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MPTK: Matching pursuit made tractable
 in Proc. Int. Conf. on Acoustic Speech and Signal Processing
, 2006
"... Matching Pursuit (MP) aims at finding sparse decompositions of signals over redundant bases of elementary waveforms. Traditionally, MP has been considered too slow an algorithm to be applied to reallife problems with highdimensional signals. Indeed, in terms of floating points operations, its typi ..."
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Cited by 57 (6 self)
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Matching Pursuit (MP) aims at finding sparse decompositions of signals over redundant bases of elementary waveforms. Traditionally, MP has been considered too slow an algorithm to be applied to reallife problems with highdimensional signals. Indeed, in terms of floating points operations, its typical numerical implementations have a complexity of ¢¤£¦¥¨§� © and are associated with impractical runtimes. In this paper, we propose a new architecture which exploits the structure shared by many redundant MP dictionaries, and thus decreases its complexity to ¢¤£¦¥�������¥¨ ©. This architecture is implemented in a new software toolkit, called MPTK (the Matching Pursuit Toolkit), which is able to reach, e.g., ������� � real time for a typical MP analysis scenario applied to a 1 hour long audio track. This substantial acceleration makes it possible, from now on, to explore and apply MP in the framework of reallife, highdimensional data processing problems. 1.
Kernel Matching Pursuit for Large Datasets Abstract
"... Kernel Matching Pursuit is a greedy algorithm for building an approximation of a discriminant function as a linear combination of some basis functions selected from a kernel–induced dictionary. Here we propose a modification of the Kernel Matching Pursuit algorithm that aims at making the method pra ..."
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Kernel Matching Pursuit is a greedy algorithm for building an approximation of a discriminant function as a linear combination of some basis functions selected from a kernel–induced dictionary. Here we propose a modification of the Kernel Matching Pursuit algorithm that aims at making the method practical for large datasets. Starting from an approximating algorithm, the Weak Greedy Algorithm, we introduce a stochastic method for reducing the search space at each iteration. Then we study the implications of using an approximate algorithm and we show how one can control the trade–off between the accuracy and the need for resources. Finally we present some experiments performed on a large dataset that support our approach and illustrate its applicability. Key words: kernel matching pursuit, greedy algorithm, sparse classifier 1
Kernel matching pursuit for large datasets
, 2004
"... www.elsevier.com/locate/patcog ..."
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Harmonic Decomposition of Audio Signals with Matching
, 2001
"... We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely the Fast Har ..."
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We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely the Fast Harmonic Matching Pursuit, to approximate Ndimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in di#cult situations, e.g., very di#erent note durations, lots of reverberation, and overlapping notes.
1 Harmonic Decomposition of Audio Signals with Matching Pursuit
"... Abstract—We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the “standard ” matching pursuit, we define a new pursuit along with a fast algorithm, namely the Fast Har ..."
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Abstract—We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the “standard ” matching pursuit, we define a new pursuit along with a fast algorithm, namely the Fast Harmonic Matching Pursuit, to approximate Ndimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes.