Lecture 11: Clustering Introduction and Projects Machine Learning

Transcription

1 Lecture 11: Clustering Introduction and Projects Machine Learning Andrew Rosenberg March 12, /1

2 Last Time Junction Tree Algorithm Efficient Marginals in Graphical Models 2/1

3 Today Clustering Project Details 3/1

4 Clustering Clustering Clustering is an unsupervised Machine Learning application The task is to group similar entities into groups. 4/1

5 We do this all the time 5/1

6 We do this all the time 6/1

7 We do this all the time 7/1

8 We can do this in many dimensions 8/1

9 We can do this to many degrees 9/1

10 We can do this in many dimensions 10 /1

11 We do this all the time 11 /1

12 How do we set this up computationally? In Machine Learning, we optimize objective functions to find the best solution. Maximum Likelihood (for Frequentists) Maximum A Posteriori (for Bayesians) Empirical Risk Minimization Loss function Minimization What makes a good cluster? How do we define loss or likelihood in a clustering solution? 12 /1

13 Cluster Evaluation Intrinsic Evaluation Evaluate the compactness of the clusters Extrinsic Evaluation Compare the results to some gold standard labeled data. (Not covered today) 13 /1

14 Intrinsic Evaluation Intercluster Variability (IV) How different are the data points within the same cluster Extracluster Variability (EV) How different are the data points that are in distinct clusters Minimize IV while maximizing EV. Minimize IV EV IV = C d(x, c) x C d(x,c) = x c 14 /1

15 Degenerate Clustering Solutions One Cluster 15 /1

16 Degenerate Clustering Solutions N Clusters 16 /1

17 Clustering Approaches Hierarchical Clustering Partitional Clustering 17 /1

18 Hierarchical Clustering Recursive Partitioning 18 /1

19 Hierarchical Clustering Recursive Partitioning 19 /1

20 Hierarchical Clustering Recursive Partitioning 20 /1

21 Hierarchical Clustering Recursive Partitioning 21 /1

22 Hierarchical Clustering Recursive Partitioning 22 /1

23 Hierarchical Clustering Agglomerative Clustering 23 /1

24 Hierarchical Clustering Agglomerative Clustering 24 /1

25 Hierarchical Clustering Agglomerative Clustering 25 /1

26 Hierarchical Clustering Agglomerative Clustering 26 /1

27 Hierarchical Clustering Agglomerative Clustering 27 /1

28 Hierarchical Clustering Agglomerative Clustering 28 /1

29 Hierarchical Clustering Agglomerative Clustering 29 /1

30 Hierarchical Clustering Agglomerative Clustering 30 /1

31 Hierarchical Clustering Agglomerative Clustering 31 /1

32 Hierarchical Clustering Agglomerative Clustering 32 /1

33 Hierarchical Clustering Agglomerative Clustering 33 /1

34 K-Means Clustering K-Means clustering is a Partitional Clustering Algorithm. Identify different partitions of the space for a fixed number of clusters Input: a value for K the number of clusters. Output: the K centers of clusters centroids 34 /1

35 K-Means Clustering 35 /1

36 K-Means Clustering Algorithm: Given an integer K specifying the number of clusters. Initialize K cluster centroids Select K points from the data set at random Select K points from the space at random For each point in the data set, assign it to the cluster whose center it is closest to. argmin Ci d(x, C i ) Update the centroid based on the points assigned to the cluster. c i = 1 C i x C i x If any data point has changed clusters, repeat. 36 /1

37 Why does K-Means Work? When an assignment is changed, the sum of squared distances of the data point to its assigned cluster is reduced. IV is reduced. When a cluster centroid is moved the sum of squared distances of the data points within that cluster is reduced IV is reduced. At convergence we have found a local minimum of IV 37 /1

