Related papers: Stable Sparse Subspace Embedding for Dimensionalit…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Recently, SimCSE has shown the feasibility of contrastive learning in training sentence embeddings and illustrates its expressiveness in spanning an aligned and uniform embedding space. However, prior studies have shown that dense models…
Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with…
Sparse Subspace Clustering (SSC) is a popular unsupervised machine learning method for clustering data lying close to an unknown union of low-dimensional linear subspaces; a problem with numerous applications in pattern recognition and…
Fr\'echet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fr\'echet…
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…
We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or…
We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, called TS-SpGEMM, has important applications in multi-source breadth-first search,…
Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…
In compressed sensing (CS), sparse signals can be reconstructed from significantly fewer samples than required by the Nyquist-Shannon sampling theorem. While non-sparse signals can be sparsely represented in appropriate transformation…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…
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…
This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a tensor train (TT) representation with…
Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
This paper introduces the Reed Muller Sieve, a deterministic measurement matrix for compressed sensing. The columns of this matrix are obtained by exponentiating codewords in the quaternary second order Reed Muller code of length $N$. For…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
Modern state-space models (SSMs) often utilize transition matrices which enable efficient computation but pose restrictions on the model's expressivity, as measured in terms of the ability to emulate finite-state automata (FSA). While…
There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…