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Inner Product Representation of Two-dimensional Array of Data Derived from Singular Value Decomposition
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Description: _ Cross tables or contingency tables are special kinds of two dimensional array of data , cells of which are frequencies or counts. General types of two dimensional array of data, i.e., matrices, can be analyzed by singular value decomposition (SVD). From SVD, we can derive inner product representation of two dimensional array of data, which helps a researcher to comprehend the data intuitively. TwoDimArraySVD.pfd in Files box below explains (1) how to construct inner product representation from SVD, (2) relation of distances in the representation and the data, (3) rotation of the representation, (4) examples (bipolar rating and mono-polar rating), and discussion are presented. In discussion, the proposed method is compared with correspondence analysis. Script files and sample data files are archived in the file iprfiles.zip in Files box below. An example of execution of the file for jupyter notebook is shown in ExecExample.pdf in Files box below.