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We propose a pair of completely data-driven algorithms for unsupervised classification and dimension reduction, and we empirically study their performance on a number of data sets, both simulated data in three-dimensions and images from the…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral…

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 first show that the commonly used dimensionality reduction (DR) methods such as t-SNE and LargeVis poorly capture the global structure of the data in the low dimensional embedding. We show this via a number of tests for the DR methods…

Stochastic neighbor embedding (SNE) methods $t$-SNE, UMAP are two most popular dimensionality reduction methods for data visualization. Contrastive learning, especially self-supervised contrastive learning (SSCL), has showed great success…

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…

Dimensionality reduction techniques are essential for visualizing and analyzing high-dimensional biological sequencing data. t-distributed Stochastic Neighbor Embedding (t-SNE) is widely used for this purpose, traditionally employing the…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

t-SNE has gained popularity as a dimension reduction technique, especially for visualizing data. It is well-known that all dimension reduction techniques may lose important features of the data. We provide a mathematical framework for…

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,…

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication…

This work is concerned with the continuum limit of a graph-based data visualization technique called the t-Distributed Stochastic Neighbor Embedding (t-SNE), which is widely used for visualizing data in a variety of applications, but is…

Neighbor Embedding (NE) aims to preserve pairwise similarities between data items and has been shown to yield an effective principle for data visualization. However, even the best existing NE methods such as Stochastic Neighbor Embedding…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

Modern methods for data visualization via dimensionality reduction, such as t-SNE, usually have performance issues that prohibit their application to large amounts of high-dimensional data. In this work, we propose NCVis -- a…

Applying dimensionality reduction (DR) to large, high-dimensional data sets can be challenging when distinguishing the underlying high-dimensional data clusters in a 2D projection for exploratory analysis. We address this problem by first…

Visualizing high-dimensional data is an essential task in Data Science and Machine Learning. The Centroid-Encoder (CE) method is similar to the autoencoder but incorporates label information to keep objects of a class close together in the…

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…

Generating interpretable visualizations from complex data is a common problem in many applications. Two key ingredients for tackling this issue are clustering and representation learning. However, current methods do not yet successfully…