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PCA-linreg feature
This commit is contained in:
John Kerl
parent
506dc22f00
commit
40f1209df4
5 changed files with 287 additions and 22 deletions
146
c/lib/mlrmath.c
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146
c/lib/mlrmath.c
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@ -0,0 +1,146 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include "mlrmath.h"
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#define JACOBI_TOLERANCE 1e-12
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#define JACOBI_MAXITER 20
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static void matmul2(double C[2][2], double A[2][2], double B[2][2]);
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static void matmul2t(double C[2][2], double A[2][2], double B[2][2]);
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// ----------------------------------------------------------------
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// Jacobi real-symmetric eigensolver. Loosely adapted from Numerical Recipes.
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//
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// Note: this is coded for n=2 (to implement PCA linear regression on 2
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// variables) but the algorithm is quite general. Changing from 2 to n is a
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// matter of updating the top and bottom of the function: function signature to
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// take double** matrix, double* eigenvector_1, double* eigenvector_2, and n;
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// create copy-matrix and make-identity matrix functions; free temp matrices at
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// the end; etc.
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void mlr_get_real_symmetric_eigensystem(
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double matrix[2][2], // Input
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double *peigenvalue_1, // Output: dominant eigenvalue
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double *peigenvalue_2, // Output: less-dominant eigenvalue
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double eigenvector_1[2], // Output: corresponding to dominant eigenvalue
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double eigenvector_2[2]) // Output: corresponding to less-dominant eigenvalue
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{
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double L[2][2] = {
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{ matrix[0][0], matrix[0][1] },
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{ matrix[1][0], matrix[1][1] }
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};
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double V[2][2] = {
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{ 1.0, 0.0 },
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{ 0.0, 1.0 },
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};
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double P[2][2], PT_A[2][2];
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int n = 2;
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int found = 0;
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for (int iter = 0; iter < JACOBI_MAXITER; iter++) {
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double sum = 0.0;
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for (int i = 1; i < n; i++)
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for (int j = 0; j < i; j++)
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sum += fabs(L[i][j]);
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if (fabs(sum*sum) < JACOBI_TOLERANCE) {
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found = 1;
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break;
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}
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for (int p = 0; p < n; p++) {
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for (int q = p+1; q < n; q++) {
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double numer = L[p][p] - L[q][q];
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double denom = L[p][q] + L[q][p];
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if (fabs(denom) < JACOBI_TOLERANCE)
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continue;
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double theta = numer / denom;
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int sign_theta = (theta < 0) ? -1 : 1;
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double t = sign_theta / (fabs(theta) + sqrt(theta*theta + 1));
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double c = 1.0 / sqrt(t*t + 1);
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double s = t * c;
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for (int pi = 0; pi < n; pi++)
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for (int pj = 0; pj < n; pj++)
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P[pi][pj] = (pi == pj) ? 1.0 : 0.0;
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P[p][p] = c;
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P[p][q] = -s;
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P[q][p] = s;
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P[q][q] = c;
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// L = P.transpose() * L * P
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// V = V * P
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matmul2t(PT_A, P, L);
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matmul2(L, PT_A, P);
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matmul2(V, V, P);
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}
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}
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}
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if (!found) {
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fprintf(stderr,
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"Jacobi eigensolver: max iterations (%d) exceeded. Non-symmetric input?\n", JACOBI_MAXITER);
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exit(1);
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}
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double eigenvalue_1 = L[0][0];
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double eigenvalue_2 = L[1][1];
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double abs1 = fabs(eigenvalue_1);
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double abs2 = fabs(eigenvalue_2);
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if (abs1 > abs2) {
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*peigenvalue_1 = eigenvalue_1;
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*peigenvalue_2 = eigenvalue_2;
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eigenvector_1[0] = V[0][0]; // Column 0 of V
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eigenvector_1[1] = V[1][0];
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eigenvector_2[0] = V[0][1]; // Column 1 of V
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eigenvector_2[1] = V[1][1];
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} else {
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*peigenvalue_1 = eigenvalue_2;
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*peigenvalue_2 = eigenvalue_1;
