Principle Component Analysis (PCA)
Principle Component Analysis is a way of identifying patterns in data, and expressing the data in such a way as to highlight their similarities and differences. Since patterns in data can be hard to find in data of high dimension, where the luxury of graphical representation is not available, PCA is a powerful tool for analyzing data.
The other main advantage of PCA is that once you have found these patterns in the data, and you compress the data, ie. by reducing the number of dimensions, without much loss of information. This technique used a lot in image compression.
- PCA completely decorrelates the original signal. Formally speaking, the transform coefficients are statistically independent for a Gaussian signal
- PCA optimizes the repacking of the signal energy, such that most of the signal energy is contained in the fewest transforms coefficients.
- It minimizes the total entropy of the signal
- For any amount of compression the mean square errir in the reconstruction is minimized.
About this code
The PCA is generic, and will run on a variety of matrices. In my particular case, I was analyzing time series of power consumption for various pieces of large equipment (compressors, large fans, etc)