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Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear…
Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The…
The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block…
Dimensionality reduction (DR) techniques have been consistently supporting high-dimensional data analysis in various applications. Besides the patterns uncovered by these techniques, the interpretation of DR results based on each feature's…
Robust state estimation in coupled dynamical systems depends critically not only on sensor quality but on the structural alignment between observation channels and the system's intrinsic dynamics. This paper develops a rigorous framework…
Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is…
We introduce the QuadratiK package that incorporates innovative data analysis methodologies. The presented software, implemented in both R and Python, offers a comprehensive set of goodness-of-fit tests and clustering techniques using…
Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Recent geospatial machine learning studies have shown that the results of model evaluation via cross-validation (CV) are strongly affected by the dissimilarity between the sample data and the prediction locations. In this paper, we propose…
Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…
Private data analysis faces a significant challenge known as the curse of dimensionality, leading to increased costs. However, many datasets possess an inherent low-dimensional structure. For instance, during optimization via gradient…
Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a…
Clustering and visualizing high-dimensional (HD) data are important tasks in a variety of fields. For example, in bioinformatics, they are crucial for analyses of single-cell data such as mass cytometry (CyTOF) data. Some of the most…
Image registration is an important tool for medical image analysis and is used to bring images into the same reference frame by warping the coordinate field of one image, such that some similarity measure is minimized. We study similarity…
Geographic experiments are a widely-used methodology for measuring incremental return on ad spend (iROAS) at scale, yet their design presents significant challenges. The unit count is small, heterogeneity is large, and the optimal Supergeo…
Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem…
In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given…
3D object detection is an important capability needed in various practical applications such as driver assistance systems. Monocular 3D detection, as a representative general setting among image-based approaches, provides a more economical…
We have developed a multiscale structure identification algorithm for the detection of overdensities in galaxy data that identifies structures having radii within a user-defined range. Our "multiscale probability mapping" technique combines…