Questions tagged [eigenvalues]
For questions involving calculation or interpretation of eigenvalues or eigenvectors.
430 questions
2 votes
1 answer
178 views
Factor Analysis: Theoretically Five Factors Expected, but Only One Emerges – What Should I Do?
I am currently conducting a factor analysis on a scale that theoretically consists of five factors. However, both Principal Component Analysis (PCA) and Maximum Likelihood (ML) extraction methods in ...
0 votes
0 answers
35 views
Rotated loadings as input to hierarchical clustering
How do we feed the rotated loadings obtained through varimax rotation using psych package to hierarchial clustering in the FactomineR package (HCPCC())? I want to use the rotated components instead of ...
- 81
1 vote
0 answers
60 views
What do the rows of SVD tell us about PCA?
If we have a matrix $X\in\mathbb{R}^{n\times p}$ with SVD $X = UDV^T$, we can say for example that the columns of $V$ are the principal directions and the columns of $UD$ are the principal components (...
- 294
1 vote
1 answer
108 views
Does Fisher's Discriminant Analysis (FDA) whiten the within-classes covariance? Intuition behind it?
The objective of Fisher's Discriminant Analysis, or Linear Discriminant Analysis as a dimensionality reduction technique is to find the set of features $W$ that maximize the ratio between the between-...
- 2,352
1 vote
1 answer
84 views
Stationarity Conditions VECM
Suppose we have a vector error correction model (VECM) $$ \Delta y_{t}=\Pi y_{t-1}+\Gamma_{1}\Delta y_{t-1}+\cdot\cdot\cdot+\Gamma_{p-1}\Delta y_{t-p+1}+u_{t} $$ A simple way to confirm that it is a ...
- 2,317
6 votes
1 answer
222 views
Interpretation of generalized eigenvalues, matrix distance, information geometry
This question is about how generalized eigenvalues of two covariance matrices relate to the discriminability of their associated Gaussian distributions. The generalized eigenvalue problem for two ...
- 2,352
3 votes
2 answers
161 views
Why is the amount of Eigenvalue of the first Principal component much higher than the rest of the PCs?
I have the time series of 16 water quality parameters, and after standardizing them using the zscore method, I performed principal component analysis. These are my eigenvalues [7.62675203795075 2....
- 33
0 votes
0 answers
22 views
Variance after factor analysis in Stata [duplicate]
I run a factor analysis in Stata (-factor- command) and get the eigenvalues for each factor. Then, I do a rotation, and the table presents not the eigenvalues, but the variance. I have two questions: ...
- 397
4 votes
2 answers
264 views
Linear algebra properties of a confusion matrix (eigenvalues, eigenvectors, and determinants)
This answer to a question on Math Stack Exchange got me thinking about a confusion matrix as more than just a rectangular array of numbers. We don’t talk about a confusion matrix as a linear ...
- 72.9k
4 votes
1 answer
238 views
Expected value of largest eigen value of sample correlation matrix
Suppose $X$ follows some multivariate distribution with zero mean and Identity covariance matrix. Suppose $X$ is N dimensional. Suppose $R$ is the sample correlation matrix, calculated based on n ...
- 265
2 votes
1 answer
122 views
Distribution of Maximum Eigen Value
Suppose I have X, k*n, where $M=X'X$. Suppose $n>>k$, and $rank(M) =k-1$. Suppose $\lambda_1, \cdots, \lambda_{k-1}$ are the eigen values of M. Under the assumption that the columns of X are ...
- 265
2 votes
0 answers
69 views
Interpreting eigenvalues of non-normalized covariance matrix of physical system
Cross-posted from physics stackexchange Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). ...
- 714
4 votes
1 answer
273 views
The eigen values of Johansen's cointegration procedure
Assume a K dimension VECM model for cointegration analysis $$\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta y_{t-p+1}+u_t$$ The Johansen approach for maximum eigenvalue test or ...
- 41
1 vote
0 answers
217 views
How to balance PCA and LDA in subspace learning?
PCA is a generative model, by which input images or data can be reconstructed. LDA (Linear Discriminant Analysis) is a discriminative model, which extracts better features for classification. How to ...
- 61
2 votes
0 answers
100 views
Solving an exercise about admissible coefficient values for a MA(1) process
I'm studying "Principles of system identification : Theory and Pratice" by Arun K. Tangirala and well... I've just entered the part about moving averages and I'm confused. I don't understand ...
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