CSE 40171: Artificial Intelligence. Learning from Data: Unsupervised Learning
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1 CSE 40171: Artificial Intelligence Learning from Data: Unsupervised Learning 32
2 Homework #6 has been released. It is due at 11:59PM on 11/7. 33
3 CSE Seminar: 11/1 Amy Reibman Purdue University 3:30pm DBART 138 Video Quality in an Age of Universal Cameras 34
4 Recap: Classification Classification systems: Supervised learning Make a prediction given evidence Useful when you have labeled data Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188 Image credit:
5 Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188 Clustering
6 Clustering Basic idea: group together similar instances Example: 2D point patterns What could similar mean? One option: small (squared) Euclidean distance Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
7 Clustering: K-means Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS
8 K-Means An iterative clustering algorithm Pick K random points as cluster centers (means) Alternate: - Assign data instances to closest mean -Assign each mean to the average of its assigned points Stop when no points assignments change Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
9 K-means Example
10 K-Means as Optimization Consider the total distance to the means: points assignments means Each iteration reduces phi Two stages each iteration: Update assignments: fix means c, change assignments a Update means: fix assignments a, change means c Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
11 Phase I: Update Assignments For each point, re-assign to closest mean: Can only decrease total distance phi! Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
12 Phase II: Update Means Move each mean to the average of its assigned points: Also can only decrease total distance (Why?) Fun fact: the point y with minimum squared Euclidean distance to a set of points {x} is their mean Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
13 Initialization K-means is non-deterministic Requires initial means It does matter what you pick! What can go wrong? Various schemes for preventing this kind of thing: variance-based split / merge, initialization heuristics Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
14 K-Means Getting Stuck A local optimum: Why doesn t this work out like the earlier example, with the purple taking over half the blue? Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
15 K-Means Questions Will K-means converge? To a global optimum? Will it always find the true patterns in the data? If the patterns are very very clear? Will it find something interesting? Do people ever use it? How many clusters to pick? Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
16 Clustering: PCA 47
17 Principal Components Analysis Technique used to emphasize variation and bring out strong patterns in a dataset It's often used to make data easy to explore and visualize Can also be used for data clustering Intuitive visual explanation:
18 Principal Components Analysis Intuitive visual explanation:
19 Eigenvalue Decomposition Define a transformation matrix, W: y j =W T x j,j =1, 2...N m-dimensional orthonormal (W R m n ) n-dimensional S T = NX (x j x)(x j x) T Data Scatter Matrix j=1!50
20 Eigenvalue Decomposition fs T = NX (y j ȳ)(y j ȳ) T =W T S T W j=1 Trans. Data Scatter Matrix Eigenvectors of ST W opt = arg max W T S T W = {v 1,v 2...v k } W!51
21 Intuitive visual explanation:
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24 Clustering with PCA
25 Clustering: Agglomerative Clustering Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
26 Agglomerative Clustering Agglomerative (hierarchical) clustering: First merge very similar instances Incrementally build larger clusters out of smaller clusters Algorithm: Maintain a set of clusters Initially, each instance in its own cluster Repeat: Pick the two closest clusters Merge them into a new cluster Stop when there s only one cluster left Produces not one clustering, but a family of clusterings represented by a dendrogram Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
27 Agglomerative Clustering How should we define closest for clusters with multiple elements? Many options Closest pair (single-link clustering) Farthest pair (complete-link clustering) Average of all pairs Ward s method (min variance, like k- means) Different choices create different clustering behaviors Slide credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188
28 Example: Google News Story groupings: unsupervised clustering Top-level categories: supervised classification
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