Questions tagged [spectral-analysis]

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

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Regressing Singular Spectral Analysis Eigenvectors on data

I'm trying to model some time series economic data using mostly regression with other independent variables following the Error Correction Model (or Engle Granger approach). The ultimate goal is to ...
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Interpreting results from preforming Power spectral analysis on Hourly Temperature data

I'm analyzing hourly temperature data for a school project. Analysis data set 1 | Hourly data from 01/01/2020-12/31/2020. So I have n=24*365 = 8760 data points. I did the analysis using R. Let x be ...
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Obtaining frequency content of time sequence

I have a long sequence of time values (instants in time where events happened) and I would like to detect perodicities in this data. It's possible to sample these points onto a gigantic grid and take ...
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Generating a surrogate time series from unevenly spaced time series

I work in the atmospheric sciences and I have data from an automated weather station measuring mean sea level pressure. Due to an extreme event(and consequent loss of electricity)the measurement is ...
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Building up to the periodogram

I have seen in multiple sources that if we start with writing a time series as follows (assuming $n$ is odd): $$x_t = a_o + \sum_{j=1}^{(n-1)/2}{[a_jcos(2\pi tj/n) + b_jsin(2\pi tj/n)]}$$ Then we will ...
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Discover a pattern in a set of spectrograms given a real rating

I'm trying to find patterns in a sorted set of spectrograms, each with a rating. The main idea is to train the CNN in such a way that it understands how the pattern "evolves" at each step, ...
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Why wavelet power spectrum is a measure of the local variance of a time series

The integral wavelet transform is the integral transform defined as $$\left[W_{\psi }f\right](a,b)={\frac {1}{\sqrt {|a|}}}\int _{-\infty }^{\infty }{\overline {\psi \left({\frac {x-b}{a}}\right)}}f(x)...
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Power spectral density and frequency of noise

I have a vector of 1280 000 data points, representing a bioelectrical signal (Evoked Potentials). It consists of 2500 stimuli and responses, and therefor has 2500 individual "signals". The ...
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PCA to identify patterns in the data, forced to a particular variable?

Dataset: I have a hyperspectral dataset that consists 250 wavelength bands (x1,...x250) and corresponding reflectance measurements (y) for each band. Plotting X vs Y yields a spectral profile. I have ...
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multitaperTrend function in R

How would you determine the "B" in multitaperTrend function? I have been trying to estimate trend for Southern Oscillation index data using ...
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Phillips-Perron Test

I'd like to have a confirmation about the interpretation of the Philipps-Perron Test (PP-Test): The PP-test is a unit root test for testing the non-stationarity of a time series. It is constructed by ...
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Fast Approximate Spectral Clustering in Practice?

Spectral clustering takes $O(n^3)$ time. Over the last fifteen years, a huge number of heuristics have been published on speeding up spectral clustering (e.g. Nystrom method, PCA, sample size ...
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Spectral Graph Convolutions: What are the spectral filters functions

I am trying to understand the mathematical meaning of one of the steps that appear in the Convolution Theorem (Step 4 here). To give some context, this is related to applying the convolution theorem ...
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How to optimally select window sizes for filters on spectral data

I am trying to find an efficient method of selecting a window size for a Savitzky-Golay filter. The applications is mainly to find an smooth representation of a spectra containing sharp peaks in noisy ...
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Why is coherence of this wavelet transform almost always near 1?

I'm trying to understand the different aspects of a wavelet transform. Wavelet power has made enough sense to me as an analogy of the covariance. However, the wavelet coherence does not make sense to ...
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What is the sampling rate of quarterly time series data?

I am doing spectral analysis of quarterly data. I am very new to spectral analysis and have been using Shumway & Stoffer's textbook as a guide, but I am not understanding exactly what is going on. ...
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The length of spectral density is longer than the data using spectrum() in R

I'm using spectrum(method = "pgram") in R to calculate the spectral density in my time series. spectrum() returns the spectral density for each frequency(from 1/n, 2/n to 1/2, n is the time ...
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External loss functions for Spectral/Density-based clustering

In this article, Abou-Mustafa and Schuurmans proposed a method that makes it easy to decide what unsupervised learning algorithm generalizes 'better' to the entire dataset. In particular, this needs ...
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Does bi-spectral function completely describe the non-Gaussian feature of a random field?

Suppose we have a density field $\delta$, and denote the Fourier transform of which by $\hat{\delta}$. We denote the Dirac delta function by $\delta_D$. The power spectral function is defined by the ...
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How to compute significance between powers of spectrum components (Fourier frequencies) of two EEG signals

We have two EEG signals, and ran standard NeuroDSP Spectral Analyses to compute the power spectral densities of both signals. Moreover, because NeuroDSP uses standard Welch’s spectrogram and averages ...
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Normalization, centering and PCA [duplicate]

I have a feature matrix composed of frequency responses (in dB) from individual acoustic events. Frequencies in the columns, events in the rows and the matrix is the response The responses decrease ...
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Relation between Fourier transforms and coherence of signals

My overall aim is to compare the edges of two images by comparing their Fourier Transforms (FFT) and to calculate one number as a key performance indicator that describes how much they are similar to ...
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Identifying a single dominant number with high probability in a data point array of 4 to 20 numbers

Example readings, and second graph identified Actual Number I am looking for EDIT: These numbers on the left are period time values in micro seconds (us) in the "time domain" and they need ...
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How to translate eigenvectors and eigenvalues to the number of clusters in spectral clustering?

I have generated this output, where L is the Laplacian Matrix, D is the degree and A is the adjacency matrix: I can see the eigenvalues and eigenvectors are returned. I am unsure how to interpret ...
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How to Understand Autoregressive Process MATLAB Code?

