Kernel Trick PCA

kt_pca.py

from typing import Tuple
import numpy as np

def kt_pca(X:np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
    """
    This is an implementation of the linear kernel PCA method ("kernel trick")
    described in "Kernel PCA Pattern Reconstruction via Approximate Pre-Images"
    by Schölkopf et al, ICANN, 1998, pp 147-15

    Parameters
    ----------
    X : np.ndarray
        Matrix of data in (T x N). Only need this trick if T>>N

    Returns
    -------
    E : np.ndarray (T x N)
        Eigenvectors of the kernel matrix, in descending order
    S : np.ndarray (1 x N)
        Eigenvalues of the kernel matrix, in descending order
    """

    S2, F = np.linalg.eigh(np.matmul(X.T, X))
    F = F[:,::-1]
    S2 = S2[::-1]

    S = np.sqrt(S2)

    ES = np.matmul(X,F)
    E = ES/S

    return E, S