Multivariate statistics | Signal processing
Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary . The basic idea is to approximately represent a signal from Hilbert space as a weighted sum of finitely many functions (called atoms) taken from . An approximation with atoms has the form where is the th column of the matrix and is the scalar weighting factor (amplitude) for the atom . Normally, not every atom in will be used in this sum. Instead, matching pursuit chooses the atoms one at a time in order to maximally (greedily) reduce the approximation error. This is achieved by finding the atom that has the highest inner product with the signal (assuming the atoms are normalized), subtracting from the signal an approximation that uses only that one atom, and repeating the process until the signal is satisfactorily decomposed, i.e., the norm of the residual is small,where the residual after calculating and is denoted by . If converges quickly to zero, then only a few atoms are needed to get a good approximation to . Such sparse representations are desirable for signal coding and compression. More precisely, the sparsity problem that matching pursuit is intended to approximately solve is where is the pseudo-norm (i.e. the number of nonzero elements of ). In the previous notation, the nonzero entries of are . Solving the sparsity problem exactly is NP-hard, which is why approximation methods like MP are used. For comparison, consider the Fourier transform representation of a signal - this can be described using the terms given above, where the dictionary is built from sinusoidal basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only the global features of the signals and does not adapt to the analysed signals . By taking an extremely redundant dictionary, we can look in it for atoms (functions) that best match a signal . (Wikipedia).
Arnur Nigmetov 6/29/20: Efficient approximation of the matching distance for 2-parameter persistence
Title: Efficient approximation of the matching distance for 2-parameter persistence Abstract: The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes or, more generally, multi-parameter persistence modules (it provides a lowe
From playlist ATMCS/AATRN 2020
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3 Vector-based Methods for Similarity Search (TF-IDF, BM25, SBERT)
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From playlist Pattern Matching with Computation Layer
Determining Signal Similarities
Get a Free Trial: https://goo.gl/C2Y9A5 Get Pricing Info: https://goo.gl/kDvGHt Ready to Buy: https://goo.gl/vsIeA5 Find a signal of interest within another signal, and align signals by determining the delay between them using Signal Processing Toolbox™. For more on Signal Processing To
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From playlist Pattern Matching with Computation Layer
We are given a bipartite graph where each vertex has a strict preference list ranking its neighbors. A matching M is stable if there is no unmatched pair ab, so that a and b both prefer each other to their partners in M. A matching M is popular if there is no matching M' such that the num
From playlist HIM Lectures 2015
Arthur Szlam: "A Tutorial on Sparse Modeling"
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Michael Elad: "Sparse Modeling in Image Processing and Deep Learning"
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From playlist Excalibur
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Support My Channel! Download Free ⚔️ Vikings War Of Clans Here ➤ IOS: https://bit.ly/2TN00Z9 ➤ Android: https://bit.ly/2Y7Qxdr And Get 200 💰 Gold, And a 🏥 Protective Shield for FREE Join my Vikings clan under my nickname: Caspian Support CaspianReport ✔ Patreon ► https://www.patreon.com/
From playlist Geopolitics
Simon Foucart: Essentials of Compressive Sensing (Lecture 2)
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From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
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From playlist Pattern Matching with Computation Layer