## Author

Cheolmin Kim, Ph.D candidate in Industrial Engineering and Management Sciences, Northwestern University

CheolminKim2019@u.northwestern.edu

**Introduction**

Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques. Given a large set of possibly correlated features, it attempts to find a small set of features

*principal components*that retain as much information as possible. To generate such new dimensions, it linearly transforms original features by multiplying

*loading vectors*in a way that newly generated features are orthogonal and have the largest variances with respect to the L2-norm.

Although PCA has enjoyed great popularity, it still has some limitations. First, since it generates new dimensions through a linear combination of original features, it is not able to capture non-linear relationships between features. Second, as it uses the L2-norm for measuring variance, its solutions tend to be substantially affected by influential outliers. To overcome these limitations of PCA, we present L1-norm kernel PCA model that is robust to outliers as well as captures non-linear relationship between features.