Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [spectral-analysis]

For questions involving spectral clustering algorithms, frequency domain analysis or correlated subjects. May include Fourier transform and graph theoretic questions.

186 questions
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Testing significance of peaks in spectral density

We sometimes use spectral density plot to analyze periodicity in time series. Normally we analyze the plot by visual inspection and then try to draw a conclusion about the periodicity. But have the statisticians developed any test to check whether…
Pantera
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Why eigenvectors reveal the groups in Spectral Clustering

According to Handbook of Cluster Analysis Spectral Clustering is done with following algorithm: Input Similarity Matrix $S$, number of clusters $K$ Form the transition matrix $P$ with $P_{ij} = S_{ij} / d_i$ for $i,j = 1:n$ where $d_i= \sum_{j=1}^n…
jakes
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PCA, ICA and Laplacian eigenmaps

Question I am very interested in the Laplacian Eigenmaps method. Currently, I am using it to do dimension reduction on my medical data sets. However, I have run into a problem using the method. For example, I have some data (spectra signals), and I…
Samo Jerom
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What approaches use multiple eigenvectors in graph spectral clustering?

Background: In Newman's PNAS 2006 paper Modularity and community structure in networks, the first eigenvector splits the graph in two clusters, and then each cluster can be further divided by eigenvector of a modified Laplacian of the nodes within…
highBandWidth
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Why do we build the Laplacian graph in Spectral Clustering?

What advantage does creating the Laplacian Matrix from the Similarity Matrix bring us in spectral clustering? Why do we create it? Here is the algorithm: A Tutorial on Spectral Clustering (pp.5-6)
user2806363
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Difference between PCA and spectral clustering for a small sample set of Boolean features

I have a dataset of 50 samples. Each sample is composed of 11 (possibly correlated) Boolean features. I would like to some how visualize these samples on a 2D plot and examine if there are clusters/groupings among the 50 samples. I've tried the…
user2602740
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Theoretical link between the graph diffusion/heat kernel and spectral clustering

The graph diffusion kernel of a Graph is the exponential of its Laplacian $\exp(-\beta L)$ (or a similar expression depending on how you define the kernel). If you have labels on some vertices, you can get labels on the rest of the vertices by a…
highBandWidth
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Finding peaks in power spectrum of a signal in R

I am analyzing some eeg waveforms and developing a classifier based on them. In the data I have, I usually find a strong peak at a very low frequency (I am not interested in this peak) followed by another peak at a higher frequency (call it f0) and…
morpheus
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Are spectral decompositions of time-series useful for modeling/forecasting, or are they more of a tool for analysis?

This is a bit of a theoretical question. I'm also new to time-series analysis, and trying to learn fast. Sorry if some of my terminology is off. You can loosely categorize methods to analyze and model time-series into time-domain and…
MatthewO
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Why do we use the eigenvectors of the Laplacian and not the Affinity matrix in spectral clustering?

In spectral clustering, it's standard practice to solve the eigenvector problem $$L v = \lambda v$$ where $L$ is the graph Laplacian, $v$ is the eigenvector related to eigenvalue $\lambda$. My question: why bother taking the graph Laplacian?…
felipeduque
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What's the purpose of window function in spectral analysis?

I'd like to see the answer with qualitative view on the problem, not just definition. Examples and analogous from other areas of applied math also would be good. I understand, my question is silly, but I can't find good and intuitive introduction…
Andrey Popp
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Clear steps to calculate coherence between two time series

I originally posted this on stackoverflow.com and then deleted it and moved it here My question is similar to Similarity of two discrete fourier tranforms (specifically the selected answer). I've also gleaned some helpful information from this R…
Nan
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Eigenvalues of correlation matrices exhibit exponential decay

I have a data-set of $P$ samples of size $N$, and noticed that the eigenvalues of the correlation matrices $A^TA$, when presented in descending order, can in many cases be described as an exponential decaying function. That is, there is a good fit…
Uri Cohen
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When should I use k-means instead of Spectral Clustering?

From the image linked to below, it looks like when the data actually consists of K isotropic clusters, Spectral Clustering does as well as K-means. But for other, non-convex clusters, Spectral Clustering outperforms k-means. Is this true? When…
user3279453
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Probability density from Hilbert-Schmidt integral operator

The Hilbert-Schmidt integral operator determines the underlying measure, if a universal kernel is used. Now, do eigenvalues of the Hilbert-Schmidt integral operator determine the underlying measure up to translation, reflection and…
Uzu Lim
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