Related papers: On the continuum limit of t-SNE for data visualiza…

The paper presents an O(N log N)-implementation of t-SNE -- an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots and that normally runs in O(N^2). The new implementation uses…

Data features and class probabilities are two main perspectives when, e.g., evaluating model results and identifying problematic items. Class probabilities represent the likelihood that each instance belongs to a particular class, which can…

Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high…

To what extent is it possible to visualize high-dimensional data in two- or three-dimensional plots? We reframe this question in terms of embedding $n$-vertex graphs (representing the neighborhood structure of the input points) into metric…

In this work, the use of t-SNE is proposed to embed 3D point clouds of plants into 2D space for plant characterization. It is demonstrated that t-SNE operates as a practical tool to flatten and visualize a complete 3D plant model in 2D…

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…

Contrastive learning, especially self-supervised contrastive learning (SSCL), has achieved great success in extracting powerful features from unlabeled data. In this work, we contribute to the theoretical understanding of SSCL and uncover…

High-dimensional data visualization is crucial in the big data era and these techniques such as t-SNE and UMAP have been widely used in science and engineering. Big data, however, is often distributed across multiple data centers and…

Data visualisation is a key tool in data mining for understanding big datasets. Many visualisation methods have been proposed, including the well-regarded state-of-the-art method t-Distributed Stochastic Neighbour Embedding. However, the…

Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

Graph representations have increasingly grown in popularity during the last years. Existing representation learning approaches explicitly encode network structure. Despite their good performance in downstream processes (e.g., node…

Neighbor embedding methods $t$-SNE and UMAP are the de facto standard for visualizing high-dimensional datasets. Motivated from entirely different viewpoints, their loss functions appear to be unrelated. In practice, they yield strongly…

Virtual Network Embedding (VNE) is a fundamental resource allocation challenge that is associated with hard and multifaceted constraints in network function virtualization (NFV). Existing works for VNE struggle to handle such complex…

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…

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

Due to the sequential sample arrival, changing experiment conditions, and evolution of knowledge, the demand to continually visualize evolving structures of sequential and diverse single-cell RNA-sequencing (scRNA-seq) data becomes…

In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of…

Bobkov, Houdr\'e, and the last author [2000] introduced a Poincar\'e-type functional parameter, $\lambda_\infty$, of a graph and related it to connectivity of the graph via Cheeger-type inequalities. A work by the second author,…

Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…