This is supposed to be a code to calculate the true PSD of a 4th order autoregressive process: ...
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Finding autocorrelation coefficients given PSD values at 2 frequencies

Assuming that $S_X(w)$ denotes powers spectral density function at frequency $w$, we are given $$S_X\left(\frac{\pi}{4}\right)=10+3\sqrt{2},\quad S_X\left(\frac{\pi}{6}\right)=11+3\sqrt{3}.$$ We also ...
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Reference request: (spectral) convergence rate of sample covariance matrix with fixed dimension $p$

I am looking for a reference on convergence of sample covariance matrix (in some reasonable sense) when the dimension $p$ is fixed, but the number of samples $n$ goes to infinity. The ideal result I ...
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Frequency of timeseries greater than half the number of datapoints in timeseries

as suggested in the following thread: Period detection of a generic time series I'm testing the function findfrequency() to automatize the estimation of the period ...
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Why does fast graph convolution need Chebyshev polynomials?

I'm reading the paper Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering and find it difficult to understand the motivation for using Chebyshev polynomials. With localized ...
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How to calculate the expected value of a time series just from the data

in this question Can stationary time series contain regulary cycles and periods with different fluctuations I was told that stationary time series do not have regular cycles and that having constant ...
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Solver for the true auto-covariance function in AR(p)

Suppose I have the following $AR(p)$ model. $$X_t = \sum_{i=1}^{p} \phi_i X_{t-i} + \epsilon_t\,, $$ where $\epsilon_t$ has mean 0 variance $\sigma^2$. I am in the situation where the $\phi$s are ...
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Coherence using FFT: how to calculate coherence for one frame

I want to calculate coherence between two time series that are of equal lengths. Since coherence is given by Pxy/(sqrt(Pxx)*sqrt(Pyy)) , I did the following steps. Step 1: Divide both time series (...
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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 ...
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Are people still researching the use of spectral decomposition on finite groups for data analysis?

In A GENERALIZATION OF SPECTRAL ANALYSIS WITH APPLICATION TO RANKED DATA (Diaconis 1989), the author discusses a dataset of election results. There were 5 candidates, and each voter was asked to rank ...
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K means clustering breakup---galaxy spectrum data set

I have a spectrum data set (total 22000). Similar to an electronic wave data, two dimensional (Flux vs Wavelength). A typical set of wavelength plot looks like below Now I am doing kmeans on this ...
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Years as continuous variable [duplicate]

Can I use "years" as a continuous variable ("years" as calendar years from 1984 to 2014) to see if NDVI (normalized difference vegetation index), of the same area at the same time (...
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Are colored noises correlated / uncorrelated?

Let, $x$ be a random variable (r.v) that is white Gaussian, has a flat power spectrum. $y$ can be any colored noise. I think another term for uncorrelated is i.i.d (identically and independently ...
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For which clustering algorithms is the Gap statistic useful?

How can i know for which clustering algorithms (with a parameter that represents number of clusters) it makes sense to use the Gap statistic? I've read in the paper by Tibshirani, Walter & Hastie ...
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Comparing two absorption spectra as time series

I would like to compare two absorption spectra ( or interferograms) and conclude whether between these two there are statistically significant differences at particular wavelength intervals. At the ...
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Intuition behind spectral density of time series

Is there any intuition behind the spectral density $f(\lambda)$ of a time series, where $$ f(\lambda)= \frac{1}{2\pi}\sum_{h=-\infty}^{+\infty}{e^{-ih\lambda}\gamma(h)}, -\infty < \lambda < \...
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Estimating Fourier spectrum from multiple time series of a system

I have a set of N time series, each of length T, that describe separate realisations of a single physical system. For each series, I can compute an FFT to find the Fourier spectrum up to a period 2/T, ...
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HC Covariance Matrix Estimators

I'm looking for assistance in understanding/implementating the following paper Covariance Matrix Estimation in Time Series Where I need help is Eq 33 Assume $EX_i = 0$. Using the idea of lag window ...
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2 votes
1 answer
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Interpretation of pooling in Graph Neural Networks

The paper Hierarchical Graph Pooling with Structure Learning (2019) introduces a distance measure between: a graph's node-representation matrix $\text{H}$, and an approximation of this constructed ...
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1 vote
1 answer
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Periodogram explained

If I plot a periodogram of let's say sin(20x) + 2sin(80x) and it looks like this: What does it say, i.e., how do I interpret this periodogram? How could I compute ...
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What is the difference between Spectral Clustering and Laplacian Eigenmaps?

It seems like Spectral Clustering is just a term for dimension reduction via Laplacian Eigenmaps + a clustering algorithm on the output. Is this the case, or am I missing some fundamental difference?
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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_{...
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For spectral clustering,

My professor is teaching us spectral clustering but unfortunately he gave a hand-wavy introduction and left most of the details out, so I'm trying to fill them in on my own. He stated, suppose we ...
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Spectral analysis how coefficient are aj and bj are found?

I'm reading chapter 4 on spectral analysis from the "Time series analysis and its application", and I hit a bit of a confussion when it comes to how coefficients $a_j$ and $b_j$ are found. It said ...
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Spectral Density Estimators

I'm interested in showing that if we allow the kernel $h$ defined by $$h((x_1,y_1)^T,(x_2,y_2)^T,(x_3,y_3)^T)=\frac{1}{6}\sum_{\gamma \in \Gamma\{1,2,3\}}[12I(x_{\gamma(1)}<x_{\gamma(2)},y_{\gamma(...
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Estimating autocovariance from repeated time series

Consider a parent process $Z_t$ whose characteristics I wish to estimate. Consider two time series (or any stochastic process) realizations of this parent process $$X_1, X_2, \dots, X_T\,, $$ and $$...
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