wavelet coefficients for data clustering
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From: David on 27 Apr 2010 13:09 Hello, I have a single channel in which I attempting to detect different kinds of signals (i.e. different sudden(transient) sounds in the background) I would like to use a multi-resolution method i've seen else-where (e.g. spike-sorting) that looks for clustering in the coefficients of a wavelet analysis. I've successfully employed wavelets in other domains, but have never used the coefficients explicitly. even after "googling," i have not found clear description of what the approx. and detail coefficients are and, further, which would be best used for clustering. thank you, dave
From: Wayne King on 27 Apr 2010 13:35 "David " <dhherman(a)usc.edu> wrote in message <hr75ng$t47$1(a)fred.mathworks.com>... > Hello, > I have a single channel in which I attempting to detect different kinds of signals (i.e. different sudden(transient) sounds in the background) > > I would like to use a multi-resolution method i've seen else-where (e.g. spike-sorting) that looks for clustering in the coefficients of a wavelet analysis. > > I've successfully employed wavelets in other domains, but have never used the coefficients explicitly. > > even after "googling," i have not found clear description of what the approx. and detail coefficients are and, further, which would be best used for clustering. > > thank you, > dave Hi Dave, In the multiresolution analysis, each level is decomposed into a smooth part (or lowpass part) called the approximation coefficients and a detail part (or high pass part) called the detail (or wavelet) coefficients. Going the other way, the detail coefficients at each level give you what's missing from the approximation at that level to get you to the next finer level of resolution. In other words, the detail you have to add to the approximation to get to the next finer level in resolution. As a very simple example, take the vector x = [1 1 2 4 3 5 5 1]; With the Haar wavelet, the detail coefficients would be proportional to the differences between every pair of elements [x(2)-x(1), x(4)-x(3), x(6)-x(5), x(8)-x(7)] and the approximation coefficients would be proportional to the average of each pair of elements [x(2)+x(1), x(4)+x(3), x(6)+x(5), x(8)+x(7)]. Sounds like the detail (wavelet) coefficients are what you need to look at. Wayne
From: David on 27 Apr 2010 14:08
"Wayne King" <wmkingty(a)gmail.com> wrote in message <hr778q$cam$1(a)fred.mathworks.com>... > "David " <dhherman(a)usc.edu> wrote in message <hr75ng$t47$1(a)fred.mathworks.com>... > > Hello, > > I have a single channel in which I attempting to detect different kinds of signals (i.e. different sudden(transient) sounds in the background) > > > > I would like to use a multi-resolution method i've seen else-where (e.g. spike-sorting) that looks for clustering in the coefficients of a wavelet analysis. > > > > I've successfully employed wavelets in other domains, but have never used the coefficients explicitly. > > > > even after "googling," i have not found clear description of what the approx. and detail coefficients are and, further, which would be best used for clustering. > > > > thank you, > > dave > > Hi Dave, In the multiresolution analysis, each level is decomposed into a smooth part (or lowpass part) called the approximation coefficients and a detail part (or high pass part) called the detail (or wavelet) coefficients. Going the other way, the detail coefficients at each level give you what's missing from the approximation at that level to get you to the next finer level of resolution. In other words, the detail you have to add to the approximation to get to the next finer level in resolution. > > As a very simple example, take the vector > > x = [1 1 2 4 3 5 5 1]; > > With the Haar wavelet, the detail coefficients would be proportional to the differences between every pair of elements [x(2)-x(1), x(4)-x(3), x(6)-x(5), x(8)-x(7)] and the approximation coefficients would be proportional to the average of each pair of elements > [x(2)+x(1), x(4)+x(3), x(6)+x(5), x(8)+x(7)]. > > Sounds like the detail (wavelet) coefficients are what you need to look at. > > Wayne That was perfect, thank you very much!..humans still better than google. |