SnFFT
swMATH ID:  14298 
Software Authors:  Plumb, Gregory; Pachauri, Deepti; Kondor, Risi; Singh, Vikas 
Description:  SnFFT: a Julia toolkit for Fourier analysis of functions over permutations. π n FFT is an easy to use software library written in the Julia language to facilitate Fourier analysis on the symmetric group (set of permutations) of degree n, denoted π n and make it more easily deployable within statistical machine learning algorithms. Our implementation internally creates the irreducible matrix representations of π n , and efficiently computes fast Fourier transforms (FFTs) and inverse fast Fourier transforms (iFFTs). Advanced users can achieve scalability and promising practical performance by exploiting various other forms of sparsity. Further, the library also supports the partial inverse Fourier transforms which utilizes the smoothness properties of functions by maintaining only the first few Fourier coefficients. Out of the box, π n FFT currently offers two nontrivial operations for functions defined on π n , namely convolution and correlation. While the potential applicability of π n FFT is fairly broad, as an example, we show how it can be used for clustering ranked data, where each ranking is modeled as a distribution on π n . 
Homepage:  http://jmlr.org/papers/v16/plumb15a.html 
Keywords:  permutations; Fourier analysis; last Fourier transform; Julia 
Related Software:  SnOB; Julia; rankdist; PerMallows; PRMLT; Fizzy; Lingvo; Kpax3; pyGCluster; GmmFlow.jl; EmpiriciSN; LIBSVM.jl; BSMac; Jlnv; GCNv2; TensorFlow.jl; DLL; Metalhead.jl; ImageProjectiveGeometry.jl; LightNLP.jl 
Referenced in:  3 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

\(\mathbb S_n\)FFT: a Julia toolkit for Fourier analysis of functions over permutations. Zbl 1351.68006 Plumb, Gregory; Pachauri, Deepti; Kondor, Risi; Singh, Vikas 
2015

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Referenced by 14 Authors
Referenced in 3 Serials
1  The Journal of Fourier Analysis and Applications 
1  Journal of Machine Learning Research (JMLR) 
1  Computer Science Review 
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