In this work, we present optimal and approximate algorithms
for L1-norm Principal-Component Analysis (L1-PCA), recently introduced
in the Signal Processing and Machine Learning literature. In
the first chapter, we start with an introduction of standard PrincipalComponent
Analysis(PCA) and discuss its general application for
dimensionality reduction. In chapter 2, we introduce and formulate
optimal algorithms for L1-subspace signal processing, the first optimal
algorithm for its exact computation. In the chapters that follow,
we present four more published algorithms for the approximate calculation
of the L1-norm principle components (L1-PC) of a general
real-valued matrix, as well as any optimal algorithm for the special
case of non-negative data. In the last chapter, we conclude with remarks
on the efficiency of the presented algorithms and the value of
L1-PCA as a new paradigm outlier-resistant signal processing and
data analysis.
Principal Component Analysis
