Principle Components Analysis

It is a set of variables that define a projection that encapsulates the maximum amount of variation in a dataset and is orthogonal (and therefore uncorrelated) to the previous principle component of the same dataset.

PCA is commonly used in micro array research as a cluster analysis tool.

It is designed to capture the variance in a dataset in terms of principle components.

In effect, one is trying to reduce the dimensionality of the data to summarize the most important (i.e. defining) parts whilst simultaneously filtering out noise. Normalization, however, can sometimes remove this noise and make the data less variate, which could affect the ability of PCA to capture data structure.

Principal component analysis has in practice been used to reduce the dimensionality of problems, and to transform interdependent coordinates into significant and independent ones.

An example used in several particle physics experiments is that of reducing redundant observations of a particle track in a detector to a low-dimensional subspace whose axes correspond to parameters describing the track. Another example is in image processing; where it can be used for color quantization.

Actually, the original descriptors are 'orthogonal' since they can be written as basis vectors (1,0,0,0,...0), (0,1,0,0,...0),...,(0,0,0,0,...1) but may be correlated, whereas the principal components will also be orthogonal to one another, since they are eigenvectors, but will also be uncorrelated since they are eigenvectors of the correlation/covariance matrix.

Hi All,

I'm a research student in data mining. Would you please help me with the PCA codes either in C or C++?

Thanks