The Mathematics behind Principle Component Analysis

The Mathematics behind Principle Component Analysis

Basic Knowledge of Mathematics behind PCA. The Logic behind Principle Component Analysis is to reduce the dimensionality of data sets .


The Logic behind Principle Component Analysis is to _reduce the dimensionality _of data sets . There are so many features or columns in our datasets which are not much helpful in prediction as well as they don’t have much knowledge about the data due to which model take much time to compute and predict the result. So with the help of PCA we are going to transform a new set of features which are uncorrelated as well as ordered.

For Understanding the maths Behind PCA we have some Knowledge about the term which we are going to use to reduce the dimensionality.

  • Mean
  • Variance
  • Covariance
  • Linear Transformation
  • EigenValue
  • EigenVector


The Mean is the most basic quantity in statistics.The means tell us where the measurement are centered.

Let there is a columns X in which we have record of weight of 10 students.

{ a1 ,a2 ,a3…….a10 }

μA = 1/n(a1 +...+a10)

Variance :-

In variance we understand how spread out are the measurements ?

In this we calculate each difference from the mean and Square of it and then take average of it , gives us the variance.

Var(A)= 1/n (a1 −μA)2 +…….+(an −μA)2

data analysis

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