1 / 28

Linear Classifiers

Explore linear classifiers for image classification, understanding distance projection, separating hyperplanes, Perceptron algorithm, and two-layer neural networks. Learn the basics and try an interactive demo.

dennisi
Download Presentation

Linear Classifiers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Linear Classifiers Based on slides by William Cohen, Andrej Karpathy, Piyush Rai

  2. Linear Classifiers • Let’s simplify life by assuming: • Every instance is a vector of real numbers, x=(x1,…,xn). (Notation: boldface x is a vector.) • First we consider only two classes, y=(+1) and y=(-1) • A linear classifier is vector w of the same dimension as x that is used to make this prediction:

  3. x2 Visually, x · w is the distance you get if you “project x onto w” w X1 . w X1 In 3d: lineplane In 4d: planehyperplane … X2 . w The line perpendicular to w divides the vectors classified as positive from the vectors classified as negative. -W

  4. w -W Wolfram MathWorld Mediaboost.com

  5. w -W Notice that the separating hyperplane goes through the origin…if we don’t want this we can preprocess our examples: or where b=w0 is called bias

  6. Question

  7. Back to Image Classification

  8. 3072 numbers in total reshaped into a column vector x

  9. Interactive Web Demo: http://vision.stanford.edu/teaching/cs231n/linear-classify-demo/

  10. ^ ^ Compute: yi = sign(wk . xi ) If mistake: wk+1 = wk + yixi yi yi Perceptron learning instancexi B A • 1957: The perceptron algorithm by Frank Rosenblatt • 1960: Perceptron Mark 1 Computer – hardware implementation • 1969: Minksky & Papert book shows perceptrons limited to linearly separable data • 1970’s: learning methods for two-layer neural networks

More Related