind the approaches proposed in this paper is to partition the dataset into homogeneous…

A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance…

Motivated by a $2$-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are…

Accurate pipe roughness estimation in large-scale water distribution networks is often hindered by the high cost of traditional field methods. This study investigates whether network partitioning, by utilizing hydraulic and graph-derived…

Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…

The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple…

Gaussian process (GP) models are widely used to analyze spatially referenced data and to predict values at locations without observations. In contrast to many algorithmic procedures, GP models are based on a statistical framework, which…

Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the…

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

VC-dimension and $\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon$-net theorem, a fundamental result in Discrete Geometry,…

Visual Place Recognition (VPR) aims to match query images against a database using visual cues. State-of-the-art methods aggregate features from deep backbones to form global descriptors. Optimal transport-based aggregation methods…

Real-space mutual information (RSMI) was shown to be an important quantity, formally and from a numerical standpoint, in finding coarse-grained descriptions of physical systems. It very generally quantifies spatial correlations, and can…

Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuroscience. While early algorithms leveraged…

Stereo matching estimates the disparity between a rectified image pair, which is of great importance to depth sensing, autonomous driving, and other related tasks. Previous works built cost volumes with cross-correlation or concatenation of…