23 papers · ranked by Valyu relevance
Astha Saini, Petre Stoica, Prabhu Babu, Aakash Arora
| 1 | Introduction | 312 | | --- | --- | --- | | | 1.1 | MM Summary 313 | | | 1.2 | Need for MM4MM 314 | | | 1.3 | Organization 315 | | | 1.4 | Notation 316 | | 2 | | Max Formulation 318 | | | 2.1 | Conjugate Function 319 | | | 2.2 | Max Formulation for Certain Non-Convex Functions 320 | | | 2.3 | Illustrative Examples…
Jyothi Rikhab Chand, Prabhu Babu
—We consider the problem of localizing the source using range and range-difference measurements. Both the problems are non-convex and non-smooth and are challenging to solve. In this paper, we develop an iterative algorithm - Source Localization Via an Iterative technique (SOLVIT) to localize the source using all the…
Ali Hashemi, Chang Cai, Gitta Kutyniok, Klaus-Robert Müller + 2 more
Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of…
Junxiao Song, Prabhu Babu, Daniel P. Palomar
—In this paper, we consider an ℓ 0-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a discontinuous nonconcave objective function over a nonconvex constraint set, and is…
Bangyue Ren, Yansong Hao, Huaqing Wang, Liuyang Song + 2 more
'Hongfang Yuan'] Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the…
Jyothi Rikhab Chand, Prabhu Babu, Rajendar Bahl
Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a nonnegative matrix into a product of two nonnegative matrices which gives some meaningful…
Paul Magron, Cédric Févotte
This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an…
C. Eric, Hua Zhou, Kenneth Lange
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's…
Yuxue Chen, Shuisheng Zhou, Boris Ryabko
Possibilistic fuzzy c-means (PFCM) clustering is a kind of hybrid clustering method based on fuzzy c-means (FCM) and possibilistic c-means (PCM), which not only has the stability of FCM but also partly inherits the robustness of PCM. However, as an extension of FCM on the objective function, PFCM tends to find a…
Charles L. Byrne, Jong‐Soo Lee
Let Φ : X × Y → R+, where X and Y are arbitrary nonempty sets. The objective in alternating minimization (AM) is to find ˆx ∈ X and ˆy ∈ Y such that Φ(ˆx, yˆ) ≤ Φ(x, y) for all x ∈ X and y ∈ Y . For each k we minimize Φ(x, yk−1 ) to get x k−1 and then minimize Φ(x k−1 , y) to get y k . For each x ∈ X, let y(x) ∈ Y be…
Pascal Fernsel, Fabiana Zama, Elena Loli Piccolomini
Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
Zhao Kang, Chong Peng, Jie Cheng, Qiang Cheng
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems.…
Stéphane Chrétien, Christophe Guyeux, Bastien Conesa, Régis Delage-Mouroux + 3 more
'Régis Delage-Mouroux' 'Michèle Jouvenot' 'Philippe Huetz' 'Françoise Descôtes'] Background Non-Negative Matrix factorization has become an essential tool for feature extraction in a wide spectrum of applications. In the present work, our objective is to extend the applicability of the method to the case of missing…
Ping Yang, E. Adrian Henle, Xiaoli Fern, Cory M. Simon
Pesticides benefit agriculture by increasing crop yield, quality, and security. However, pesticides may inadvertently harm bees, which are agriculturally and ecologically vital as pollinators. The development of new pesticides---driven by pest resistance to and demands to reduce negative environmental impacts of…
Ludger Starke, Dirk Ostwald
Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation…
Anqi Wu, Samuel A. Nastase, Christopher A. Baldassano, Nicholas B. Turk-Browne + 3 more
A key problem in functional magnetic resonance imaging (fMRI) is to estimate spatial activity patterns from noisy high-dimensional signals. Spatial smoothing provides one approach to regularizing such estimates. However, standard smoothing methods ignore the fact that correlations in neural activity may fall off at…
Feng Liu, Jay Rosenberger, Jing Qin, Yifei Lou + 1 more
To infer brain source activation patterns under different cognitive tasks is an integral step to understand how our brain works. Traditional electroencephalogram (EEG) Source Imaging (ESI) methods usually do not distinguish task-related and spurious non-task-related sources that jointly generate EEG signals, which…
Jing Wu, Wenbo Li, Lijun Su, Huiru Wang + 2 more
In this paper, we present a modified nonmonotone line search algorithm that employs a variable parameter to control the degree of nonmonotonicity. This modification enhances both the probability of identifying the global minimum and the rate of convergence. Within the framework of alternating nonnegative least squares…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…
David M. Bradley, J. Andrew Bagnell
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation…
Yifeng Li, Alioune Ngom
Background High-throughput genomic and proteomic data have important applications in medicine including prevention, diagnosis, treatment, and prognosis of diseases, and molecular biology, for example pathway identification. Many of such applications can be formulated to classification and dimension reduction problems…
Deborah Weighill, Marouen Ben Guebila, Camila Lopes-Ramos, Kimberly Glass + 3 more
Gene regulatory network inference is instrumental to the discovery of genetic mechanisms driving diverse diseases, including cancer. Here, we present a theoretical framework for PANDA, an established method for gene regulatory network inference. PANDA is based on iterative message passing updates that resemble the…