Related papers: Constant rank factorizations of smooth maps

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…

Each year, numerous segmentation and classification algorithms are invented or reused to solve problems where machine vision is needed. Generally, the efficiency of these algorithms is compared against the results given by one or many human…

Automatic classification of sound commands is becoming increasingly important, especially for mobile and embedded devices. Many of these devices contain both cameras and microphones, and companies that develop them would like to use the…

Here, we propose a new reconstruction method of smooth time-series signals. A key concept of this study is not considering the model in signal space, but in delay-embedded space. In other words, we indirectly represent a time-series signal…

In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…

Spectral envelope is one of the most important features that characterize the timbre of an instrument sound. However, it is difficult to use spectral information in the framework of conventional spectrogram decomposition methods. We…

In machine learning, classifiers are typically susceptible to noise in the training data. In this work, we aim at reducing intra-class noise with the help of graph filtering to improve the classification performance. Considered graphs are…

Trajectory analysis is not only about obtaining movement data, but it is also of paramount importance in understanding the pattern in which an object moves through space and time, as well as in predicting its next move. Due to the…

We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…

The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…

When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decompositions or…

Chord recognition systems depend on robust feature extraction pipelines. While these pipelines are traditionally hand-crafted, recent advances in end-to-end machine learning have begun to inspire researchers to explore data-driven methods…

Target localization is a critical task for mobile sensors and has many applications. However, generating informative trajectories for these sensors is a challenging research problem. A common method uses information maps that estimate the…

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

This article presents a Non-negative Tensor Factorization based method for sound source separation from Ambisonic microphone signals. The proposed method enables the use of prior knowledge about the Directions-of-Arrival (DOAs) of the…