There are two tasks that we are mostly concerned with in unsupervised learning: dimensionality reduction and clustering.
Dimensionality reduction is used to help visualize higher-dimensional data in a systematic way. This is useful because our human brains can visualize only three spatial dimensions (and possibly, a temporal one), but most datasets involve much higher dimensions.
The typical technique used in dimensionality reduction is Principal Component Analysis (PCA). PCA involves using linear algebra techniques to project higher-dimensional data onto a lower-dimensional space. This inevitably involves the loss of information, but often by projecting along the correct set and number of dimensions, the information loss can be minimized. A common dimensionality reduction technique is to find the combination of variables that explain the most variance (proxy for information) in our data and project along these dimensions.
In the case...