38 K-Means Clustering 38 /1

39 K-Means Clustering 39 /1

40 K-Means Clustering 40 /1

41 K-Means Clustering 41 /1

42 K-Means Clustering 42 /1

43 K-Means Clustering 43 /1

44 K-Means Clustering 44 /1

45 K-Means Clustering 45 /1

46 K-Means Clustering 46 /1

47 K-Means Clustering 47 /1

48 K-Means Clustering 48 /1

49 Soft K-Means In K-means, we forced every data point to be the member of exactly one cluster. We can relax this constraint. p(x,c i ) = d(x,c i) j d(x,c j) p(x,c i ) = Based on minimizing entropy of cluster assignment. exp{ d(x,c i)} j exp{ d(x,c j)} We still define a cluster by a centroid, but we calculate the centroid as a weighted center of all the data points. x c i = x p(x,c i) x p(x,c i) Convergence is based on a stopping threshold rather than changing assignments. 49 /1

50 Potential Problems with K-Means Optimal? K-means approaches a local minimum, but this is not guaranteed to be globally optimal. Could you design an approach which is globally optimal? Consistent? Different starting clusters can lead to different cluster solutions 50 /1

51 Potential Problems with K-Means Optimal? K-means approaches a local minimum, but this is not guaranteed to be globally optimal. Could you design an approach which is globally optimal? Sure, in NP. Consistent? Different starting clusters can lead to different cluster solutions 51 /1

52 Suboptimality in K-Means 52 /1

53 Inconsistency in K-Means 53 /1

54 Inconsistency in K-Means 54 /1

55 Inconsistency in K-Means 55 /1

56 Inconsistency in K-Means 56 /1

57 More Clustering K-Nearest Neighbors Gaussian Mixture Models Spectral Clustering We will return to these. 57 /1

58 The Project Research Paper Project 58 /1

59 Research Paper 8-10 pages Reporting on work in 4-5 papers. Scope: One application area or One technique 59 /1

60 Research Paper: Application Areas Identify an application that has made use of machine learning and discuss how. Graphics Game Playing Object Recognition Scrabble Optical Character Recognition Craps Superresolution Prisoner s Dilemma Segmentation Financials Natural Language Processing Stock Prediction Parsing Review Systems Sentiment Analysis Amazon Information Extraction Netflix Speech Facebook Recognition Synthesis Discourse Analysis Intonation 60 /1

61 Research Paper: Techniques Identify a machine learning technique. Describe its use and variants. L1-regularization Non-linear Kernels Loopy Belief Propagation Non-parametric Belief Propagation Soft-Decision Trees Analysis of Neural Network Hidden Layers Structured Learning Generalized Expectation Evaluation Measures Cluster Evaluation Semi-supervised Evaluation Graph Embedding Dimensionality Reduction Feature Selection Graphical Model Construction Non-parametric Bayesian Methods Latent Dirichlet Allocation 61 /1

62 Project Run a Machine Learning Experiment Identify a problem/task data set. Implement one or more ML algorithm Evaluate the approach. Write a Report of the Experiment 4 pages including references. Abstract 1 paragraph summarizing the experiment Introduction describe the Problem Data Describe the data set, features extracted, etc. Method Describe the algorithm/approach Results Present and discuss results Conclusion Summarize the experiment and results. 62 /1

63 Project Ideas: Tasks Projects can take any combination of Tasks and Approaches Graphics Object Classification Facial Recognition Fingerprint Identification Optical Character Recognition Handwriting recognition (for languages/character systems other than English...) Language Topic Classification Sentiment Analysis Speech Recognition Speaker Identification Punctuation Restoration Semantic Segmentation Recognition of Emotion, Sarcasm, etc. SMS Text normalization Chat participant identification Twitter classification/threading 63 /1

64 Games Chess Checkers Poker (Poker Academy Pro) Blackjack Recommenders (Collaborative Filtering) Netflix Courses Jokes Books Facebook? Video Classification Motion classification Segmentation 64 /1

65 Bye Next Hidden Markov Models Viterbi Decoding 65 /1