multi-objective evolutionary clustering : a survey
TRANSCRIPT
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Multiobjective Evolutionary Clustering
Aiswarya Issac
27 January, 2016
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 1 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Overview
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 2 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Clustering
I Partitioning into homogeneous groups based on somesimilarity metric.
I Click Here
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 3 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 4 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Optimization Problem
I Single Objective OptimizationI Only one objective function to be minimized.I Eg. Knapsack problem
I Multiple Objective OptimizationI Two or more conflicting objectives need to be
optimized.I There will be a set of possible solutions rather than a
single optimal solution - Pareto optimal solutions.I Eg. Minimizing cost while maximizing comfort while
buying a car.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 5 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Optimization Problem
Figure: 1 Illustration of knapsack problem[Source:wikipedia]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 6 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 7 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Multiobjective clustering
I Single Objective Clustering
Figure: 2 Comparison of different clustering[1]
I The final clusters do not represent a global optimizationresult.
I Different final clustering can happen based on the initialselection of cluster center.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 8 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Multiobjective Clustering
I Multi Objective Clustering
I Decompose a data-set into similar groups maximizingmultiple objectives in parallel.
Figure: 3 Output for multiobjective clustering[1]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 9 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsProcess of Evolution
Figure: 4 Schematic representation of evolutionary algorithm[2]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 10 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsProcess of Evolution
Figure: 5 Schematic representation datastructures[2]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 11 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 12 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsWhy Evolutionary Method? [3]
I Antennas developed by NASA’s Evolvable SystemsGroup for use on satellites.
I Free of any human preconceptions or biases
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 13 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsWhy Evolutionary Method? [3]
I Antennas developed by NASA’s Evolvable SystemsGroup for use on satellites.
I Free of any human preconceptions or biases
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 13 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsWhy Evolutionary Method? [3]
I Antennas developed by NASA’s Evolvable SystemsGroup for use on satellites.
I Free of any human preconceptions or biases
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 13 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Evolutionary AlgorithmsMultiobjective Clustering Steps[3]
I Choose a possible encoding of chromosome to representa clustering solution.
I Generate the initial population of chromosomes.
I Choose a suitable set of objective functions that are tobe optimized simultaneously.
I Design suitable evolutionary operators such as selection,crossover, and mutation.
I Define a fitness function to evaluate the clusteringsolutions.
I Develop a technique to obtain a single clusteringsolution from Pareto optimal set.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 14 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 15 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Solution Representation
Figure: 6 Classification of solution representation[4]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 16 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Solution RepresentationPrototype based
I Centroid-based:I The coordinates of the cluster centers will be encoded
in the chromosome.I Eg: [2.4 5.9, 0.36 2.7, 5.3 10.2]
I Medoid-based:I Used when coordinates are not known.I An actual point that is most centrally located in a
cluster is used to represent that cluster.I Eg. datapoints = [1,2,3,4,5,6,7,8]
encoding = [3,7]
I Mode-based:I Similar to medoid basedI Computation is less expensive when compared with
medoid based.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 17 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Solution RepresentationPrototype based
I Centroid-based:I The coordinates of the cluster centers will be encoded
in the chromosome.I Eg: [2.4 5.9, 0.36 2.7, 5.3 10.2]
I Medoid-based:I Used when coordinates are not known.I An actual point that is most centrally located in a
cluster is used to represent that cluster.I Eg. datapoints = [1,2,3,4,5,6,7,8]
encoding = [3,7]
I Mode-based:I Similar to medoid basedI Computation is less expensive when compared with
medoid based.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 17 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Solution RepresentationPrototype based
I Centroid-based:I The coordinates of the cluster centers will be encoded
in the chromosome.I Eg: [2.4 5.9, 0.36 2.7, 5.3 10.2]
I Medoid-based:I Used when coordinates are not known.I An actual point that is most centrally located in a
cluster is used to represent that cluster.I Eg. datapoints = [1,2,3,4,5,6,7,8]
encoding = [3,7]
I Mode-based:I Similar to medoid basedI Computation is less expensive when compared with
medoid based.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 17 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Solution RepresentationPoint based
I Cluster Label-based:
Figure: 7 Cluster Label based encoding scheme[4]
I Locus-based Adjacency Graph:
Figure: 8 Locus based encoding scheme[4]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 18 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Solution RepresentationPoint based
I Cluster Label-based:
Figure: 7 Cluster Label based encoding scheme[4]
I Locus-based Adjacency Graph:
Figure: 8 Locus based encoding scheme[4]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 18 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 19 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Initializing Population
I Prototype-based encodingI The prototypes in the initial population are usually
some randomly selected data points.
I Point based encodingI The cluster labels will be initialized with random strings
so that each point gets a random cluster label.
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 20 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 21 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Objective functions
I Overall Cluster Deviation
I Cluster Connectedness
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 22 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 23 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsSelection[5]
Selection is based on fitness function.
I Tournament selection.
I Ranking
I Proportionate Selection
Figure: 9 Roulette wheel selection[2]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 24 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsSelection[5]
Selection is based on fitness function.
I Tournament selection.
I Ranking
I Proportionate Selection
Figure: 9 Roulette wheel selection[2]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 24 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsSelection[5]
Selection is based on fitness function.
I Tournament selection.
