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Nonnegative Matrix Factorization on GPU
"... Abstract. Today, the need of large data collection processing increase. Such type of data can has very large dimension and hidden relationships. Analyzing this type of data leads to many errors and noise, therefore, dimension reduction techniques are applied. Many techniques of reduction were develo ..."
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developed, e.g. SVD, SDD, PCA, ICA and NMF. Nonnegative matrix factorization (NMF) has main advantage in processing of nonnegative values which are easily interpretable as images, but other applications can be found in different areas as well. Both, data analysis and dimension reduction methods, need a lot
Scaling IDS Construction Based on Nonnegative Matrix Factorization Using GPU computing
"... Abstract—Attacks on the computer infrastructures are becoming an increasingly serious problem. Whether it is banking, ecommerce businesses, health care, law enforcement, air transportation, or education, we are all becoming increasingly reliant upon the networked computers. The possibilities and op ..."
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Cited by 1 (0 self)
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to security, which provides important information for timely countermeasures. This paper presents some improvements to some of our previous approaches using a Nonnegative Matrix factorization approach. To improve the performance (detection accuracy) and computational speed (scaling) a GPU implementation
Algorithms for Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative 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 ..."
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Cited by 1230 (5 self)
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Nonnegative 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
Nonnegative matrix factorization with sparseness constraints
 Jour. of
, 2004
"... www.cs.helsinki.fi/patrik.hoyer ..."
Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 1766 (74 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null
Nonnegative matrix factorization for polyphonic music transcription
 in Proc. IEEE Workshop Applications of Signal Processing to Audio and Acoustics
, 2003
"... In this paper we present a methodology for analyzing polyphonic musical passages comprised by notes that exhibit a harmonically fixed spectral profile (such as piano notes). Taking advantage of this unique note structure we can model the audio content of the musical passage by a linear basis transfo ..."
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Cited by 240 (14 self)
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transform and use nonnegative matrix decomposition methods to estimate the spectral profile and the temporal information of every note. This approach results in a very simple and compact system that is not knowledge based, but rather learns notes by observation.
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Lambertian Reflectance and Linear Subspaces
, 2000
"... We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wi ..."
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Cited by 514 (20 self)
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the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. Finally, we show a simple way to enforce nonnegative
FAST VOLUME RENDERING USING A SHEARWARP FACTORIZATION OF THE VIEWING TRANSFORMATION
, 1995
"... Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that req ..."
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Cited by 541 (2 self)
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Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that require on the order of 100 seconds to render typical data sets on a workstation. Algorithms with optimizations that exploit coherence in the data have reduced rendering times to the range of ten seconds but are still not fast enough for interactive visualization applications. In this thesis we present a family of volume rendering algorithms that reduces rendering times to one second. First we present a scanlineorder volume rendering algorithm that exploits coherence in both the volume data and the image. We show that scanlineorder algorithms are fundamentally more efficient than commonlyused ray casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axisaligned boxes). The new scanlineorder algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective projections and
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 526 (72 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
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