Results 1  10
of
35
Stable recovery of sparse overcomplete representations in the presence of noise
 IEEE TRANS. INFORM. THEORY
, 2006
"... Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes t ..."
Abstract

Cited by 462 (20 self)
 Add to MetaCart
(Show Context)
Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further that the overcomplete system is incoherent, it is shown that the optimally sparse approximation to the noisy data differs from the optimally sparse decomposition of the ideal noiseless signal by at most a constant multiple of the noise level. As this optimalsparsity method requires heavy (combinatorial) computational effort, approximation algorithms are considered. It is shown that similar stability is also available using the basis and the matching pursuit algorithms. Furthermore, it is shown that these methods result in sparse approximation of the noisy data that contains only terms also appearing in the unique sparsest representation of the ideal noiseless sparse signal.
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
Abstract

Cited by 423 (37 self)
 Add to MetaCart
(Show Context)
A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several wellknown signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical
Survey of clustering data mining techniques
, 2002
"... Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in math ..."
Abstract

Cited by 400 (0 self)
 Add to MetaCart
(Show Context)
Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique
Formulae and Applications of Interconnect Estimation Considering Shield Insertion and Net Ordering
, 2001
"... It has been shown recently that simultaneous shield insertion and net ordering (called SINO/R as only random shields are used) provides an areaefficient solution to reduce the RLC noise. In this paper, we first develop simple formulae with errors less than 10% to estimate the number of shields in t ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
It has been shown recently that simultaneous shield insertion and net ordering (called SINO/R as only random shields are used) provides an areaefficient solution to reduce the RLC noise. In this paper, we first develop simple formulae with errors less than 10% to estimate the number of shields in the minarea SINO/R solution. In order to accommodate prerouted P/G wires that also serve as shields, we then formulate two new SINO problems: SINO/SPR and SINO/UPG, and propose effective and efficient twophase algorithms to solve them. Compared to the existing dense wiring fabric scheme, the resulting SINO/SPR and SINO/UPG schemes maintain the regularity of the P/G structure, have negligible penalty on noise and delay variation, and reduce the total routing area by up to 42% and 36%, respectively. Various estimation results developed in this paper can be readily used to guide global routing and highlevel design decisions.
Calibration for Simultaneity: (Re)Sampling Methods for Simultaneous Inference with Applications to Function Estimation and Functional Data
"... We survey and illustrate a Monte Carlo technique for carrying out simple simultaneous inference with arbitrarily many statistics. Special cases of the technique have appeared in the literature, but there exists widespread unawareness of the simplicity and broad applicability of this solution to simu ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We survey and illustrate a Monte Carlo technique for carrying out simple simultaneous inference with arbitrarily many statistics. Special cases of the technique have appeared in the literature, but there exists widespread unawareness of the simplicity and broad applicability of this solution to simultaneous inference. The technique, here called “calibration for simultaneity ” or CfS, consists of 1) limiting the search for coverage regions to a oneparameter family of nested regions, and 2) selecting from the family that region whose estimated coverage probability has the desired value. Natural oneparameter families are almost always available. CfS applies whenever inference is based on a single distribution, for example: 1) fixed distributions such as Gaussians when diagnosing distributional assumptions, 2) conditional null distributions in exact tests with Neyman structure, in particular permutation tests, 3) bootstrap distributions for bootstrap standard error bands, 4) Bayesian posterior distributions for highdimensional posterior probability regions, or 5) predictive distributions for multiple prediction intervals. CfS is particularly useful for estimation of any type of function, such as empirical QQ curves, empirical CDFs, density estimates, smooths, generally any type of fit, and functions estimated from functional data. A special case of CfS is equivalent to pvalue adjustment (Westfall and Young, 1993). Conversely, the notion of a pvalue can be extended to any simultaneous coverage problem that is solved with a oneparameter family of coverage regions.
Effective Data Conversion Algorithm for RealTime Vision Based Human Computer Interface
"... Abstract:Human computer interfaces (HCI) for assisting persons with disabilities may employ eye gazing as the primary computer input mechanism. These systems rely on the use of remote eyegaze tracking (EGT) devices to compute the direction of gaze and employ it to control the mouse cursor. Regrett ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract:Human computer interfaces (HCI) for assisting persons with disabilities may employ eye gazing as the primary computer input mechanism. These systems rely on the use of remote eyegaze tracking (EGT) devices to compute the direction of gaze and employ it to control the mouse cursor. Regrettably, the performance of these interfaces is traditionally affected by inaccuracies inherited from the eye tracking devices and ineffective EGT to mousepointer data conversion mechanisms. This study addresses this problem and proposes a new optimized data conversion mechanism. It analyzes in more details the correlation between the two data types resulting in a considerable increment in the accuracy of the system. This improved data conversion interface integrates the following procedures: (a) map the correlation between the EGT data and the mouse cursor position, (b) apply a curve fitting method that best suits the behavior of the data, (c) interpret the direction of gaze in order to determine the appropriate mouse cursor response, and (d) use effective means to monitor and evaluate the system performance. Keywords: Humancomputer interaction, eye gaze tracking, leastsquares line 1.
Estimation under multicollinearity application of restricted Liu and maximum entropy estimators to the Portland cement dataset,” MPRA Paper 1809
, 2004
"... ..."
(Show Context)
limb motion tracking
"... This article was published in an Elsevier journal. The attached copy is furnished to the author for noncommercial research and education use, including for instruction at the author’s institution, sharing with colleagues and providing to institution administration. Other uses, including reproductio ..."
Abstract
 Add to MetaCart
(Show Context)
This article was published in an Elsevier journal. The attached copy is furnished to the author for noncommercial research and education use, including for instruction at the author’s institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: