Related papers: Neighbor Embedding for High-Dimensional Sparse Poi…
The t-Distributed Stochastic Neighbor Embedding (t-SNE) has emerged as a popular dimensionality reduction technique for visualizing high-dimensional data. It computes pairwise similarities between data points by default using an RBF kernel…
Unsupervised machine learning has recently gained much attention in the field of molecular dynamics (MD). Particularly, dimensionality reduction techniques have been regularly employed to analyze large volumes of high-dimensional MD data to…
Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a…
T-distributed stochastic neighbor embedding (t-SNE) is a well-known algorithm for visualizing high-dimensional data by finding low-dimensional representations. In this paper, we study the convergence of t-SNE with generalized kernels and…
Sparse embeddings of data form an attractive class due to their inherent interpretability: Every dimension is tied to a term in some vocabulary, making it easy to visually decipher the latent space. Sparsity, however, poses unique…
Dense embedding models are commonly deployed in commercial search engines, wherein all the document vectors are pre-computed, and near-neighbor search (NNS) is performed with the query vector to find relevant documents. However, the…
Spiking neural networks offer a promising path toward energy-efficient, brain-like associative memory. This paper introduces Word2Spike, a novel rate coding mechanism that combines continuous word embeddings and neuromorphic architectures.…
In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data, with sparsity exhibited by an over-abundance of zeros and small non-zero counts. Existing approaches for analyzing multivariate…
Network embedding has numerous practical applications and has received extensive attention in graph learning, which aims at mapping vertices into a low-dimensional and continuous dense vector space by preserving the underlying structural…
Recent advances in the field of network embedding have shown that low-dimensional network representation is playing a critical role in network analysis. Most existing network embedding methods encode the local proximity of a node, such as…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the…
With the development of information technology, we have witnessed an age of data explosion which produces a large variety of data filled with redundant information. Because dimension reduction is an essential tool which embeds…
Scientific datasets often have hierarchical structure: for example, in surveys, individual participants (samples) might be grouped at a higher level (units) such as their geographical region. In these settings, the interest is often in…
Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly…
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…
Widely used pipelines for analyzing high-dimensional data utilize two-dimensional visualizations. These are created, for instance, via t-distributed stochastic neighbor embedding (t-SNE). A crucial element of the t-SNE embedding procedure…
High-dimensional inference methods often rely on coefficient sparsity, an assumption that can be restrictive when signals are dense but individually weak. In such settings, valid inference may still be possible if the covariates exhibit…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula…