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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7 views

Appropriate machine learning technique for spectral data and low-frequency feedback

I have a performance measure and a data source that basically supplies a complex and varying waveform. I would like to apply some unstructured learning technique to try and find a pattern in the ...
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44 views

Why is spectral density only defined for stationary processes?

I read Brockwell and Davis(2016), Shumway and Stoffer(2016), and Stoica and Moses(2004). However, none of them laid out clearly the reasoning behind the presumption of stationarity when conducting ...
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power spectrum density (V**2/Hz) for nonuniform logarithmic array?

I have nonuniform logarithmic time data array which have 1000pts/decade. that means sampling rate is changing in each intervals or decade. How can I calculate and plot power spectrum density (V**2/Hz)...
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24 views

Implementing a graph convolutional layer, pixel2mesh example

I'm trying to read through some python code in order to understand how to implement a Graph Convolutional Layer. I was particularly interested in pixel2mesh, digging through the code I've found the ...
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12 views

What does a high silhouette score for assigning everything to 1 cluster mean?

I'm writing my bachelor's thesis and I'm running into an oddity. When running k-means and hierarchical, the clustering is fairly evenly distributed - there isn't a clear preponderance of data points ...
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29 views

Singular Spectrum Analysis Explanation

I need you to help me understand the Singular Spectrum Analysis algorithm. I already read a lot of articles about the subject but they never answered my questions like what is the mathematical reason ...
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12 views

Spectral graph convolutional network, re-assigning indices

This is a silly question for whom is familiar with the theory. I came across few papers that use a particular definition of convolution, designed to work with graphs, for example see section 2.1. of ...
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14 views

Calculating Variable Importance for Feature Selection - PLSR

I have used the plsr() function in R (from the pls package) to predict a Y variable using many X variables (spectral bands) - and am wanting to calculate variable importance (ViP) to begin to reduce ...
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15 views

Power spectral density attenuation confidence interval

I am trying to compare power spectral density (PSD) estimates of two stochastic signals. I compute the attenuation by dividing one PSD by the other (both PSDs are computed and smoothed within the same ...
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1answer
63 views

Retrieving time series from a smoothed periodogram

If I were to smooth a periodogram and then filter out low level frequencies, how can I derive the filtered time series? For example, in the case of a non-smoothed periodogram: https://folk.uib.no/...
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29 views

Preprocessing of time series data to spectral analysis

If we want to find the periodicities of a time series, we can use spectral analysis. We can plot the the periodogram and find the major component, then we can find the major periods. But to do this, ...
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23 views

Distribution of the periodogram of non-Gaussian time series

I know that a periodogram of a Gaussian time series has a scaled chi-square distribution, is it the same for of a non-Gaussian time series?
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1answer
188 views

Interpretation of spectral entropy of a timeseries

The tsfeatures package for R has an entropy() function. The vignette for the package describes it as: The spectral entropy is ...
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24 views

How do I calculate my RCs for SSA for prediction (like I would for principle components)?

So the essential structure of what I am hoping to do is to create a neural network that uses the Reconstructed Components (RCs) from Singular Spectrum Analysis (SSA) to predict my outcome variable in ...
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21 views

About the power spectrum and confidence upper limit

For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate. ...
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1answer
146 views

Compute the $k$ largest eigenvector in spectral clustering

In Spectral Clustering, we need to compute the top $k$ largest eigenvector of normalized $L$. $$L = D^{-\frac{1}{2}}SD^{-\frac{1}{2}}$$ In Andrew NG's paper, L is not positive definite (unless ...
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215 views

Detecting seasonality from periodogram and seasonplots

I want to determine whether a time series contains seasonality, and if so, what the periodicity is so I can include this as Fourier terms in my model. Because I have to do this for approximately 100 ...
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1answer
216 views

Sum of autocovariances for AR(p) model

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 not interested in fitting this model, but ...
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12 views

Upper bound on single frequency error based on SSE of the full signal

I have an empirical signal: $y(t) = A_0 + \sum_{i=1}^{M}A_i \cos(\omega_i t + \phi_i) + \epsilon(t)$ The signal is tidal, and so dominated by a small number of frequencies and in particular there is ...
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156 views

Periodogram interpretaion to get main cycles for time serie

I try to use the periodogram in order to get main cycle on my time series. My time series is a the result of measure every hour of one variable related with the atmosphere. So in one day I have 24 ...
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97 views

Intuition behind finding number of clusters in spectral clustering according to Zelnik-Manor and Perona

I have a quick question on the intuition behind the estimation strategy for the number of clusters presented in the paper "Self-Tuning Spectral Clustering" by Lihi Zelnik-Manor and Pietro Perona. See ...
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109 views

Spectral separability

I'm new in the forum and with R.. I have already read a post about this topic (spectral separability: Jeffries-Matusita, Divergence and Bhattacharryya index), but i need calculate a spectral ...
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1answer
20 views

Matching of graph peaks over time

I am a programmer but my data analyses/statics skills are non-existent. I am a quick learner though and no problem I have set to solve has yet to become unattainable (let's hope this is not the first ...
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61 views

matrix factorization with non-negative constraint only on one of the factors

I have a 2D spectral data time series with a wavelength dimension and a time dimension, and I'd like to decompose it to the time evolution ($SV^T$ for SVD and $H$ for NNMF) of several spectral ...
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54 views

How do I extract transformed axes from a PCA on spectral data to carry out further analysis and determine important wavelengths using R?

I am using R to work with a large set of spectral data from 48 different samples (a combination of different types of waste fines and soils) and trying to determine if these can be differentiated by ...
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1answer
44 views

Is (1 - Coherence) a metric, at a given frequency?

