Feature analysis and dimensionality reduction
Among the first tools to master are the different feature analysis and dimensionality reduction techniques. As in supervised learning, the need for reducing dimensionality arises from numerous reasons similar to those discussed earlier for feature selection and reduction.
A smaller number of discriminating dimensions makes visualization of data and clusters much easier. In many applications, unsupervised dimensionality reduction techniques are used for compression, which can then be used for transmission or storage of data. This is particularly useful when the larger data has an overhead. Moreover, applying dimensionality reduction techniques can improve the scalability in terms of memory and computation speeds of many algorithms.
Notation
We will use similar notation to what was used in the chapter on supervised learning. The examples are in d dimensions and are represented as vector:
x = (x1,x2,…xd )T
The entire dataset containing n examples...
