# Principal Components Decomposition Algorithm

A Principal Components Decomposition Algorithm is a matrix decomposition algorithm that can be applied by a PCA system (to solve a PCA task to return principal components of a matrix).

• AKA: PCA.
• Context:
• In a large data set most of the data are spread around its mean. If we can shift our parameter axes along with this mean point which is of maximum variance then there is a chance that all the hidden nature of the data will be revealed and can be measured through these parameter axes.The PCA provides the algorithm to find the axes around which most of the data are spread. [math]\longrightarrow[/math] [math]\longrightarrow[/math] Here in the first graph the data are plotted in a 2-dimensional space.Then the coordinate axes [math]X[/math] and [math]Y[/math] are shifted to the eigen axes [math]e_1[/math] and [math]e_2[/math].Again most of the data are spread around the eigen axis [math]e_1[/math] then [math]e_2[/math], so the data can be studied with respect to one axis [math]e_1[/math]. This is called dimensionality reduction.PCA provides the algorithm to perform all such task.

• It can be used as a Matrix Dimensionality Compression Algorithm.
• Example(s):
• Counter-Example(s):
• See: Linear Combination, Covariance Matrix, Linear Model, Linear Combination, PCA Score.