I Ranking
I Proportionate Selection
Figure: 9 Roulette wheel selection[2]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 24 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsSelection[5]
Selection is based on fitness function.
I Tournament selection.
I Ranking
I Proportionate Selection
Figure: 9 Roulette wheel selection[2]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 24 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsCrossover
Figure: 10 Classification of crossover schemes[4]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 25 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsCrossover
I Single or multiple point crossover
I For prototype based:Parent1: [2.4 5.9, 0.36 2.7, 5.3 10.2]Parent2: [2.5 5.5, 1.2 2.3, 6.0 10.2]Offspring1: [2.4 5.9, 1.2 2.3, 6.0 10.2]Offspring2: [2.5 5.5, 0.36 2.7, 5.3 10.2]
I For point based:Uniform crossover approachParent1: [1 1 1 2 3 3 2 3 ]Parent2: [1 1 2 2 2 3 3 2 ]Mask : [0 0 1 1 1 1 0 1 ]Offspring1: [1 1 2 2 2 3 2 2 ]Offspring2: [1 1 1 2 3 3 3 3 ]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 26 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsCrossover
I Single or multiple point crossover
I For prototype based:Parent1: [2.4 5.9, 0.36 2.7, 5.3 10.2]Parent2: [2.5 5.5, 1.2 2.3, 6.0 10.2]Offspring1: [2.4 5.9, 1.2 2.3, 6.0 10.2]Offspring2: [2.5 5.5, 0.36 2.7, 5.3 10.2]
I For point based:Uniform crossover approachParent1: [1 1 1 2 3 3 2 3 ]Parent2: [1 1 2 2 2 3 3 2 ]Mask : [0 0 1 1 1 1 0 1 ]Offspring1: [1 1 2 2 2 3 2 2 ]Offspring2: [1 1 1 2 3 3 3 3 ]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 26 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsMutation
Figure: 11 Classification of mutation schemes[4]
Aiswarya Issac Multiobjective Evolutionary Clustering 27 January, 2016 27 / 37
MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsMutation
I For prototype based encoding:The cluster center is modified as follows:
z ′k l = (1 ± 2ε)zk l
I For point based encoding:A point is chosen with probability 1/n.Its cluster label is randomly mutated, along withpredefined number of neighbours.
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
OperationsMutation
I For prototype based encoding:The cluster center is modified as follows:
z ′k l = (1 ± 2ε)zk lI For point based encoding:
A point is chosen with probability 1/n.Its cluster label is randomly mutated, along withpredefined number of neighbours.
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Final Solution Selection
Figure: 12 Classification of approaches for final solutions[4]
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Final Solution Selection
I Independent Objective-based:Objective functions are used to evaluate the best
solution.
I Knee-based:Knee solution is one for which change in one
objective value induces maximum change in others.
I Cluster Ensemble-based:If some points are always clustered together by a
majority of the solutions, then these points may beassumed to be clustered appropriately.
So, this can be used to train a supervised classifier.
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Outline
Clustering
Multi-objective clusteringOptimization ProblemsMultiobjective Clustering
Evolutionary Algorithms
Multiobjective Evolutionary ClusteringEvolutionary MethodSolution RepresentationInitializing PopulationSelection of Objective functionsOperationsFinal Solution SelectionApplications
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Applications
Applications Tasks
BioinformaticsGrouping co-expressed genes
Clustering samplesProtein complex identification
Social Network Analytics Social network clustering
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Different Algorithms
Figure: Caption
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Clustering
Multi-objectiveclustering
OptimizationProblems
MultiobjectiveClustering
EvolutionaryAlgorithms
MultiobjectiveEvolutionaryClustering
Evolutionary Method
SolutionRepresentation
Initializing Population
Selection of Objectivefunctions
Operations
Final SolutionSelection
Applications
Conclusion
Conclusion
I Evolutionary Algorithms can be used to obtain solutionsfor unconventional problems like multiobjectiveclustering.
I Suggestions:I Chromosome Encoding: Fast decoding and small length.I Initialization: Pre-processing of input.I Final solution selection: Use multiple objectives
together.
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Appendix
For Further Reading
Reference I
[1] Martin H. C. Law, Alexander P. Topchy, Anil K.Jain, ’Multiobjective Data Clustering’, IEEE ComputerSociety Conference on Computer Vision and PatternRecognition, 2004.
[2] Carlos A , Gary B and David A, Chapter 1 and 2, in’Evolutionary Algorithms for solving Multiobjectiveproblem’., 2nd ed, Springer, 2007.
[3] Daniel W. Dyer, ’The power of evolution’, in’Evolutionary Computation in Java’,’http://watchmaker.uncommons.org/manual/index.html’,2010
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MultiobjectiveEvolutionaryClustering
Aiswarya Issac
Appendix
For Further Reading
Reference II
[4] Anirban Mukhopadhyay, Ujjwal Maulik, andSanghamitra Bandyopadhyay. 2015. ’A survey ofmultiobjective evolutionary clustering’. ACM Comput.Surv. 47, 4, Article 61 (May 2015).
[5] Abdullah Konak, David W. Coit, Alice E. Smith,Multi-objective optimization using genetic algorithms: Atutorial’. Reliability Engineering and SystemSafety,Elsevier,2006
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