Analysis of multivariate and high-dimensional data

Table of contents:

I - Classical Methods
1 - Multidimensional Data
2 - Principal Component Analysis
3 - Canonical Correlation Analysis
4 - Discriminant Analysis

II - Factors and Groupings
5 - Norms, Proximities, Features and Dualities
6 - Cluster Analysis
7 - Factor Analysis
8 - Multidimensional Scaling

III - Non-Gaussian Analysis
9 - Towards Non-Gaussianity
10 - Independent Component Analysis
11 - Projection Pursuit
12 - Kernel and More Independent Component Methods
13 - Feature Selection and Principal Component Analysis Revisited

“Big data ” poses challenges that require both classical multivariate methods and contemporary techniques from machine learning and engineering. This modern text equips you for the new world – integrating the old and the new, fusing theory and practice and bridging the gap to statistical learning. The theoretical framework includes formal statements that set out clearly the guaranteed “safe operating zone” for the methods and allow you to assess whether data is in the zone, or near enough. Extensive examples showcase the strengths and limitations of different methods with small classical data, data from medicine, biology, marketing and finance, high-dimensional data from bioinformatics, functional data from proteomics, and simulated data. High-dimension low-sample-size data gets special attention. Several data sets are revisited repeatedly to allow comparison of methods. Generous use of colour, algorithms, Matlab code, and problem sets complete the package. Suitable for master's/ graduate students in statistics and researchers in data -rich disciplines.