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Bayesian Reasoning and Machine Learning by David Barber

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15

Unsupervised linear dimension reduction

High-dimensional data is prevalent in machine learning and related areas. Indeed, there often arises the situation in which there are more data dimensions than there are data examples. In such cases we seek a lower-dimensional representation of the data. In this chapter we discuss some standard methods which can also improve the prediction performance by removing ‘noise’ from the representation.

15.1   High-dimensional spaces – low-dimensional manifolds

In machine learning problems data is often high dimensional – images, bag-of-word descriptions, gene-expressions etc. In such cases we cannot expect the training data to densely populate the space, meaning that there will be large parts in which little ...

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