Related papers: Preserving clusters and correlations: a dimensiona…
Dimensionality Reduction (DR) techniques are commonly used for the visual exploration and analysis of high-dimensional data due to their ability to project datasets of high-dimensional points onto the 2D plane. However, projecting datasets…
Correlation Clustering (CC) is a fundamental unsupervised learning primitive whose strongest LP-based approximation guarantees require $\Theta(n^3)$ triangle inequality constraints and are prohibitive at scale. We initiate the study of…
Rehearsal-based Continual Learning (CL) maintains a limited memory buffer to store replay samples for knowledge retention, making these approaches heavily reliant on the quality of the stored samples. Current Rehearsal-based CL methods…
A new method that accurately describes strongly correlated states and captures dynamical correlation is presented. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of…
Data stream clustering reveals patterns within continuously arriving, potentially unbounded data sequences. Numerous data stream algorithms have been proposed to cluster data streams. The existing data stream clustering algorithms still…
Next to the directed percolation (DP) universality class, parity conserving directed percolation (pcDP; also called parity conserving branching annihilating random walks, pcBARW) is the second-most important model with an absorbing state…
Large-scale sparse precision matrix estimation has attracted wide interest from the statistics community. The convex partial correlation selection method (CONCORD) developed by Khare et al. (2015) has recently been credited with some…
Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full…
We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…
Modern challenges arising in the fields of theoretical and experimental physics require new powerful tools for high-precision electronic structure modelling; one of the most perspective tools is the relativistic Fock space coupled cluster…
The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…
The current study proposes a dimension reduction method, stepwise support vector machine (SVM), to reduce the dimensions of large p small n datasets. The proposed method is compared with other dimension reduction methods, namely, the…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
In this work, we propose a new data visualization and clustering technique for discovering discriminative structures in high-dimensional data. This technique, referred to as cPCA++, utilizes the fact that the interesting features of a…
Dimensionality reduction (DR) techniques map high-dimensional data into lower-dimensional spaces. Yet, current DR techniques are not designed to explore semantic structure that is not directly available in the form of variables or class…
Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…
"Addition-by-subtraction" coupled cluster (CC) approaches provide a promising approach to treating the difficult strong correlation problem by simplifying the standard CC equations. In a separate vein, linearized CC methods have drawn…
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small…
The most essential concept in concurrent multiscale methods involving atomistic-continuum coupling is how to define the relation between atomistic and continuum regions. A well-known coupling method that has been frequently employed in…
High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…