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eigenvector_1[0] = V[0][1];
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eigenvector_1[1] = V[1][1];
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eigenvector_2[0] = V[0][0];
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eigenvector_2[1] = V[1][0];
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}
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}
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// xxx cmt mem-mgmt
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static void matmul2(
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double C[2][2], // Output
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double A[2][2], // Input
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double B[2][2]) // Input
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{
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double T[2][2];
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int n = 2;
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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double sum = 0.0;
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for (int k = 0; k < n; k++)
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sum += A[i][k] * B[k][j];
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T[i][j] = sum;
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}
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}
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for (int i = 0; i < n; i++)
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for (int j = 0; j < n; j++)
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C[i][j] = T[i][j];
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}
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static void matmul2t(
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double C[2][2], // Output
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double A[2][2], // Input
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double B[2][2]) // Input
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{
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double T[2][2];
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int n = 2;
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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double sum = 0.0;
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for (int k = 0; k < n; k++)
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sum += A[k][i] * B[k][j];
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T[i][j] = sum;
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}
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}
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for (int i = 0; i < n; i++)
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for (int j = 0; j < n; j++)
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C[i][j] = T[i][j];
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}
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11
c/lib/mlrmath.h
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11
c/lib/mlrmath.h
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@ -0,0 +1,11 @@
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#ifndef MLRMATH_H
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#define MLRMATH_H
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void mlr_get_real_symmetric_eigensystem(
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double matrix[2][2], // Input
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double *peigenvalue_1, // Output: dominant eigenvalue
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double *peigenvalue_2, // Output: less-dominant eigenvalue
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double eigenvector_1[2], // Output: corresponding to dominant eigenvalue
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double eigenvector_2[2]); // Output: corresponding to less-dominant eigenvalue
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#endif // MLRMATH_H
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@ -22,12 +22,57 @@ double mlr_get_cov(unsigned long long n, double sumx, double sumy, double sumxy)
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void mlr_get_cov_matrix(unsigned long long n,
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double sumx, double sumx2, double sumy, double sumy2, double sumxy,
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double* pq00, double* pq01, double* pq10, double* pq11)
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double Q[2][2])
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{
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double denominator = n - 1;
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*pq00 = (sumx2 - sumx*sumx/n) / denominator;
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*pq01 = (sumxy - sumx*sumy/n) / denominator;
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*pq10 = *pq01;
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*pq11 = (sumy2 - sumy*sumy/n) / denominator;
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Q[0][0] = (sumx2 - sumx*sumx/n) / denominator;
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Q[0][1] = (sumxy - sumx*sumy/n) / denominator;
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Q[1][0] = Q[0][1];
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Q[1][1] = (sumy2 - sumy*sumy/n) / denominator;
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}
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// ----------------------------------------------------------------
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// Principal component analysis can be used for linear regression:
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// * Compute the covariance matrix for the x's and y's.
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// * Find its eigenvalues and eigenvectors of the cov. (This is real-symmetric
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// so Jacobi iteration is simple and fine.)
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// * The principal eigenvector points in the direction of the fit.
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// * The covariance matrix is computed on zero-mean data so the intercept
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// is zero, of the form (y - nu) = m*(x - mu) where mu and nu are x and y
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// means, respectively.
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// * If the fit is perfect then the 2nd eigenvalue will be zero; if the fit is
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// good then the 2nd eigenvalue will be smaller; if the fit is bad then
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// they'll be about the same. I use 1 minus ratio of absolute values
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// of 2nd to 1st eigenvalues as an indication of quality of the fit.
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//
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// Standard ("ordinary least-squares") linear regression is appropriate when
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// the errors are thought to be all in the y's. PCA ("total least-squares") is
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// appropriate when the x's and the y's are thought to both have errors.
