Related papers: Sparse Circular Coordinates via Principal $\mathbb…

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Calculation of near-neighbor interactions among high dimensional, irregularly distributed data points is a fundamental task to many graph-based or kernel-based machine learning algorithms and applications. Such calculations, involving…

We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…

This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…

Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…

We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…

Motivated by applications to the theory of rank-metric codes, we study the problem of estimating the number of common complements of a family of subspaces over a finite field in terms of the cardinality of the family and its intersection…

We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In…

A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…

In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…

In this paper we describe the structure of the space of parabolic reductions, and their compactifications, of principal $G$-bundles over a smooth projective curve over an algebraically closed field of arbitrary characteristic. We first…

High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of…

In this paper we consider the problem of clustering collections of very short texts using subspace clustering. This problem arises in many applications such as product categorisation, fraud detection, and sentiment analysis. The main…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to…

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…

Combining simple elements from the literature, we define a linear model that is geared toward sparse data, in particular implicit feedback data for recommender systems. We show that its training objective has a closed-form solution, and…