Data Visualization STAT 890, STAT 442, CM 462

1. Data VisualizationSTAT 890, STAT 442, CM 462 Ali Ghodsi Department of Statistics School of Computer Science University of Waterloo aghodsib @uwaterloo.ca September 2006

2. Two Problems Classical Statistics • Infer information from small data sets (Not enough data) Machine Learning • Infer information from large data sets (Too many data)

3. Other Names for ML • Data mining, • Applied statistics • Adaptive (stochastic) signal processing • Probabilistic planning or reasoning are all closely related to the second problem.

4. Applications Machine Learning is most useful when the structure of the task is not well understood but can be characterized by a dataset with strong statistical regularity. • Search and recommendation (e.g. Google, Amazon) • Automatic speech recognition and speaker verification • Text parsing • Face identification • Tracking objects in video • Financial prediction, fraud detection (e.g. credit cards) • Medical diagnosis

5. Tasks • Supervised Learning: given examples of inputs and corresponding desired outputs, predict outputs on future inputs. e.g.: classification, regression • Unsupervised Learning: given only inputs, automatically discover representations, features, structure, etc. e.g.: clustering, dimensionality reduction, Feature extraction

6. Dimensionality Reduction • Dimensionality: The number of measurements available for each item in a data set. • The dimensionality of real world items is very high. • For example: The dimensionality of a 600 by 600 image is 360,000. • The Key to analyzing data is comparing these measurements to find relationships among this plethora of data points. • Usually these measurements are highly redundant, and relationships among data points are predictable.

7. Dimensionality Reduction • Knowing the value of a pixel in an image, it is easy to predict the value of nearby pixels since they tend to be similar. • Knowing that the word “corporation” occurs often in articles about economics, but not very often in articles about art and poetry then it is easy to predict that it will not occur very often in articles about love. • Although there are lots of measurements per item, there are far fewer that are likely to vary. Using a data set that only includes the items likely to vary allows humans to quickly and easily recognize changes in high dimensionality data.

8. Data Representation

9. Data Representation

10. Data Representation

12. -2.19 -3.19 -0.02 1.02 2 by 103 644 by 103 644 by 2 23 by 28 2 by 1 2 by 1 23 by 28

21. Arranging words: Each word was initially represented by a high-dimensional vector that counted the number of times it appeared in different encyclopedia articles. Words with similar contexts are collocated

26. Different Features

27. Glasses vs. No Glasses

28. Beard vs. No Beard

29. Beard Distinction

30. Glasses Distinction

31. Multiple-Attribute Metric

32. Embedding of sparse music similarity graph Platt, 2004

33. Reinforcement learning Mahadevan and Maggioini, 2005

34. Semi-supervised learning Use graph-based discretization of manifold to infer missing labels. Belkin & Niyogi, 2004; Zien et al, Eds., 2005 Build classifiers from bottom eigenvectors of graph Laplacian.

35. c et al, 2003, 2005 Learning correspondences How can we learn manifold structure that is shared across multiple data sets?

36. Mapping and robot localization • Bowling, Ghodsi, Wilkinson 2005 Ham, Lin, D.D. 2005

37. The Big Picture

38. Manifold and Hidden Variables

39. Reading • Journals: Neural Computation, JMLR, ML, IEEE PAMI • Conferences: NIPS, UAI, ICML, AI-STATS, IJCAI, IJCNN • Vision: CVPR, ECCV, SIGGRAPH • Speech: EuroSpeech, ICSLP, ICASSP • Online: citesser, google • Books: • Elements of Statistical Learning, Hastie, Tibshirani, Friedman • Learning from Data, Cherkassky, Mulier • Machine Learning, Mitchell • Neural Networks for pattern Recognition, Bishop • Introduction to Graphical Models, Jordan et. al