Related papers: CBMAP: Clustering-based manifold approximation and…

Subspace clustering aims to find groups of similar objects (clusters) that exist in lower dimensional subspaces from a high dimensional dataset. It has a wide range of applications, such as analysing high dimensional sensor data or DNA…

Dimension reduction and visualization of high-dimensional data have become very important research topics because of the rapid growth of large databases in data science. In this paper, we propose using a generalized sigmoid function to…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

Motor impairments, frequently caused by neurological incidents like strokes or traumatic brain injuries, present substantial obstacles in rehabilitation therapy. This research aims to elevate the field by optimizing motor imagery…

Recent studies increasingly adopt simulation-based machine learning (ML) models to analyze critical infrastructure system resilience. For realistic applications, these ML models consider the component-level characteristics that influence…

We study the topic of dimensionality reduction for $k$-means clustering. Dimensionality reduction encompasses the union of two approaches: \emph{feature selection} and \emph{feature extraction}. A feature selection based algorithm for…

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the…

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…

We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a…

Due to rapid advancements in technology, datasets are available from various domains. In order to carry out more relevant and appropriate analysis, it is often necessary to project the dataset into a higher or lower dimensional space based…

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…

Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…

Mixture models are a standard approach to dealing with heterogeneous data with non-i.i.d. structure. However, when the dimension $p$ is large relative to sample size $n$ and where either or both of means and covariances/graphical models may…

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…

Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…