Karhunen–Loève transform

Definition

The Karhunen-Loève transform (KLT) is an orthogonal transform in form $\mathbf{y} = \mathbf{V}^T \mathbf{x}$ where orthogonal transform matrix $\mathbf{V} = [\mathbf{v}_1,...,\mathbf{v}_d]$ is the eigenvector matrix of covariance matrix $\mathbf{\Sigma}_x$ of $\mathbf{x}$, composed of $d$ normalized eigenvectors of $\mathbf{\Sigma}_x$.

Notes

See also

• covariance
• principal component analysis
• orthonormal basis

References

1. https://pages.hmc.edu/ruye/MachineLearning/lectures/ch8/node4.html
2. https://en.wikipedia.org/wiki/Kosambi–Karhunen–Loève_theorem