Beijing, China August 17, 2009<br />A Framework for Multi-objective Clustering and<br />Its Application to Co-location Min...
Talk  Outline<br />What is unique about this work with respect to clustering? <br />Multi-objective Clustering (MOC)—Objec...
1. What is unique about this work with respect to clustering? <br />Clustering algorithms that support plug-in fitness fun...
2. Multi-Objective Clustering (MOC) <br />The particular problem investigated in this work: <br /><ul><li>Input: Given a s...
Task: Find sets of clusters that a good with respect to two or more objectives</li></ul>Texas<br />Multi-Objective<br />Cl...
 Survey MOC Approach<br />Clustering algorithms are run multiple times maximizing different subsets of objectives that are...
An Architecture for MOC<br />S1<br />S2<br />Q’<br />Clustering <br />Algorithm<br />Goal-driven Fitness <br />Function Ge...
3. Clustering with Plug-in Fitness Functions<br />Motivation:<br />Finding subgroups in geo-referenced datasets has many a...
Current Suite of Spatial Clustering Algorithms<br />Representative-based: SCEC, SRIDHCR, SPAM, CLEVER<br />Grid-based: SCM...
4. Filling the Repository with Clusters<br />Plug-in Reward functions Rewardq(x) are used to assess to which extend an obj...
Dominance and Multi-Objective Clusters<br />Dominance between clusters x and y with respect to multiple objectives Q.<br /...
Compound Fitness Functions<br />The goal-driven fitness function generator selects a subset Q’(Q) of the objectives Q and...
Updating the Cluster Repository<br />M:= clusters in the repository<br />X:= “new” clusters generated by a single run of t...
5. Creating a Final Clustering<br />Final clusterings are subsets of the clusters in the repository M.<br />Inputs: The us...
MO-Dominance-guided Cluster Reduction(MO-DCR) algorithm (MO-DCR)<br />: a dominant <br />cluster<br />: dominated<br />clu...
6. Related Work<br />Multi-objective clustering based on evolutionary algorithms (MOEA): VIENNA [Handl and Knowles 2004] ,...
7. Case Study: Co-location Mining<br />Goal: Finding regional co-location patterns where high concentrations of Arsenic ar...
Objective Functions Used<br />.<br />Q’ Q<br />Q = {q{As,Mo}, q{As,V}, q{As,B}, q{As,F-}, q{As,Cl-}, q{As,SO42...
Steps of the Experiment<br /><ul><li>Step 1-3:use CLEVER with all pairs of 7 different objective functions: </li></ul>q{As...
Experimental Results<br />MOC is able to identify:<br />Multi-objective clusters<br />Alternative clusters e.g. Rank1 regi...
8. Conclusion and Future Work<br />Building blocks for Future Multi-Objective Clustering Systems were provided in this wor...
Challenges in Multi-objective Clustering (MOC)<br />Find clusters that are individually good with respect to multiple obje...
Traditional Clustering Algorithms & Fitness Functions<br />Clustering<br />Algorithms<br />No <br />Fitness Function<br />...
Code MO-DCR Algorithm<br />23<br />
Challenges Cluster Summarization<br />Original<br />Clusters<br />A<br />X<br />A<br />B<br />: Eliminated clusters<br />X...
Interestingness of a Pattern<br />Interestingness of a pattern B (e.g. B= {C, D, E}) for an object o,<br />Interestingn...
Characteristics of the Top5 Regions<br />Table 7.7 Top 5 Regions Ranked by Reward of the Query {As­,Mo­}<br />Table 7.8 To...
Representative-based Clustering<br />2<br />Attribute1<br />1 <br />3<br />Attribute2<br />4<br />Objective: Find a set of...
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Mining Regional Knowledge in Spatial Dataset

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  • —radical depart from traditional clustering, MOC Relies on clustering algorithms that support plug-in fitness functions, and multi-run clustering with repository to generate a large number of clusters.It generates clusters satisfying two or more objectives (not clustering level), and supports different domain specific tasks assigned by users.Is incremental approach that collects and refines clusters on the fly, and the search for alternative clusters takes into consideration what clusters already have been generated, rewarding novelty.Support different domain specific tasks assigned by users.Provide search engine type capabilities to users, enabling them to query a large set of clusters with respect to different objectives and thresholds to generate final clusterings.
