# 6.6 - More Examples

6.6 - More Examples## Example 1: Handwritten Digit Recognition

- Goal: Identify single digits 0 \(\sim\) 9 based on images.
- Raw data: Images that are scaled segments from five digit ZIP codes.
- \(16\times16\) eight-bit grayscale maps
- Pixel intensities range from 0 (black) to 255 (white)
- Input data: represent each image as a high-dimensional vector \(x \in \mathbb{R}^{256}\).

PCA can help you to transform the high dimension image data into lower dimension principal components.

## Example 2: Face Recognition

The cumulative effect of nine principal components, adding one PC at a time, for "sad". The more principal components we use the better resolution we get. However, 4 or 5 principal components lead to a good judgment on a sad expression. It is a dramatic dimension reduction considering the original number of variables which is the number of pixels for a figure.

Why do dimensionality reduction?

- Computational: compress data \(\Rightarrow\) time/space efficiency.
- Statistical: fewer dimensions \(\Rightarrow\) better generalization.
- Visualization: understand the structure of data.
- Anomaly detection: describe normal data, detect outliers.

When faced with situations involving high-dimensional data, it is natural to consider projecting those data onto a lower-dimensional subspace without losing important information.

- Variable selection also called
.*feature selection* - Shrinkage: Ridge regression and Lasso.
- Creating a reduced set of linear or nonlinear transformations of the input variables, also called
, e.g. PCA.*feature extraction*

Please finish the quiz for this lesson and the team project on Canvas (check the course schedule for due dates).