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void mlr_get_linear_regression_pca(
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// Inputs:
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double eigenvalue_1,
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double eigenvalue_2,
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double eigenvector_1[2],
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double eigenvector_2[2],
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double x_mean, double y_mean,
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// Outputs:
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double* pm, double* pb, double* pquality)
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{
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double abs_1 = fabs(eigenvalue_1);
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double abs_2 = fabs(eigenvalue_2);
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double quality = 1.0;
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if (abs_1 == 0.0)
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quality = 0.0;
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else if (abs_2 > 0.0)
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quality = 1.0 - abs_2 / abs_1;
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double a0 = eigenvector_1[0];
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double a1 = eigenvector_1[1];
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double m = a1 / a0;
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double b = y_mean - m * x_mean;
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*pm = m;
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*pb = b;
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*pquality = quality;
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}
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@ -2,9 +2,20 @@
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#define MLRSTAT_H
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double mlr_get_stddev(unsigned long long count, double sum, double sum2);
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double mlr_get_cov(unsigned long long count, double sumx, double sumy, double sumxy);
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void mlr_get_cov_matrix(unsigned long long n,
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double sumx, double sumx2, double sumy, double sumy2, double sumxy,
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double* pq00, double* pq01, double* pq10, double* pq11);
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double sumx, double sumx2, double sumy, double sumy2, double sumxy, double Q[2][2]);
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void mlr_get_linear_regression_pca(
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// Inputs:
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double eigenvalue_1,
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double eigenvalue_2,
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double eigenvector_1[2],
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double eigenvector_2[2],
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double x_mean, double y_mean,
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// Outputs, with quality 1 being a tight fit and quality 0 being a loose one.
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double* pm, double* pb, double* pquality);
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#endif // MLRSTAT_H
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@ -3,6 +3,7 @@
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#include <string.h>
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#include <math.h>
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#include "lib/mlrutil.h"
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#include "lib/mlrmath.h"
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#include "lib/mlrstat.h"
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#include "containers/sllv.h"
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#include "containers/slls.h"
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@ -13,9 +14,10 @@
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#include "mapping/mappers.h"
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#include "cli/argparse.h"
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#define DO_CORR 0x11
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#define DO_COV 0x22
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#define DO_COVX 0x33
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#define DO_CORR 0x11
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#define DO_COV 0x22
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#define DO_COVX 0x33
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#define DO_LINREG_PCA 0x44
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// ----------------------------------------------------------------
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typedef void stats2_put_func_t(void* pvstate, double x, double y);
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@ -29,6 +31,8 @@ typedef struct _stats2_t {
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typedef stats2_t* stats2_alloc_func_t(static_context_t* pstatx);
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// xxx move to mlrstat.h/c
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// ----------------------------------------------------------------
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// Univariate linear regression
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// ----------------------------------------------------------------
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@ -216,6 +220,7 @@ typedef struct _stats2_corr_cov_state_t {
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double sumxy;
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double sumy2;
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int do_which;
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// xxx do_verbose;
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static_context_t* pstatx;
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} stats2_corr_cov_state_t;
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void stats2_corr_cov_put(void* pvstate, double x, double y) {
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@ -241,19 +246,62 @@ void stats2_corr_cov_get(void* pvstate, char* name1, char* name2, lrec_t* poutre
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lrec_put(poutrec, key10, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, key11, "", LREC_FREE_ENTRY_KEY);
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} else {
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double q00, q01, q10, q11;
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double Q[2][2];
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mlr_get_cov_matrix(pstate->count,
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pstate->sumx, pstate->sumx2, pstate->sumy, pstate->sumy2, pstate->sumxy,
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&q00, &q01, &q10, &q11);
