Related papers: Perplexity-free Parametric t-SNE
Semiparametric statistics play a pivotal role in a wide range of domains, including but not limited to missing data, causal inference, and transfer learning, to name a few. In many settings, semiparametric theory leads to (nearly)…
Recommender systems inherently exhibit a low-rank structure in latent space. A key challenge is to define meaningful and measurable distances in the latent space to capture user-user, item-item, user-item relationships effectively. In this…
ParaDime is a framework for parametric dimensionality reduction (DR). In parametric DR, neural networks are trained to embed high-dimensional data items in a low-dimensional space while minimizing an objective function. ParaDime builds on…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMAP have demonstrated impressive visualization performance on many real world datasets. One tension that has always faced these methods is the trade-off between preservation of…
Unsupervised text embedding methods, such as Skip-gram and Paragraph Vector, have been attracting increasing attention due to their simplicity, scalability, and effectiveness. However, comparing to sophisticated deep learning architectures…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
Recent advancements in discrete image generation showed that scaling the VQ codebook size significantly improves reconstruction fidelity. However, training generative models with a large VQ codebook remains challenging, typically requiring…
Phase-Based Ranging (PBR) offers several advantages for estimating distances between wirelessly connected devices, including high accuracy over large distances and the removal of the need for antenna arrays at each transceiver. This study…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…
Localizing more sources than sensors with a sparse linear array (SLA) has long relied on minimizing a distance between two covariance matrices and recent algorithms often utilize semidefinite programming (SDP). Although deep neural network…
Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming…
In this paper, we propose a novel self-supervised representation learning by taking advantage of a neighborhood-relational encoding (NRE) among the training data. Conventional unsupervised learning methods only focused on training deep…
t-SNE and hierarchical clustering are popular methods of exploratory data analysis, particularly in biology. Building on recent advances in speeding up t-SNE and obtaining finer-grained structure, we combine the two to create tree-SNE, a…
Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and…