Visual Analytics - Linear Dimension Reduction

This lecture motivates the frequent use of dimension reduction (DR) in visual analytics and gives examples for linear DR techniques. Often larger datasets contain dimensions where the variance is very low or where the values are strongly correlated to values of other dimensions. This gives rise to reduce the set of dimensions to the number of „intrinisc dimensions“ of the dataset. Dimension reduction is related to but different from feature selection – an essential data mining technique. We compare both approaches. Among the linear techniques, we discuss principal component analysis (PCA) in more detail. Pre-processing is often necessary to make the dimensions appropriate for a PCA. It may include autoscaling and zero transformation. The discussion of PCA is focussed on the visual representation of the results and in the interpretation of these visualizations. Interpretation is challenging with PCA since a new coordinate system is created where the axis do not correspond to the original data. For both linear as well as non-linear techniques we can compute a quality metric that represents how well the projected data correspond to the original high dimensional data. However, this is just one global measure – whether the relations the analyst is interested in are well-preserved cannot be guaranteed. We discuss visual aids for pre-processing the data and for exploring the results. As further linear techniques we briefly explain factor analysis, a dimension reduction technique from psychology and projection pursuit, a technique that leads to visualizations where clusters can be perceived well. Chapters: 00:00 - Outline and Introduction 19:26 - Feature Selection 22:24 - Dimension Reduction 30:17 - Linear Techniques 53:13 - Factor Analysis 1:02:09 - Summary