prVis: Polynomial-Based Visualization

Data can be found here. The datasets contains transactions made by credit cards in September 2013 by european cardholders. Feature 'Time' contains the seconds elapsed between each transaction and the first transaction in the dataset. Thus, we preprocess the 'Time' column to be the time needed for each single transaction, rather than the accumulated time.

Also, since the dataset is highly unbalanced (492 frauds out of 284,807 transactions, which means 492 cases have label 1, and all others have label 0 ), we sample the data to make the sample "balanced". Below the graphs consist of 492 frauds and 492 normal transaction so that for each group they have same number of data points.

prVis

The two groups are nearly perpendicular to each other, suggesting the distict natures of the fraud transactions and normal transactions. Whereas the plot from umap and t-sne reveal no obvious pattern.

prcomp

prcomp produces a similar result to prVis, which reminds us that prVis is essentially polynomial regression + PCA. In this case, PCA along can exploit the data, and prVis preserves that advantage. In other dataset such as Swissroll, prVis can uncover nonlinear relationship of the dataset whereas PCA along produces rather meaningless result.