# 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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24 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 ...
32 views

### 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,...
31 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) ...
54 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 ...
74 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 ...
8 views

### Understanding Spectral Density of a time series in terms of Regression on Sinusoids

This may be a very trivial question but I would like to understand spectrum density of a time series in terms of regression. This is what I know from reading on the net: A time series can be ...
8 views

### What data should be used for Spectral Analysis?

I am using time series data. I've done my analysis using the first difference of the log, of my data, diff(log(data)). So I found my model, and everything. However, ...
11 views

### Spectral methods for time series analysis

What are the most used spectral methods of time-series analysis? Are those packages available and readily used (in R or Python)? And what are the better performing methods available out there?
26 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,...
23 views

### 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 ...
36 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 ...
11 views

### 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 ...
18 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 ...
22 views

### Super-resolution approach applied on vibration data

I have low-resolution(LR) vibration data (e.g 3khz), and I mainly want to detect machine fault on that data. Is it a good idea, to train a convolutional neuronal network to create a high-resolution(HR)...
86 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 $K(h) = \Gamma(-\alpha/2) |h|^{\alpha}, ~0<\alpha<2.$ ...
38 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 ...
19 views

### 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 ...
8 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 ...
66 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 ...
12 views

### 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)...
58 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 ...
73 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 ...
194 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 ...
15 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 ...
101 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 ...
20 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 ...
109 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/...
62 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, ...
485 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 ...
256 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 ...
376 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 ...
409 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 ...
153 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 ...
23 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 ...
74 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 ...
69 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 ...
52 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,...
1k 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 ...
2k 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?
375 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: ...
229 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. ...
89 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 ...
67 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 ...
165 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 ...
443 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) ...
581 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 ...
430 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 ...
108 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 ...