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PCA analysis

Principal Component Analysis (PCA) is an important for many applications.

Snippet from Wikipedia: Principal component analysis

Principal component analysis (PCA) is a statistical procedure that uses orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to (i.e., uncorrelated with) the preceding components. Principal components are guaranteed to be independent if the data set is jointly normally distributed.

Below we will show examples of Principal Component Analysis (PCA) data transformation using matrices as input. We will consider a situation when some of the columns in the data matrix are linearly dependent or when there are more columns than rows in the data matrix i.e. there are more dimensions than samples in the data set. In the above example we train the data and then apply to a test data.

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-0.9999999999999998, -0.5773502691896268
-0.08571428571428596, 1.732050807568878