  • The architecture of the MOC system that we propose is depicted in the figure given; it consists of 4 main components: a clustering algorithm, storage unit, goal-driven fitness function generator and cluster summarization unit. Steps in MOC include: first, the goal-driven fitness function generator selects a new compound fitness function for the clustering algorithm, which generates a new clustering X in the second step. Third, the storage unit updates its repository M using the clusters in X. The algorithm iterates over these three steps until a large number of clusters has been obtained. Later, in the fourth step, the cluster summarization unit produces final clusters based on user preferences which are subsets of the clusters in M.
  • In general, M should only store non-dominated clusters, and algorithms that update M should not violate this constraint
  • In particular to step 1, the goal-driven fitness function generator selects pairs of single-objectivefitness functions (q, q’) with q, q’Qto create a compound fitness function Q’ by considering all combinations of two fitness functions in Q. In general, the compound fitness function qQ’ is the sums of the rewards for all objectives qQ’; however, it gives more reward to clusters xi that satisfy all objectives in order to motivate theclustering algorithm to seek for multi-objective clusters.
  • The algorithm loops over the following 2 steps until there is no cluster to be removed in the second step:1. Compute dominant clusters which are the highest quality clusters, and2. remove their dominated clusters in the rem-proximity.We illustrate MO-DCR algorithm using dominance graphs.In the first iteration A is a dominant cluster, and its dominated clusters B and C, which are very similar to A (in close proximity), are removed.In the second iteration D is found as a dominant cluster, and its dominated clusters E and F, are removed.Consequently, the final clustering consists of two clusters: A and D.
  • Related work are Multi-objective clustering based on evolutionary algorithms and scatter tabu search.Similar to MOEA, our approach evaluates cluster quality by using a combination of fitness functions. In contrast, we selectively store and refine clusters on the fly to maintain efficacy of storage management and cluster comparison.
  • We demonstrate the benefits of the proposed multi-objective clustering framework in a real world water pollution case study. The goal is to find regional co-location patterns of high concentrations of Arsenic with other factors in Texas.TWDB has monitored water quality and collected the data for 105,814 wells in Texas over last 25 years. For this experiment we used a water well dataset called Arsenic_10_avg that contains3 spatial attributes and other 8 non-spatial attributes of chemical concentrations including Arsenic concentrations
  • Challenges in Multi-objective Clustering includeFind clusters that are individually good with respect to multiple fitness functions in automated fashion.Provide search engine style capabilities to summarize final clustering obtained from multiple runs of clustering algorithms.
  • We can categorize clustering algorithms into 4 types based on the use of fitness functions.First, the clustering algorithms that do not use fitness function, for example, DBSCAN and hierarchical clustering.Second, the algorithms that use fitness function implicitly, for example, k-means.Third, the algorithms that use fixed fitness function, for example, PAM.And Forth, the algorithms that provide plug-in fitness function, for example, CHAMELEON and MOSAIC.Using traditional clustering algorithms for region discovery face significant limitations:As we just mentioned, traditional clustering algorithms consider only domain independent and task independent characteristics; for example. k-means algorithm considers cluster compactness to form a solution. However, in region discovery, such as hotspot discovery of high arsenic concentration, it requires the clustering algorithm to find clusters based on task specific characteristics. Therefore, clustering with plug-in fitness functions is desirable because it can capture what groupings are of particular interest to domain experts. 2) To the best of our knowledge, there is no single fitness function that effectively serves different domain tasks. Therefore, it is necessary to design task specific families of fitness functions.
  • Step 4 provides search engine type capabilities to users, enabling them to query a large set of clusters with respect to different objectives and thresholds to generate final clusterings.Goal of MO-Dominance-guided Cluster Reduction algorithm (MO-DCR) isto return a clustering that is good with respect to multiple objectivesselected by a user, and to remove clusters that are highly overlapping.
  • DCR algorithm is one of effective algorithms that generate final clustering. Normally we can straightforwardly produce the result by removing all dominated clusters. However, this way will remove too many clusters, for example, clusters A dominates and overlaps B, and B dominates and overlaps C. DCR does not remove C because it does not spatially overlap with A.Finally, MRC perform the tasks of parameter selections, finding alternative clusters and summarizing clusters in a highly automated fashion.
