View source for DMelt:Numeric/7 PCA Analysis


{{sidebar box|[[DMelt:Start|Table of contents]]}}

= PCA analysis =

Principal Component Analysis (PCA) is an important for many applications. Read [[Principal_component_analysis]].

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. 

<ifauth>
<jcode lang="python">
from jhplot.math.pca import *
from Jama import Matrix

trainingData = Matrix([[1, 2, 3, 4, 5, 6],[6, 5, 4, 3, 2, 1],[2, 2, 2, 2, 2, 2]])
pca = PCA(trainingData)
testData = Matrix([[1, 2, 3, 4, 5, 6],[1, 2, 1, 2, 1, 2]]);

transformedData = pca.transform(testData, PCA.TransformationType.WHITENING);
print transformedData.toString() 
</jcode>

More details on the corresponding Java code is in [https://github.com/mkobos/pca_transform pca_transform].

</ifauth>

The output of this code is shown below:

<jcode lang="python">
-0.9999999999999998, -0.5773502691896268
-0.08571428571428596, 1.732050807568878
</jcode>

[[Principal_component_analysis]] is used for [[Dimensionality_reduction]],  a method of transforming complex data in large dimensions 
into data with lesser dimensions  ensuring that it conveys similar information. 

It was described in [DMelt:Statistics/6_Dimensionality_reduction]. 
Let us consider [http://datamelt.org/examples/data/iris_org.arff  IRIS dataset] <ref>Fisher,R.A. "The use of multiple measurements in taxonomic problems", Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to Mathematical Statistics" (John Wiley, NY, 1950).</ref>. 
The IRIS data set has 4 numerical attributes. Therefore, it is difficult for  humans to visualize such data.
Therefore, one can reduce the dimensionality of this dataset down to two. 
We will use [[Principal component analysis]] (PCA)  which 
convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.
PCA needs the data samples to have a mean of ZERO, so we need a transform to ensue this property as well.

Here is the code that uses the Java package <javadoc sc>jsat.datatransform.PCA</javadoc> to perform this transformation:

<jcode lang="python">
dmelt 76974242.py
</jcode>

The output image is shown here: 

<jput>
image 76974242
</jput>

[[Category: Statistics]]
[[Category:Data mining]]