I'm performing some signal analysis and was using coherence (magnitude-squared coherence) to inference signals similarity. Now, I need to extend the framework by introducing a metric. I was wondering,...
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1answer
859 views

Interpretation of modes in periodogram

I have a dataset sampled at 1000 Hz to 3 minutes. So there are 180000 data points. I plotted the periodogram for this data and I get a range of peaks. The strength seems highest at 0. What does this ...
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1answer
1k views

What is the time complexity of spectral clustering and why is it so?

What is the time complexity of spectral clustering and why (mathematically speaking) is it so? What are possible existing alternatives to speed up the computations required by the algorithm?
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213 views

How to handle disconnected graphs in spectral clustering?

I am writing a clustering algorithm based on Normalized spectral clustering. When I try and compute the generalized eigenvectors like so: ...
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177 views

Why is long-run variance a positive function of the spectral density at frequency zero?

Müller (2014) provides the following definition of the long-run variance $\omega^2$: $\omega^2=2\pi f(0)$ where $f(0)$ is the spectral density of a time series process, evaluated at frequency zero. ...
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65 views

Time series/ ARMA Simulation

Given: I have a question, given a continuous real spectral density f(w), -infinity my idea: I would folding, discretize and truncate the spectral density to get a real (one-sided) discrete spectral ...
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1answer
44 views

What is the spectral domain?

From https://arxiv.org/pdf/1611.08097.pdf, "Geometric deep learning: going beyond Euclidean data". Here are some uses: "methods of signal processing on graphs, which have previously been reviewed in ...
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145 views

Spectral Clustering using Negative Euclidean Distances

In most spectral clustering papers I've seen (von Luxburg's tutorial, Michael Jordan's NIPS paper, and some papers that predate those), they like using the affinity matrix generated by the Gaussian ...
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277 views

What is the difference between spectral clustering and kernel spectral clustering?

I have been reading about spectral clustering (SC) technique. So far I understood that it is based on computing the similarity between datapoints (using some function like the gausian kernel function) ...
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1answer
482 views

Proof of Herglotz Theorem in Time Series Analysis

I am studying time series, following Time Series Theory and Methods by Brockwell and Davis. I am reading the proof of the Herglotz Theorem, I have the following questions. First, the proof given in ...
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1answer
256 views

Power Spectral Density of Random Walk

The Brownian motion has a power spectral density (PSD) dependency on frequency like $\frac{1}{f^2}$. As far as I understand, power spectral density is defined only for wide sense stationary processes ...
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1answer
88 views

Spectral density and Riemann Stieltjes Integral

I am confused with a part about spectral densities. I found it in Time Series Theory and Methods by Brockwell and Davis. I don´t understand how is applied the Riemann Stieltjes Integral in this ...
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2answers
165 views

Is this a well-studied problem? Problem: Optimally unlagging multiple time-series

Is the problem of optimally lagging/unlagging multiple time-series with integer lags to maximize a sum of pairs of cross correlations or coherence an already well-studied problem? If so, references? ...
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1answer
147 views

Nonparametric estimate for spectral density and smoothing

We've just learned nonparametric estimate of spectral density, and the book doesn't explain it well. We have a r assignment that need to find a nonparametric estimate and find predominant periods. I ...
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1answer
452 views

Clustering symmetric distance matrix

Below is a symmetric matrix $A$ with distances between observation $i$ and $j$. $$ \begin{matrix} 0 & 9 & 8 & 6 & 3\\ 9 & 0 & 1 & 7 & 8\\ 8 & 1 & 0 & 6 &...
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3answers
2k views

Spectral Analysis in R - the periodogram

I am doing a spectral analysis in R using the spec.pgram() function. Suppose I have observations for $y_1$ to $y_n$ which are a time series with annual observations....
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1answer
45 views

differences in forecast and reconstruction in SSA, in R

I was playing around with the Rssa when I discovered this: Firstly: I created to sequences: library Rssa x<-1:100 x1<-1:80 then the corresponding function:...
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1answer
49 views

What is the frequency range for a discrete time series?

We're covering spectral analysis for discrete time stationary processes in lectures, and I can't really get my head around something which seemingly should be easy. "Because time is discrete, we only ...
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78 views

detect if time series follow/lead each other

Apart from the Granger test for Granger causality, which tests whether one time series contains information to help predict the other time series, are there any methods to test if on time series lags/...
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1answer
844 views

Finding out frequency of peaks using the Fourier transform

I have a signal that varies in time as shown below. I have just shown a 5 s interval of data (from 97 s to 102 s). The sampling frequency is 1000 Hz. My goal is to find out the frequency of the ...
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1answer
97 views

Spectral density of square of AWGN

Additive white Gaussian noise (AWGN), $w(t)$, is usually modeled with the following assumptions For a given $t_0$, $w(t_0)$ follows a normal distribution and $R_{ww} = \sigma^2 \delta(t)$, where $\...
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346 views

When is LASSO better in dimension reduction?

Are there any cases that it is better to use Lasso for dimension reduction in comparison to other methods such as PCA/ Kernel PCA/ LLE and ISOMAP and SPECTRAL EMBEDDING? Can you add an example (most ...
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236 views

Periodogram Interpretation

I'm trying to understand why the following definition describes a function that does the job of producing a graph where the highest point indicates the frequency of the strongest periodic signal. I've ...
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1answer
61 views

How to deal with changing variance in data sets

I've done an entry level stats course, so my knowledge is very limited in regards to this topic. I'm dealing with large datasets (~3000-9000 data points), and trying to pick signals out of the noise ...
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29 views

Where is studying the Bispectrum useful?

In cosmology it is well known that studying the bispectrum of the large scale structure of the universe is a powerful way to distinguish different models of cosmic initial conditions. I had assumed ...