1. 1 Local search and optimization Local search= use single current state and move to neighboring states. Advantages: –Use very little memory –Find often reasonable solutions in large or infinite state spaces. Are also useful for pure optimization problems. –Find best state according to some objective function. –e.g. survival of the fittest as a metaphor for optimization.

2. 2 Local search and optimization

3. 3 Hill-climbing search “ is a loop that continuously moves in the direction of increasing value ” –It terminates when a peak is reached. Hill climbing does not look ahead of the immediate neighbors of the current state. Hill-climbing chooses randomly among the set of best successors, if there is more than one. Hill-climbing a.k.a. greedy local search

4. 4 Hill-climbing search function HILL-CLIMBING( problem) return a state that is a local maximum input: problem, a problem local variables: current, a node. neighbor, a node. current  MAKE-NODE(INITIAL-STATE[problem]) loop do neighbor  a highest valued successor of current if VALUE [neighbor] ≤ VALUE[current] then return STATE[current] current  neighbor

5. 5 3.3 The K-Means Algorithm 1.Choose a value for K, the total number of clusters. 2.Randomly choose K points as cluster centers. 3.Assign the remaining instances to their closest cluster center. 4.Calculate a new cluster center for each cluster. 5.Repeat steps 3-5 until the cluster centers do not change.

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10. 10 Simulated annealing Escape local maxima by allowing “ bad ” moves. –Idea: but gradually decrease their size and frequency. Origin; metallurgical annealing Bouncing ball analogy: –Shaking hard (= high temperature). –Shaking less (= lower the temperature). If T decreases slowly enough, best state is reached. Applied for VLSI layout, airline scheduling, etc.

11. 11 Simulated annealing function SIMULATED-ANNEALING( problem, schedule) return a solution state input: problem, a problem schedule, a mapping from time to temperature local variables: current, a node. next, a node. T, a “ temperature ” controlling the probability of downward steps current  MAKE-NODE(INITIAL-STATE[problem]) for t  1 to ∞ do T  schedule[t] if T = 0 then return current next  a randomly selected successor of current ∆E  VALUE[next] - VALUE[current] if ∆E > 0 then current  next else current  next only with probability e ∆E /T

12. 12 Local beam search Keep track of k states instead of one –Initially: k random states –Next: determine all successors of k states –If any of successors is goal  finished –Else select k best from successors and repeat. Major difference with random-restart search –Information is shared among k search threads. Can suffer from lack of diversity. –Stochastic variant: choose k successors at proportional to state success.

13. 13 Genetic algorithms Variant of local beam search with sexual recombination.

14. 14 The Genetic Algorithm Encoded the individual potential solutions into suitable representations –Knowledge representation Use mating and mutation in the population to produce a new generation –Operator selection A fitness function judges which individuals are the “ best ” life forms –The design of a fitness function

15. 15 The General Form

16. 16 Genetic algorithms

17. 17 An Example of Crossover

18. 18 The CNF-satisfaction Problem

19. 19 Representation A sequence of six bits 101010

20. 20 Genetic Operators Crossover Mutation

21. 21 Fitness Function Value of expression assignment –Hard to judge the “ quality ” Number of clauses that pattern satisfies

22. 22 The Traveling Salesperson Problem NP-hard problem

23. 23 Representation Bits representation –Hard to crossover and mutation Give each city a numeric name –(192465783) –Crossover and mutation?

24. 24 Genetic Operators Order crossover (Davis 1985) –Guarantee legitimate tours, visiting all cities exactly once

25. 25 Mutation Reversing the order would not work Cut out a piece and invert and replace Randomly select a city and place it in a new randomly selected location

26. 26 The Genetic Algorithm A variant of informed search –Successor states are generated by combining two parent states Procedure –Knowledge representation –Operator selection –The design of a fitness function

27. 27 Genetic Learning Operators Crossover Mutation Selection 3.4 Genetic Learning

28. 28 Genetic Algorithms and Supervised Learning

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33. 33 Genetic Algorithms and Unsupervised Clustering

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36. 36 General Considerations Global optimization is not a guarantee. The fitness function determines the complexity of the algorithm. Explain their results provided the fitness function is understandable. Transforming the data to a form suitable for genetic learning can be a challenge.

37. 37 3.5 Choosing a Data Mining Technique

38. 38 Initial Considerations Is learning supervised or unsupervised? Is explanation required? –Neural networks, regression models are black-box What is the interaction between input and output attributes? What are the data types of the input and output attributes?

39. 39 Further Considerations Do We Know the Distribution of the Data? –Many statistical techniques assume the data to be normally distributed Do We Know Which Attributes Best Define the Data? –Decision trees and certain statistical approaches –Neural network, nearest neighbor, various clustering approaches

40. 40 Further Considerations Does the Data Contain Missing Values? –Neural networks Is Time an Issue? –Decision trees Which Technique Is Most Likely to Give a Best Test Set Accuracy? –Multiple model approaches (Chp. 11)