STATS 306 B : Unsupervised Learning Spring 2014

Example 1. Digit data (Slide 2:) Here is an example taken from the textbook. This set of hand written digital images contains 130 threes, and each three is a 16 × 16 greyscale image. Hence we may represent each datapoint as a vector of 256 greyscale pixels. (Slide 3:) The figure on the left shows the first two principal components of these images. The rectangular grid is computed by selected quantiles of the two principal components. Based on the projected coordinates on the two directions, the circled points refer to the images that are closest to these vertices of the grid. The figure on the right displays the threes corresponding to the circled points. The vertical component appears to capture changes in line thickness / darkness, while the horizontal component appears to capture changes in the length of the bottom of the three. (Slide 4:) This is a visual representation of the learned two-component PCA model. The first term is the mean of all images, and the following v1 and v2 are two visualized principal directions (the loadings), which can also be called “eigen” threes.