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Algorithms for Non-negative Matrix Factorization

by Daniel D. Lee, H. Sebastian Seung - In NIPS , 2001
"... Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
Abstract - Cited by 1230 (5 self) - Add to MetaCart
. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.

Learning Long-Term Dependencies with Gradient Descent is Difficult

by Yoshua Bengio, Patrice Simard, Paolo Frasconi - TO APPEAR IN THE SPECIAL ISSUE ON RECURRENT NETWORKS OF THE IEEE TRANSACTIONS ON NEURAL NETWORKS
"... Recurrent neural networks can be used to map input sequences to output sequences, such as for recognition, production or prediction problems. However, practical difficulties have been reported in training recurrent neural networks to perform tasks in which the temporal contingencies present in th ..."
Abstract - Cited by 374 (35 self) - Add to MetaCart
in the input/output sequences span long intervals. We showwhy gradient based learning algorithms face an increasingly difficult problem as the duration of the dependencies to be captured increases. These results expose a trade-off between efficient learning by gradient descent and latching on information

Greedy Function Approximation: A Gradient Boosting Machine

by Jerome H. Friedman - Annals of Statistics , 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
Abstract - Cited by 951 (12 self) - Add to MetaCart
Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed

Optimization Flow Control, I: Basic Algorithm and Convergence

by Steven H. Low, David E. Lapsley - IEEE/ACM TRANSACTIONS ON NETWORKING , 1999
"... We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In thi ..."
Abstract - Cited by 690 (64 self) - Add to MetaCart
We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm

Global Optimization with Polynomials and the Problem of Moments

by Jean B. Lasserre - SIAM Journal on Optimization , 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear mat ..."
Abstract - Cited by 569 (47 self) - Add to MetaCart
We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear

Mean shift, mode seeking, and clustering

by Yizong Cheng - IEEE Transactions on Pattern Analysis and Machine Intelligence , 1995
"... Abstract-Mean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeki ..."
Abstract - Cited by 620 (0 self) - Add to MetaCart
in clustering and Hough transform are demon-strated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. Index Terms-Mean shift, gradient descent, global optimiza-tion, Hough transform, cluster analysis, k-means clustering. I.

Exponentiated Gradient Versus Gradient Descent for Linear Predictors

by Jyrki Kivinen, Manfred K. Warmuth - Information and Computation , 1995
"... this paper, we concentrate on linear predictors . To any vector u 2 R ..."
Abstract - Cited by 325 (14 self) - Add to MetaCart
this paper, we concentrate on linear predictors . To any vector u 2 R

Gradient flows in metric spaces and in the space of probability measures

by Luigi Ambrosio, Nicola Gigli, et al. - LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG , 2005
"... ..."
Abstract - Cited by 457 (46 self) - Add to MetaCart
Abstract not found

A fast iterative shrinkage-thresholding algorithm with application to . . .

by Amir Beck, Marc Teboulle , 2009
"... We consider the class of Iterative Shrinkage-Thresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast Iterat ..."
Abstract - Cited by 1055 (8 self) - Add to MetaCart
Iterative Shrinkage-Thresholding Algorithm (FISTA) which preserves the computational simplicity of ISTA, but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Initial promising numerical results for wavelet-based image deblurring demonstrate

Understanding Normal and Impaired Word Reading: Computational Principles in Quasi-Regular Domains

by David C. Plaut , James L. McClelland, Mark S. Seidenberg, Karalyn Patterson - PSYCHOLOGICAL REVIEW , 1996
"... We develop a connectionist approach to processing in quasi-regular domains, as exemplified by English word reading. A consideration of the shortcomings of a previous implementation (Seidenberg & McClelland, 1989, Psych. Rev.) in reading nonwords leads to the development of orthographic and phono ..."
Abstract - Cited by 583 (94 self) - Add to MetaCart
We develop a connectionist approach to processing in quasi-regular domains, as exemplified by English word reading. A consideration of the shortcomings of a previous implementation (Seidenberg & McClelland, 1989, Psych. Rev.) in reading nonwords leads to the development of orthographic and phonological representations that capture better the relevant structure among the written and spoken forms of words. In a number of simulation experiments, networks using the new representations learn to read both regular and exception words, including low-frequency exception words, and yet are still able to read pronounceable nonwords as well as skilled readers. A mathematical analysis of the effects of word frequency and spelling-sound consistency in a related but simpler system serves to clarify the close relationship of these factors in influencing naming latencies. These insights are verified in subsequent simulations, including an attractor network that reproduces the naming latency data directly in its time to settle on a response. Further analyses of the network's ability to reproduce data on impaired reading in surface dyslexia support a view of the reading system that incorporates a graded division-of-labor between semantic and phonological processes. Such a view is consistent with the more general Seidenberg and McClelland framework and has some similarities with---but also important differences from---the standard dual-route account.
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