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Results tagged with pca
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user 183201
Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.
1
vote
Accepted
Eigenvectors of covariance matrix and inertia tensor
First, let's set up the moment of inertia tensor for $N$ points, where point $n$ has mass $m_n$ and coordinates $(x_m^{(1)}, x_m^{(2)}, ...)$ and define $C_{ij} = \sum_{n=1}^N m_n x_n^{(i)} x_n^{(j)} …
- 423
2
votes
1
answer
672
views
Eigenvectors of covariance matrix and inertia tensor
The moment of inertia tensor from physics looks very similar to the covariance matrix, used for PCA. How are their eigenvectors and eigenvalues related? …
- 423
4
votes
2
answers
308
views
When is multidimensional scaling exact for a graph?
For an undirected graph with one connected component and distance matrix given by the shortest path between nodes, I would like to embed the nodes in a high dimensional Euclidean space where all dista …
- 423