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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14 views

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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10 views

Correlation estimation by the Blackman-Tukey method

Problem statement: Assume that the spectral estimation for an unknown signal is given by the Blackman-Tukey method as follows: $$ S_x(\omega) = 5+8\cos(\omega)-6\cos(2\omega)+2\cos(3\omega).$$ Assume ...
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33 views

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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17 views

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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43 views

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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24 views

What are the possible problems with using ACF to detect frequency in timeseries?

Looking for a way to detect frequency without knowing anything about the timeseries beforehand. I ended up as suggested by another user in this thread: Period detection of a generic time series Here ...
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24 views

Spectral decomposition of the DC part of the signal

The title of the question might be misleading, but it shows how clueless I am about this problem. I have a time series of some quantity $X(t)$. I can calculate autocorrelation of this quantity $Y(\tau)...
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44 views

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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2answers
380 views

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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1answer
200 views

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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98 views

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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1answer
114 views

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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1answer
44 views

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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1answer
45 views

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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1answer
281 views

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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41 views

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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41 views

What is the best practices on forecast by ssa?

I want to use the ML .NET SSA algorithm to forecast someone weight by age with upper and lower bounds. I can use someone data to train a model, but the growth paterns are little diferent per person. ...
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43 views

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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28 views

How to performe LDA on PC components in R?

I have a big dataset as 1025 FTIR spectra. They belong to 21 groups/class and have 632 features (or wavenumbers). Lets say 21 groups are 21 patient samples from which a set of spectra collected ...
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18 views

How to use Power Spectral Density in a Linear Regression

I’ve computed a vector-valued autocorrelation function $\phi_{xy}(t)$. Because I use an exponential kernel, $\phi$ is pre-windowed. In the discrete world, phi is a 3D matrix (num inputs by num outputs ...
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1answer
79 views

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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26 views

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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80 views

How can I calculate confidence intervals from residuals?

I have measured the atomic emission spectrum of a plasma. Essentially, such a spectrum consists of $N$ pixels with certain intensity values $I$, very similar to an image (only one-dimensional). Now I ...
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32 views

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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23 views

R Cluster analysis of spectra

I have measured the spectral reflectance of a number of items. I wish to determine whether it is possible to identify these items by their reflectance alone. For example, by analysing spectra alone ...
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29 views

What is the mathematical relation between spectral density and variance

I am modeling a co-variance matrix for accelerometer noise for Kalman filtering. I have been given the information that the spectral density is given in units m^2/s^3 and the variance in units m^2/s^4....
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70 views

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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how many spectogram frames per input character does text-to-speech (TTS) system Tacotron-2 generate?

I've been reading on Tacotron-2, a text-to-speech system, that generates speech just-like humans (indistinguisahble from humans) using the github https://github.com/Rayhane-mamah/Tacotron-2. I'm very ...
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1answer
69 views

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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35 views

Using RBF k-NN graph in spectral clustering

In the article Spectral Clustering with Imbalanced Data there is mentioned usage of a "RBF k-NN" graph. I haven't encountered this kind of graphs before and couldn't google anything related to it. ...
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1answer
138 views

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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373 views

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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19 views

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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15 views

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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63 views

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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53 views

Break frequency in ARMA's power spectral density (PSD)

Consider first a Lorentzian PSD: $$L(f) = \frac{\sigma^2}{\alpha^2+(2\pi f)^2}.$$ Its so-called break frequency is at $f_{\rm break} = \frac{\alpha}{2\pi}$, which nicely corresponds to the PSD's ...
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Recent advances in the use of the spectra of kernel integrals following Yoshua Bengio's 2004 paper that links kernel PCA and spectral clustering?

In Yoshua Belgio's 2003 technical report http://www.iro.umontreal.ca/~lisa/pointeurs/TR1232.pdf, and subsequent 2004 paper http://www.iro.umontreal.ca/~lisa/pointeurs/bengio_eigenfunctions_nc_2004.pdf,...
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1answer
51 views

Geometric significance of the dimensional reduction part of spectral clustering?

While performing spectral clustering of the original data $\{x_1,...x_n\}$, $ x_i\in \mathbb{R}^{d\times 1}$ (column vectors), into $k$ clusters, we Step 1: take the first (smallest) $k$ (column) ...
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64 views

Time Series Analysis Book/References not from Economists/Econometrics

Are there any time series books not written from an economics/econometrics perspective? I was hoping someone from biostatistics perspective wrote a time-series analysis book where terms like ...
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1answer
540 views

Conv2D Kernel size for audio-related tasks

So I've been working on this audio-rec task for a while now, and I've had some good luck using 2D convolutions on the spectrogram of audio (I've also tried Mel-spectrograms, the difference is minor in ...
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1answer
58 views

Clustering - Different algorithms, same results

I'm working on my first clustering assignement and I've ran K-Means, Spectral clustering, Hierarchical clustering and Mini-Batch K-Means on same data and received the exact same results (cluster sizes,...
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Determining the Total Uncertainty in the Center of a Spectral Line Fit (Physics Experiment)

Currently I am doing a Physics Experiment that requires fitting spectral lines and the fit I chose was a Voigt Profile. The data that I am fitting has multiple peaks so the fit is the superposition of ...
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1answer
66 views

Neural network vs SARIMA

In real-time data, sometimes you find that you cannot get a certain seasonality for the data because it is difficult to identify. This happens a lot in the prices of commodities and the stock market ...
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Time spans in coherence computation

Currently I'm writing my master thesis and I'm having troubles with coherence definition. My question is similar to Clear steps to calculate coherence between two time series Mathematically it's ...
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25 views

Autocorrelation fitting algorithm

I am currently working on an autocorrelation fitting algorithm, similar to this for a gaussian spectral signal I would like to calculate parameters such as velocity and spectrum width using a finite ...
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89 views

Deriving spectral measure

While reading this book, I got stuck on page 266 where the authors found the spectral measure $F(du)$ of the generalized covariance function $K(h) = \Gamma(-\alpha/2) |h|^{\alpha}, ~0<\alpha<2.$ ...
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1answer
79 views

Generate random walk from a power spectrum

I want to be able to generate a model timeseries from a given power spectrum. The power spectrum is measured from other data and hence has no fit parameters and is empirical. How does one go about ...
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How do spectral neural networks for learning on graphs work?

I've been reading this paper "Spectral Networks and Locally Connected Networks on Graphs" but for the full understanding of this paper it requires the reader to be knowledgeable about harmonic ...