1. Ch10 Machine Learning: Symbol-Based
Dr. Bernard Chen Ph.D.
University of Central Arkansas
Spring 2011

2. Machine Learning Outline
The book present four chapters on machine learning, reflecting four approaches to the problem:
Symbol Based
Connectionist
Genetic/Evolutionary
Stochastic

3. Ch.10 Outline A framework for Symbol-Based Learning ID3 Decision Tree
Unsupervised Learning

4. The Framework for Symbol-Based Learning

5. The Framework Example Data The representation:
Size(small)^color(red)^shape(round)
Size(large)^color(red)^shape(round)

6. The Framework Example A set of operations: Based on
Size(small)^color(red)^shape(round)
replace a single constant with a variable produces the generalizations:
Size(X)^color(red)^shape(round)
Size(small)^color(X)^shape(round)
Size(small)^color(red)^shape(X)

7. The Framework Example The concept space
The learner must search this space to find the desired concept.
The complexity of this concept space is a primary measure of the difficulty of a learning problem

8. The Framework Example

9. The Framework Example Heuristic search: Based on
Size(small)^color(red)^shape(round)
The learner will make that example a candidate “ball” concept; this concept correctly classifies the only positive instance
If the algorithm is given a second positive instance
Size(large)^color(red)^shape(round)
The learner may generalize the candidate “ball” concept to
Size(Y)^color(red)^shape(round)

10. Learning process
The training data is a series of positive and negative examples of the concept: examples of blocks world structures that fit category, along with near misses.
The later are instances that almost belong to the category but fail on one property or relation

11. Examples and near misses for the concept arch

12. Examples and near misses for the concept arch

13. Examples and near misses for the concept arch

14. Examples and near misses for the concept arch

15. Learning process This approach is proposed by Patrick Winston (1975)
The program performs a hill climbing search on the concept space guided by the training data
Because the program does not backtrack, its performance is highly sensitive to the order of the training examples
A bad order can lead the program to dead ends in the search space

16. Ch.10 Outline A framework for Symbol-Based Learning ID3 Decision Tree
Unsupervised Learning

17. ID3 Decision Tree
ID3, like candidate elimination, induces concepts from examples
It is particularly interesting for
Its representation of learned knowledge
Its approach to the management of complexity
Its heuristic for selecting candidate concepts
Its potential for handling noisy data

18. ID3 Decision Tree

19. ID3 Decision Tree
The previous table can be represented as the following decision tree:

20. ID3 Decision Tree
In a decision tree, each internal node represents a test on some property
Each possible value of that property corresponds to a branch of the tree
Leaf nodes represents classification, such as low or moderate risk

21. ID3 Decision Tree
A simplified decision tree for credit risk management

22. ID3 Decision Tree ID3 constructs decision trees in a top-down fashion.
ID3 selects a property to test at the current node of the tree and uses this test to partition the set of examples
The algorithm recursively constructs a sub-tree for each parturition
This continues until all members of the partition are in the same class

23. ID3 Decision Tree
For example, ID3 selects income as the root property for the first step

24. ID3 Decision Tree

25. ID3 Decision Tree
How to select the 1st node? (and the following nodes)
ID3 measures the information gained by making each property the root of current subtree
It picks the property that provides the greatest information gain

26. ID3 Decision Tree
If we assume that all the examples in the table occur with equal probability, then:
P(risk is high)=6/14
P(risk is moderate)=3/14
P(risk is low)=5/14

27. ID3 Decision Tree
ID3 Decision Tree
I[6,3,5]=
Based on

28. ID3 Decision Tree

29. ID3 Decision Tree The information gain form income is:
Gain(income)= I[6,3,5]-E[income]= =0.967
Similarly,
Gain(credit history)=0.266
Gain(debt)=0.063
Gain(colletral)=0.206

30. ID3 Decision Tree
Since income provides the greatest information gain, ID3 will select it as the root of the tree

31. Attribute Selection Measure: Information Gain (ID3/C4.5)
Select the attribute with the highest information gain
Let pi be the probability that an arbitrary tuple in D belongs to class Ci, estimated by |Ci, D|/|D|
Expected information (entropy) needed to
classify a tuple in D:

32. Attribute Selection Measure: Information Gain (ID3/C4.5)
Information needed (after using A to split D into v partitions) to classify D:
Information gained by branching on attribute A

33. ID3 Decision Tree Pseudo Code

34. Another Decision Tree Example

35. Decision Tree Example Info(Tenured)=I(3,3)=
log2(12)=log12/log2= / =
Teach you what is log2
Convenient tool:

36. Decision Tree Example InfoRANK (Tenured)=
3/6 I(1,2) + 2/6 I(1,1) + 1/6 I(1,0)=
3/6 * ( ) + 2/6 (1) + 1/6 (0)= 0.79
3/6 I(1,2) means “Assistant Prof” has 3 out of 6 samples, with 1 yes’s and 2 no’s.
2/6 I(1,1) means “Associate Prof” has 2 out of 6 samples, with 1 yes’s and 1 no’s.
1/6 I(1,0) means “Professor” has 1 out of 6 samples, with 1 yes’s and 0 no’s.