  • Mining Regional Knowledge in Spatial Dataset

    1. 1. Beijing, China August 17, 2009<br />A Framework for Multi-objective Clustering and<br />Its Application to Co-location Mining<br />RachsudaJianthapthaksin, Christoph F. Eick and Ricardo Vilalta<br />University of Houston, Texas, USA<br />
    2. 2. Talk Outline<br />What is unique about this work with respect to clustering? <br />Multi-objective Clustering (MOC)—Objectives and an Architecture<br />Clustering with Plug-in Fitness Functions<br />Filling the Repository with Clusters<br />Creating Final Clusterings<br />Related Work <br />Co-location Mining Case Study<br />Conclusion and Future Work<br />
    3. 3. 1. What is unique about this work with respect to clustering? <br />Clustering algorithms that support plug-in fitness function are used.<br />Clustering algorithms are run multiple times to create clusters.<br />Clusters are stored in a repository that is updated on the fly; cluster generation is separated from creating the final clustering.<br />The final clustering is created from the clusters in the repository based on user preferences.<br />Our approach needs to seeks for alternative, overlapping clusters.<br />
    4. 4. 2. Multi-Objective Clustering (MOC) <br />The particular problem investigated in this work: <br /><ul><li>Input: Given a spatial dataset & a set of objectives
    5. 5. Task: Find sets of clusters that a good with respect to two or more objectives</li></ul>Texas<br />Multi-Objective<br />Clustering<br />Dataset:<br />(longitude,latitude,<concentrations>+)<br />
    6. 6. Survey MOC Approach<br />Clustering algorithms are run multiple times maximizing different subsets of objectives that are captured in compound fitness functions. <br />Uses a repository to store promising candidates.<br />Only clusters that satisfying two or more objectives are considered as candidates. <br />After a sufficient number of clusters has been created, final clustering are generated based on user-preferences.<br />5<br />
    7. 7. An Architecture for MOC<br />S1<br />S2<br />Q’<br />Clustering <br />Algorithm<br />Goal-driven Fitness <br />Function Generator<br />A Spatial<br />Dataset<br />M<br />X<br />Cluster<br />Summarization<br />Unit<br />Q’<br />M’<br />Storage Unit<br />S3<br />S4<br />Steps in multi-run clustering:<br />S1: Generate a compound fitness function. <br />S2: Run a clustering algorithm. <br />S3: Update the cluster repository M.<br />S4: Summarize clusters discovered M’.<br />6<br />
    8. 8. 3. Clustering with Plug-in Fitness Functions<br />Motivation:<br />Finding subgroups in geo-referenced datasets has many applications.<br />However, in many applications the subgroups to be searched for do not share the characteristics considered by traditional clustering algorithms, such as cluster compactness and separation.<br />Domain or task knowledge frequently imposes additional requirements concerning what constitutes a “good” subgroup.<br />Consequently, it is desirable to develop clustering algorithms that provide plug-in fitness functions that allow domain experts to express desirable characteristics of subgroups they are looking for.<br />
    9. 9. Current Suite of Spatial Clustering Algorithms<br />Representative-based: SCEC, SRIDHCR, SPAM, CLEVER<br />Grid-based: SCMRG<br />Agglomerative: MOSAIC<br />Density-based: SCDE, DCONTOUR (not really plug-in but some fitness functions can be simulated)<br />Density-based<br />Grid-based<br />Agglomerative-based<br />Representative-based<br />Clustering Algorithms<br />Remark: All algorithms partition a dataset into clusters by maximizing a <br />reward-based, plug-in fitness function. <br />
    10. 10. 4. Filling the Repository with Clusters<br />Plug-in Reward functions Rewardq(x) are used to assess to which extend an objective q is satisfied for a cluster x.<br />User defined thresholds q are used to determine if an objective q is satisfied by a cluster x (Rewardq(x)>q).<br />Only clusters that satisfy 2 or more objectives are stored in the repository.<br />Only non-dominated clusters are stored in the repository.<br />Dominance relations only apply to pairs of clusters that have a certain degree of agreement (overlap) sim.<br />
