TSA Principal Component Analysis VI

TSA Principal Component Analysis Details

Principal component analysis (PCA) computes a new set of uncorrelated multivariate (vector) time series by a transform of coordinate rotation from original correlated multivariate time series.

This VI performs PCA according to the following steps:

1. Calculates the covariance/correlation coefficient matrix

This VI calculates the covariance matrix according to the following equation:

where w = N-1, N is the number of time series samples. The dimension of the covariance matrix is mxm.

This VI calculates the correlation coefficient matrix according to the following equation:

If unified? is TRUE, this VI calculates the correlation coefficients matrix first and then performs PCA. If unified? is FALSE, this VI calculates the covariance matrix first, and then performs PCA.

2. Calculates the eigenvectors and eigenvalues of the matrix

This VI obtains the m eigenvalues l_i and eigenvectors v_i from either covariance matrix or correlation matrix. l_i and v_i satisfy the following equation:

AV_i = l_iV_i, i=1,…, m

where A is an mxm covariance matrix or correlation matrix.

3. Generates the new time series

This VI then computes a new set of uncorrelated multivariate (vector) time series according to the following equation:

X_t^new=V^TX_t

where X_t^new is the new uncorrelated multivariate (vector) time series, and X_t is the original correlated multivariate (vector) time series. Both of them are mxn matrices whose row vectors represent a single channel time series. V is eigenvectors matrix [v₁, v₂,…, v_m].

V also is the weight matrix. Each column of V is one principle component. X_t^new also is the principal component scores. Each row of X_t^new is the scores for one principal component. Each l_i is variance of the scores for one principal component.

Examples

Refer to the following VIs for examples of using the TSA Principal Component Analysis VI:

• Principal Component Analysis VI: labview\examples\Time Series Analysis\TSAGettingStarted
• Image Compression with PCA VI: labview\examples\Time Series Analysis\TSAApplications