1. Data Visualization STAT 890, STAT 442, CM 462
Ali Ghodsi
Department of Statistics
School of Computer Science
University of Waterloo
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. are all closely related to the second problem.
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 1
0.5

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

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

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

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