37. Decision Tree Example InfoYEARS (Tenured)=
1/6 I(1,0) + 2/6 I(0,2) + 1/6 I(0,1) + 2/6 I (2,0)= 0
1/6 I(1,0) means “years=2” has 1 out of 6 samples, with 1 yes’s and 0 no’s.
2/6 I(0,2) means “years=3” has 2 out of 6 samples, with 0 yes’s and 2 no’s.
1/6 I(0,1) means “years=6” has 1 out of 6 samples, with 0 yes’s and 1 no’s.
2/6 I(2,0) means “years=7” has 2 out of 6 samples, with 2 yes’s and 0 no’s.

38. Ch.10 Outline A framework for Symbol-Based Learning ID3 Decision Tree
Unsupervised Learning

39. Unsupervised Learning
The learning algorithms discussed so far implement forms of supervised learning
They assume the existence of a teacher, some fitness measure, or other external method of classifying training instances
Unsupervised Learning eliminates the teacher and requires that the learners form and evaluate concepts their own

40. Unsupervised Learning
Science is perhaps the best example of unsupervised learning in humans
Scientists do not have the benefit of a teacher.
Instead, they propose hypotheses to explain observations,

41. Unsupervised Learning
The clustering problem starts with (1) a collection of unclassified objects and (2) a means for measuring the similarity of objects
The goal is to organize the objects into classes that meet some standard of quality, such as maximizing the similarity of objects in the same class

42. Unsupervised Learning
Numeric taxonomy is one of the oldest approaches to the clustering problem
A reasonable similarity metric treats each object as a point in n-dimensional space
The similarity of two objects is the Euclidean distance between them in this space

43. Unsupervised Learning
Using this similarity metric, a common clustering algorithm builds clusters in a bottom-up fashion, also known as agglomerative clustering:
Examining all pairs of objects, select the pair with the highest degree of similarity, and mark that pair a cluster
Defining the features of the cluster as some function (such as average) of the features of the component members and then replacing the component objects with this cluster definition
Repeat this process on the collection of objects until all objects have been reduced to a single cluster

44. Unsupervised Learning
The result of this algorithm is a Binary Tree whose leaf nodes are instances and whose internal nodes are clusters of increasing size
We may also extend this algorithm to objects represented as sets of symbolic features.

45. Unsupervised Learning
Object1={small, red, rubber, ball}
Object1={small, blue, rubber, ball}
Object1={large, black, wooden, ball}
This metric would compute the similary values:
Similarity(object1, object2)= ¾
Similarity(object1, object3)=1/4

46. Partitioning Algorithms: Basic Concept
Given a k, find a partition of k clusters that optimizes the chosen partitioning criterion
Global optimal: exhaustively enumerate all partitions
Heuristic methods: k-means and k-medoids algorithms
k-means (MacQueen’67): Each cluster is represented by the center of the cluster
k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster

47. The K-Means Clustering Method
Given k, the k-means algorithm is implemented in four steps:
Partition objects into k nonempty subsets
Compute seed points as the centroids of the clusters of the current partition (the centroid is the center, i.e., mean point, of the cluster)
Assign each object to the cluster with the nearest seed point
Go back to Step 2, stop when no more new assignment

48. K-means Clustering

49. K-means Clustering

50. K-means Clustering

51. K-means Clustering

52. K-means Clustering

53. The K-Means Clustering Method1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5
Update the cluster means 4
Assign each objects to most similar center 3 2 1 1 2 3 4 5 6 7 8 9 10
reassign
reassign
K=2
Arbitrarily choose K object as initial cluster center
Update the cluster means

54. Example
Run K-means clustering with 3 clusters (initial centroids: 3, 16, 25) for at least 2 iterations

55. Example Centroids: 3 – 2 3 4 7 9 new centroid: 5

56. Example Centroids: 5 – 2 3 4 7 9 new centroid: 5

57. In class Practice
Run K-means clustering with 3 clusters (initial centroids: 3, 12, 19) for at least 2 iterations