[HN Gopher] A windowed graph Fourier transform (2012)
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       A windowed graph Fourier transform (2012)
        
       Author : teleforce
       Score  : 60 points
       Date   : 2024-03-04 10:49 UTC (1 days ago)
        
 (HTM) web link (ieeexplore.ieee.org)
 (TXT) w3m dump (ieeexplore.ieee.org)
        
       | defrost wrote:
       | Sidestepping Signin:
       | 
       | https://sci-hub.ru/10.1109/SSP.2012.6319640
       | 
       | https://sci-hub.st/10.1109/SSP.2012.6319640
       | 
       | .. and for something not quite completely different:
       | Wavelet theory has its origin in several disciplines; the types
       | of functions that are now called wavelets were studied in quantum
       | field theory, signal analysis, and function space theory. In all
       | these areas, wavelet-like algorithms replaced the classical
       | Fourier-type expansion of a function. It was not until the
       | mid-1980s that these, at first, seemingly different notions were
       | described in a unified manner. Because of the restricted scope of
       | this monograph, we will not be able to address some ramifications
       | of wavelet bases for so-called wavelet frames.              The
       | wavelet transform is an alternative to the classical windowed
       | Fourier transform.              [ ... ]
       | 
       | https://www.sciencedirect.com/science/article/abs/pii/B97801...
        
       | michelpp wrote:
       | A similar and more recent example of graph decomposition is the
       | fast graphlet transform:
       | 
       | https://github.com/fcdimitr/fglt
       | 
       | This algorithm has a nice Algebraic formulation recently
       | implemented with the GraphBLAS in LAGraph:
       | 
       | https://github.com/GraphBLAS/LAGraph/blob/stable/experimenta...
        
       | CamperBob2 wrote:
       | I'm unclear on why I would want to "translate" a "signal" on an
       | arbitrary weighted graph such as the Minnesota road map example,
       | in the same sense that I might multiply a time-domain signal by a
       | complex exponential to translate it to a higher or lower
       | frequency in the frequency domain. The latter is an everyday
       | operation in signal processing but what does it mean in other
       | contexts?
       | 
       | Are there any good concrete examples of what such a translation
       | would accomplish?
        
         | teleforce wrote:
         | It is related to spectral graph theory where associations
         | between graph theory and linear algebra are being made where
         | typically power iteration algoritm is then applied not unlike
         | the venerable PageRank algorithm [1].
         | 
         | [1] The Power Iteration Algorithm in Practice:
         | 
         | https://scicoding.com/the-power-iteration-algorithm-in-pract...
        
           | CamperBob2 wrote:
           | That's interesting, but it doesn't answer my question. I
           | think I'm missing too many prereqs on this one,
           | unfortunately.
        
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