    11. 11. Dominance and Multi-Objective Clusters<br />Dominance between clusters x and y with respect to multiple objectives Q.<br />Dominance Constraint with Respect to the Repository<br />10<br />
    12. 12. Compound Fitness Functions<br />The goal-driven fitness function generator selects a subset Q’(Q) of the objectives Q and creates a compound fitness function qQ’relying on a penalty function approach [Baeck et al. 2000].<br />CmpReward(x)= (qQ’Rewardq(x)) * Penalty(Q’,x)<br />11<br />
    13. 13. Updating the Cluster Repository<br />M:= clusters in the repository<br />X:= “new” clusters generated by a single run of the clustering algorithm <br />12<br />
    14. 14. 5. Creating a Final Clustering<br />Final clusterings are subsets of the clusters in the repository M.<br />Inputs: The user provides her own individual objective function RewardU and a reward threshold U and cluster similarity threshold rem that indicates how much cluster overlap she likes to tolerate.<br />Goal: Find XM that maximizes:<br /> subject to: 1. xXx’X (xx’  Similarity(x,x’)<rem)<br />2. xX(RewardU(x)>U)<br />Our paper introduces MO-Dominance-guided Cluster Reduction algorithm (MO-DCR) to create the final clustering. <br />
    15. 15. MO-Dominance-guided Cluster Reduction(MO-DCR) algorithm (MO-DCR)<br />: a dominant <br />cluster<br />: dominated<br />clusters<br />A<br />The algorithm loops over the following 2 steps until M is empty:<br />Include dominant clusters D which are the highest reward clusters in M’<br />Remove D and their dominated clusters in the rem-proximity from M.<br />B<br />C<br />Dominance graphs<br />D<br />Remark: AB  RewardU(A)>RewardU(B)  Similarity(A,B)> rem<br />E<br />F<br />sim(A,B)=0.8<br />rem=0.5<br />M’<br />0.7<br />0.6<br />A<br />E<br />A<br />E<br />F<br />14<br />
    16. 16. 6. Related Work<br />Multi-objective clustering based on evolutionary algorithms (MOEA): VIENNA [Handl and Knowles 2004] , MOCLE [Faceli et al. 2007]<br /><ul><li>In comparison, MOC relies on clustering algorithms with plug-in fitness functions and multi-run clustering that explores different combinations of fitness objectives.</li></ul>Moreover, MOC relies on cluster repositories that store individual clusters and not clusterings and summarization algorithms to create the final clustering.<br />15<br />
    17. 17. 7. Case Study: Co-location Mining<br />Goal: Finding regional co-location patterns where high concentrations of Arsenic are co-located with a lot of other factors in Texas.<br />Remark: Each binary co-location is treated as a single objective.<br />Dataset: <br />TWDB has monitored water quality and collected the data for 105,814 wells in Texas over last 25 years. <br />we use a subset of Arsenic_10_avg data set: longitude and latitude, Arsenic (As), Molybdenum (Mo), Vanadium (V), Boron (B), Fluoride (F-), Chloride (Cl-), Sulfate (SO42-) and Total Dissolved Solids (TDS).<br />16<br />
    18. 18. Objective Functions Used<br />.<br />Q’ Q<br />Q = {q{As,Mo}, q{As,V}, q{As,B}, q{As,F-}, q{As,Cl-}, q{As,SO42-}, q{As,TDS}}<br />RewardB(x) = (B,x)|x|<br />17<br />
    19. 19. Steps of the Experiment<br /><ul><li>Step 1-3:use CLEVER with all pairs of 7 different objective functions: </li></ul>q{As,Mo}, q{As,V}, q{As,B}, q{As,F-}, q{As,Cl-}, q{As,SO42-}, q{As,TDS}.<br /><ul><li>Step 4: query clusters in the repository by separately using the given single-objective functions, the removal threshold rem = 0.1 and the following user-defined reward thresholds (7 final clusterings): </li></ul> q{As,Mo}=13, q{As,V}=15, q{As,B}=10, q{As,F-}=25, q{As,Cl-}=7, <br /> q{As, SO42-}=6, q{As,TDS}=8.<br />MOC Users<br />Queries<br />Spatial<br />dataset<br />and <br />fitness <br />functions (Q)<br />Regions M’ (M) <br />with associated <br />co-location pattern<br />MOC<br />Step 1-3<br />MOC<br />Step 4<br />Regions <br />(M)<br />18<br />
