Difference between revisions of "Principal Component Analysis"
Jump to navigation
Jump to search
Kevin Dunn (talk | contribs) |
Kevin Dunn (talk | contribs) m |
||
| Line 1: | Line 1: | ||
{{ClassSidebar | |||
| date = | |||
| dates_alt_text = | |||
| vimeoID1 = 29191853 | |||
| vimeoID2 = | |||
| vimeoID3 = | |||
| course_notes_PDF = | |||
| course_notes_alt = Course notes | |||
| overheads_PDF = | |||
| assignment_instructions = <!-- --> | |||
| assignment_solutions = <!-- --> | |||
| video_download_link_MP4 = http://connectmv.com/media/latent/video/Class-2A.mp4 | |||
| video_download_link_MP4_size = 290.1Mb | |||
| video_download_link2_MP4 = http://connectmv.com/media/latent/video/Class-2B.mp4 | |||
| video_download_link2_MP4_size = Mb | |||
| video_download_link3_MP4 = http://connectmv.com/media/latent/video/Class-2C.mp4 | |||
| video_download_link3_MP4_size = Mb | |||
| video_notes1 = | |||
* 00:00 to 21:37 Recap and overview of this class | |||
* 21:38 to 42:01 Preprocessing: centering and scaling | |||
* 42:02 to 57:07 Geometric view of PCA | |||
| video_notes2 = | |||
{{{!}} | |||
{{!}}- | |||
{{!}} 00:00 {{!}}{{!}}to{{!}}{{!}} 46:50 {{!}}{{!}} {{!}}{{!}} Details coming soon | |||
{{!}}- | |||
{{!}}} | |||
|| video_notes3 = | |||
{{{!}} | |||
{{!}}- | |||
{{!}} 00:00 {{!}}{{!}}to{{!}}{{!}} 1:03:50 {{!}}{{!}} {{!}}{{!}} Details coming soon | |||
{{!}}- | |||
{{!}}} | |||
}} | |||
== Class notes == | == Class notes == | ||
Revision as of 13:31, 18 September 2011
| |||||
|
Video timing |
|||||
| |||||
Class notes
<pdfreflow> class_date = 16 September 2011 [1.65 Mb] button_label = Create my projector slides! show_page_layout = 1 show_frame_option = 1 pdf_file = lvm-class-2.pdf </pdfreflow>
- Also download these 3 CSV files and bring them on your computer:
- Peas dataset: http://datasets.connectmv.com/info/peas
- Food texture dataset: http://datasets.connectmv.com/info/food-texture
- Food consumption dataset: http://datasets.connectmv.com/info/food-consumption
Class preparation
Class 2 (16 September)
- Reading for class 2
- Linear algebra topics you should be familiar with before class 2:
- matrix multiplication
- that matrix multiplication of a vector by a matrix is a transformation from one coordinate system to another (we will review this in class)
- linear combinations (read the first section of that website: we will review this in class)
- the dot product of 2 vectors, and that they are related by the cosine of the angle between them (see the geometric interpretation section)
Class 3 (23 September)
- Least squares:
- what is the objective function of least squares
- how to calculate the two regression coefficients \(b_0\) and \(b_1\) for \(y = b_0 + b_1x + e\)
- understand that the residuals in least squares are orthogonal to \(x\)
- Some optimization theory:
- how an optimization problem is written with equality constraints
- the Lagrange multiplier principle for solving simple, equality constrained optimization problems
- Reading on cross validation