# Questions tagged [eigenvalues]

For questions involving calculation or interpretation of eigenvalues or eigenvectors.

343 questions
Filter by
Sorted by
Tagged with
6 views

### How to Compute the Reconstruction error in Principal Component Analysis at lower dimensions

I have m examples and d features where m<<d. So I managed to compute the eigen value and corresponding its eigen vector ... I want to compute the reconstruction error for various value of ...
31 views

### Physical interpretation of $U$ and $V$ matrices in SVD

I have a question about the physical interpretation of $U$ and $V$ matrices in SVD. I collect measurements at multiple devices across time are collected into an $m$ × $T$ matrix $M$, where m is the ...
76 views

### PCA: inference on the proportion of explained variance, in a large p setting

I am interested in doing inference on the proportion of total variance explained by the first principal component, for a PCA based on the correlation matrix R. I want to know the (asymptotic) ...
14 views

### Kernel matrix decomposition

I had a look at the sklearn.kernel_approxiamtion.Nystroem implementation, which is also described in this post: Nystroem Method for Kernel Approximation Here, a ...
41 views

### Eigenvalues in Ridge regression [duplicate]

The ridge regression estimate is given by $$\beta^{*}=(X'X+kI)^{-1}X'y, k≥0,$$ where $X$ is the feature matrix. The original paper, Hoerl and Kennard's Ridge Regression: Biased Estimation for ...
39 views

### Dimensionality reduction of a large covariance matrix

I have a large covariance matrix $\Sigma$ and I am reducing its dimensionality by using a truncated eigendecomposition. $\Sigma \approx VDV^T$. I remember somewhere that you could also decompose it as ...
40 views

13 views

11 views

Let $X$ be a random vector of dimension $p$ and $\{ X_1, \dots, X_n \}$ the $n$ observations of such vector. Let $\mathbb{X}$ be the matrix with rows $X_k$ and $\mathbb{X}_c$ is the matrix with rows $... 0answers 32 views ### Sketch ellipse with variance-covariance matrix that got after PCA For X = (X1, X2, X3) distributed as N3(µ, Σ), mean of the original data is mu and variance-covarinace matrix of the original data is Sigma. I found in this section that we can derive the variance-... 1answer 203 views ### Why eigenvectors reveals the groups in Spectral Clustering According to Handbook of Cluster Analysis Spectral Clustering is done with following algorithm: Input Similarity Matrix$S$, number of clusters$K$Form the transition matrix$P$with$P_{ij} = S_{...
I was wondering if someone could provide a reference to the following result. Consider the $p\times p$ sample matrix $$\frac{1}{n} \sum_{i=1}^n x_i x_i',$$ where $x_i$ are i.i.d. $p\times 1$ random ...