    20. 20. Experimental Results<br />MOC is able to identify:<br />Multi-objective clusters<br />Alternative clusters e.g. Rank1 regions of (a) and Rank2 regions of (b)<br />Nested clusters e.g. in (b) Rank3-5 regions are sub-regions of Rank1 region.<br />Particularly discriminate among companion elements such as Vanadium (Rank3 region), or Chloride, Sulfate and Total Dissolved Solids (Rank4 region).<br />(a) (b)<br />Fig. 7.6 The top 5 regions and patterns with respect to two queries: query1={As,Mo} and query2={As,B} are shown in Figure (a) and (b), respectively.<br />19<br />
    21. 21. 8. Conclusion and Future Work<br />Building blocks for Future Multi-Objective Clustering Systems were provided in this work; namely: <br />A dominance relation for problems in which only a subset of the objectives can be satisfied was introduced. <br />Clustering algorithms with plug-in fitness functions and the capability to create compound fitness functions are excessively used in our approach. <br />Initially, a repository of potentially useful clusters is generated based on a large set of objectives. Individualized, specific clusterings are then generated based on user preferences. <br />The approach is highly generic and incorporates specific domain needs in form of single-objective fitness functions.<br />The approach was evaluated in a case study and turned out more suitable than a single-objective clustering approach that was used for the same application in a previous paper [ACM-GIS 2008]. <br />
    22. 22. Challenges in Multi-objective Clustering (MOC)<br />Find clusters that are individually good with respect to multiple objectives in an automated fashion.<br />Provide search engine style capabilities to summarize final clustering obtained from multiple runs of clustering algorithms.<br />21<br />
    23. 23. Traditional Clustering Algorithms & Fitness Functions<br />Clustering<br />Algorithms<br />No <br />Fitness Function<br />Fixed <br />Fitness Function<br />Provides Plug-in<br />Fitness Function<br />Implicit <br />Fitness Function<br />DBSCAN<br />Hierarchical Clustering<br />CHAMELEON<br />Our Work <br />PAM<br />K-Means<br />Traditional clustering algorithms consider only domain independent and task independent characteristics to form a solution. <br />Different domain tasks require different fitness functions. <br />Traditional Clustering Algorithms<br />22<br />
    24. 24. Code MO-DCR Algorithm<br />23<br />
    25. 25. Challenges Cluster Summarization<br />Original<br />Clusters<br />A<br />X<br />A<br />B<br />: Eliminated clusters<br />X<br />B<br />A<br />C<br />C<br />X<br />B<br />X<br />C<br />Typical<br />Output<br />DCR <br />Output<br />24<br />
    26. 26. Interestingness of a Pattern<br />Interestingness of a pattern B (e.g. B= {C, D, E}) for an object o,<br />Interestingness of a pattern B for a region c,<br />Remark: Purity (i(B,o)>0) measures the percentage of objects <br />that exhibit pattern B in region c. <br />
    27. 27. Characteristics of the Top5 Regions<br />Table 7.7 Top 5 Regions Ranked by Reward of the Query {As­,Mo­}<br />Table 7.8 Top 5 Regions Ranked by Reward of the Query {As­, B­}<br />26<br />
    28. 28. Representative-based Clustering<br />2<br />Attribute1<br />1 <br />3<br />Attribute2<br />4<br />Objective: Find a set of objects OR such that the clustering X <br />obtained by using the objects in OR as representatives minimizes q(X).<br />Properties: Cluster shapes are convex polygons<br />Popular Algorithms: K-means. K-medoids<br />
    29. 29. 5. CLEVER (ClustEring using representatiVEs and Randomized hill climbing)<br />Is a representative-based, sometimes called prototype-based clustering algorithm<br />Uses variable number of clusters and larger neighborhood sizes to battle premature termination and randomized hill climbing and adaptive sampling to reduce complexity.<br />Searches for optimal number of clusters<br />

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