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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21 views
Interpretation of Spectral Density
I have learned that the attached formula defines the spectral density of a time series. However, as I am unfamiliar with Fourier transforms, I am not sure about the interpretation of this series. I ...
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0answers
11 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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0answers
16 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.
...
2
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1answer
30 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 ...
2
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0answers
84 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 ...
4
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1answer
144 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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0answers
11 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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0answers
49 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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0answers
41 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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0answers
39 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 ...
1
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1answer
15 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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0answers
42 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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0answers
21 views
Community detection in a subgraph
I find myself in possession of a bipartite weighted graph $G=(V,E)$. Let $A,B$ be the partition of $V$, so that if $i\sim j\in E$ then either $i\in A,j\in B$ or $j\in A,i\in B$.
I am interested in ...
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0answers
34 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 ...
1
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1answer
22 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,...
2
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1answer
280 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 ...
1
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1answer
447 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?
3
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2answers
113 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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0answers
93 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.
...
2
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0answers
41 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 ...
2
votes
1answer
35 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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0answers
105 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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0answers
145 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) ...
3
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1answer
333 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 ...
0
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1answer
144 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
70 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
114 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
119 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
351 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
1k 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....
0
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1answer
37 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
41 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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0answers
50 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/...
2
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1answer
634 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 ...
0
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1answer
80 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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0answers
296 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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0answers
184 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 ...
0
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1answer
42 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 ...
3
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0answers
26 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 ...
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1answer
96 views
Principal component analysis on signal … dealing with replicates
I have a spectrum data (wavelength(x) versus absorption(y)) for 25 unique samples that is almost exactly to the problem presented in this thesis: https://brage.bibsys.no/xmlui//bitstream/handle/11250/...
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0answers
36 views
Asymptotically confidence interval of level $1-2\alpha$
For fixed $k$, the variables $(2k+1)\hat{f}_k(\lambda)$ are asymptotically distributed according the Gamma distribution with shape parameter $2k+1$ and mean $(2k+1)f_X(\lambda)$. It turns out that ...
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1answer
896 views
Interpreting periodogram
I have some simulated data following sin, where the pattern repeats roughly every 25th observation.
...
4
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1answer
1k views
spectral clustering/theory, is there any meaning for the magnitude of values in eigenvectors?
Basically, spectral clustering is an application of spectral graph theory, which utilizes the eigenvalues and eigenvectors of a Laplacian matrix or adjacency matrix to disclose the connected ...
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0answers
79 views
Spectral density of cos + sin + Ma(1) process
I have to find the spectral density function, (notice: the problem clearly states that I'm looking for the spectral density function, not the spectral distribution function) of the following process:
...
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1answer
47 views
Spectral Clustering in Resting-State fMRI [closed]
I have 200 .hdr/.img file pairs for person in which the carried out pre-processing using SPM. I want to apply spectral clustering for voxel time courses to find resting state networks.
How can I ...
0
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0answers
150 views
Choice of window length in Singular Spectrum Analysis
Thanks in advance for your answers, I'm trying to decompose a stock price using the Rssa package provided in R, after millions of trials, I tried to change the window Length and the eigentriples, the ...
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0answers
66 views
Largest eigenvalue of the determinantal equation
I'm reading a paper and it defines $\lambda(\omega)$ as the largest eigenvalue of the determinantal equation:
$$|A'f^{re}(\omega)A-\lambda A'VA|=0$$
Where $f^{re}(\omega)$ is the real part of $f(\...
2
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0answers
65 views
Intuition/interpretation for the value of the spectral density calculated at the zero frequency
Is there any easy way to think about the value of the spectral density at the zero frequency? How do people interpret it usually?
I have been studying some time series on my own and encountered a ...
4
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1answer
463 views
What is periodogram?
I have read about spectral density and periodogram from couple of books,still just one example from R code showed that I do not understand the theory.I have this data set
...
3
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0answers
516 views
Why does Kernel K-means work better than spectral clustering in this case?
I want to cluster a dataset using spectral clustering. Assuming $X$ is $d \times n$ data matrix as $n$ is the number of data samples. I construct a directed Adjacency matrix $W, n \times n$ in which ...