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char* val00 = mlr_alloc_string_from_double(q00, pstate->pstatx->ofmt);
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char* val01 = mlr_alloc_string_from_double(q01, pstate->pstatx->ofmt);
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char* val10 = mlr_alloc_string_from_double(q10, pstate->pstatx->ofmt);
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char* val11 = mlr_alloc_string_from_double(q11, pstate->pstatx->ofmt);
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pstate->sumx, pstate->sumx2, pstate->sumy, pstate->sumy2, pstate->sumxy, Q);
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char* val00 = mlr_alloc_string_from_double(Q[0][0], pstate->pstatx->ofmt);
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char* val01 = mlr_alloc_string_from_double(Q[0][1], pstate->pstatx->ofmt);
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char* val10 = mlr_alloc_string_from_double(Q[1][0], pstate->pstatx->ofmt);
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char* val11 = mlr_alloc_string_from_double(Q[1][1], pstate->pstatx->ofmt);
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lrec_put(poutrec, key00, val00, LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, key01, val01, LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, key10, val10, LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, key11, val11, LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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}
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} else if (pstate->do_which == DO_LINREG_PCA) {
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char* keym = mlr_paste_4_strings(name1, "_", name1, "_pca_m");
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char* keyb = mlr_paste_4_strings(name1, "_", name2, "_pca_b");
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char* keyq = mlr_paste_4_strings(name2, "_", name1, "_pca_quality");
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char* keyl1 = mlr_paste_4_strings(name2, "_", name1, "_pca_eival1");
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char* keyl2 = mlr_paste_4_strings(name2, "_", name1, "_pca_eival2");
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char* keyv11 = mlr_paste_4_strings(name2, "_", name1, "_pca_eivec11");
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char* keyv12 = mlr_paste_4_strings(name2, "_", name1, "_pca_eivec12");
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char* keyv21 = mlr_paste_4_strings(name2, "_", name1, "_pca_eivec21");
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char* keyv22 = mlr_paste_4_strings(name2, "_", name1, "_pca_eivec22");
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if (pstate->count < 2LL) {
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lrec_put(poutrec, keym, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyb, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyq, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyl1, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyl2, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyv11, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyv12, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyv21, "", LREC_FREE_ENTRY_KEY);
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lrec_put(poutrec, keyv22, "", LREC_FREE_ENTRY_KEY);
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} else {
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double Q[2][2];
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mlr_get_cov_matrix(pstate->count,
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pstate->sumx, pstate->sumx2, pstate->sumy, pstate->sumy2, pstate->sumxy, Q);
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double l1, l2; // Eigenvalues
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double v1[2], v2[2]; // Eigenvectors
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mlr_get_real_symmetric_eigensystem(Q, &l1, &l2, v1, v2);
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double x_mean = pstate->sumx / pstate->count;
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double y_mean = pstate->sumy / pstate->count;
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double m, b, q;
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mlr_get_linear_regression_pca(l1, l2, v1, v2, x_mean, y_mean, &m, &b, &q);
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lrec_put(poutrec, keym, mlr_alloc_string_from_double(m, pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyb, mlr_alloc_string_from_double(b, pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyq, mlr_alloc_string_from_double(q, pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyl1, mlr_alloc_string_from_double(l1, pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyl2, mlr_alloc_string_from_double(l2, pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyv11, mlr_alloc_string_from_double(v1[0], pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyv12, mlr_alloc_string_from_double(v1[1], pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyv21, mlr_alloc_string_from_double(v2[0], pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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lrec_put(poutrec, keyv22, mlr_alloc_string_from_double(v2[1], pstate->pstatx->ofmt), LREC_FREE_ENTRY_KEY|LREC_FREE_ENTRY_VALUE);
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}
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} else {
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char* suffix = (pstate->do_which == DO_CORR) ? "corr" : "cov";
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char* key = mlr_paste_5_strings(name1, "_", name2, "_", suffix);
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@ -296,6 +344,9 @@ stats2_t* stats2_cov_alloc(static_context_t* pstatx) {
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stats2_t* stats2_covx_alloc(static_context_t* pstatx) {
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return stats2_corr_cov_alloc(DO_COVX, pstatx);
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}
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stats2_t* stats2_linreg_pca_alloc(static_context_t* pstatx) {
|
||||
return stats2_corr_cov_alloc(DO_LINREG_PCA, pstatx);
|
||||
}
|
||||
|
||||
// ----------------------------------------------------------------
|
||||
typedef struct _stats2_lookup_t {
|
||||
|
|
@ -304,11 +355,12 @@ typedef struct _stats2_lookup_t {
|
|||
static_context_t* pstatx;
|
||||
} stats2_lookup_t;
|
||||
static stats2_lookup_t stats2_lookup_table[] = {
|
||||
{"linreg", stats2_linreg_alloc},
|
||||
{"r2", stats2_r2_alloc},
|
||||
{"corr", stats2_corr_alloc},
|
||||
{"cov", stats2_cov_alloc},
|
||||
{"covx", stats2_covx_alloc},
|
||||
{"linreg", stats2_linreg_alloc},
|
||||
{"r2", stats2_r2_alloc},
|
||||
{"corr", stats2_corr_alloc},
|
||||
{"cov", stats2_cov_alloc},
|
||||
{"covx", stats2_covx_alloc},
|
||||
{"linregpca", stats2_linreg_pca_alloc},
|
||||
};
|
||||
static int stats2_lookup_table_length = sizeof(stats2_lookup_table) / sizeof(stats2_lookup_table[0]);
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue