Practical Machine Learning Lecture: Dimensionality reduction

Linear dimensionality reduction
Lecturer: Percy Liang
Date: Feb 19

[Lecture slides]

General theory

Shawe-Taylor and Cristianini. Kernel Methods for Pattern Analysis. 2004. A generally good introduction to kernel methods. Contains a part on PCA and CCA and their kernelized versions.
de Bie, et al. Eigenproblems in Pattern Recognition. 2004. Gives some general theory on generalized eigenvalue problems, which encompases PCA, CCA, FDA, PLS, and MLR. Also gives an iterative algorithm to solve these problems.
Borga, et al. A unified approach to PCA, PLS, MLR and CCA. Another paper that uses generalized eigenproblems to unify a bunch of dimensionality reduction techniques.
Derivation of Maximum Likelihood Factor Analysis using EM.
Chen. Principal Component Analysis With Missing Data and Outliers. Summarizes some techniques to make PCA robust to outliers and handle missing data with a probabilistic model.

Non-negative matrix factorization (NMF)

Lee, Seung. Learning the parts of objects with nonnegative matrix factorization..
Hoyer. Non-negative Matrix Factorization with Sparseness Constraints.
Lin. Projected Gradient Methods for Non-negative Matrix Factorization.
Srebro. Learning with Matrix Factorizations.
Buntine, Jakulin: Discrete Principal Component Analysis.
Matlab code for NMF.

Independent component analysis (ICA)

Hyv\"arinen, Karhunen, Oja. Independent Component Analysis (introduction chapter).
Hyv\"arinen, Oja. Independent Component Analysis: Algorithms and Applications. 2000.
Bach, Jordan. Kernel Independent Component Analysis. Some ICA software. FastICA.

Applications

There are tons of papers that use these dimensionality reduction techniques. Below is a small selection; a quick Google search will turn up more.

Turk and Pentland. Face recognition using eigenfaces. 1991. Used PCA on images of faces (eigenfaces) followed by a distance-based classifier for face recognition. This work is considered the first successful face recognition system. A summary of the techniques written 11 years later.
Tutorial on component analysis for vision. 2006. Describes applications of PCA and CCA in computer vision.
Hardoon, et al. Canonical correlation analysis; An overview with application to learning methods. 2003. Applies kernel CCA on two views (one of images and one of text) for image retrieval
Yamanishi, et al. Heterogeneous data comparison and gene selection with kernel canonical correlation analysis.
Matlab code for CCA.
Schuetze. Distributional POS tagging. 1995. SVD applied in natural language processing. Each data point is the context in which a word token appears in a sentence. A lower-dimensional representation is useful because these context vectors are very high dimensional. K-means clustering is used afterwards.
Ando, Zhang. A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data. 2005. Interesting use of SVD where we find a low-dimensional representation, not of data points, but of classifiers. The situation here is multi-task learning, where we have many (linear) classifiers and would like to learn some common structure between.
Lakhina, et al. Diagnosing Network-Wide Traffic Anomalies. 2004. Use PCA as a model of "normal network traffic" on links. Traffic that deviates from the subspace is deemed anomalous.
Larsen, et al. Sensitivity of PCA for Traffic Anomaly Detection. 2007. Studies the limitations of using PCA for detecting network anomalies.