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Distance-based classifiers, such as k-nearest neighbors and support vector machines, continue to be a workhorse of machine learning, widely used in science and industry. In practice, to derive insights from these models, it is also…
There are many distance-based methods for classification and clustering, and for data with a high number of dimensions and a lower number of observations, processing distances is computationally advantageous compared to the raw data matrix.…
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If $f(\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then…
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…
This article focuses on the study of Word Embedding, a feature-learning technique in Natural Language Processing that maps words or phrases to low-dimensional vectors. Beginning with the linguistic theories concerning contextual…
Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…
Hierarchical clustering is a class of algorithms that seeks to build a hierarchy of clusters. It has been the dominant approach to constructing embedded classification schemes since it outputs dendrograms, which capture the hierarchical…
In-context learning can help Large Language Models (LLMs) to adapt new tasks without additional training. However, this performance heavily depends on the quality of the demonstrations, driving research into effective demonstration…
Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise…
Adaptations of features commonly applied in the field of visual computing, co-occurrence matrix (COM) and run-length matrix (RLM), are proposed for the similarity computation of strings in general (words, phrases, codes and texts). The…
Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…
The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…
Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…
Clustering is spotting pattern in a group of objects and resultantly grouping the similar objects together. Objects have attributes which are not always numerical, sometimes attributes have domain or categories to which they could belong…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Motivated by an application of eliciting users' preferences, we investigate the problem of learning hemimetrics, i.e., pairwise distances among a set of $n$ items that satisfy triangle inequalities and non-negativity constraints. In our…