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- 1. This is part of yourADVANCED ALGORITHMS INCOMPUTATIONAL BIOLOGY (C3), 1
- 2. Class Info• Lecturer: Chi-Yao Tseng ( 曾祺堯 ) cytseng@citi.sinica.edu.tw• Grading: – No assignments – Midterm: • 2012/04/20 • I’m in charge of 17x2 points out of 120 • No take-home questions 2
- 3. Outline• Introduction – From data warehousing to data mining• Mining Capabilities – Association rules – Classification – Clustering• More about Data Mining 3
- 4. Main Reference• Jiawei Han, Micheline Kamber, Data Mining: Concepts and Techniques, 2nd Edition, Morgan Kaufmann, 2006. – Official website: http://www.cs.uiuc.edu/homes/hanj/bk2/ 4
- 5. Why Data Mining?• The Explosive Growth of Data: from terabytes to petabytes (1015 B= 1 million GB) – Data collection and data availability • Automated data collection tools, database systems, Web, computerized society – Major sources of abundant data • Business: Web, e-commerce, transactions, stocks, … • Science: Remote sensing, bioinformatics, scientific simulation, … • Society and everyone: news, digital cameras, YouTube, Facebook• We are drowning in data, but starving for knowledge!• “Necessity is the mother of invention”—Data mining— Automated analysis of massive data sets 5
- 6. Why Not Traditional Data Analysis?• Tremendous amount of data – Algorithms must be highly scalable to handle such as terabytes of data• High-dimensionality of data – Micro-array may have tens of thousands of dimensions• High complexity of data• New and sophisticated applications 6
- 7. Evolution of Database Technology• 1960s: – Data collection, database creation, IMS and network DBMS• 1970s: – Relational data model, relational DBMS implementation• 1980s: – RDBMS, advanced data models (extended-relational, OO, deductive, etc.) – Application-oriented DBMS (spatial, scientific, engineering, etc.)• 1990s: – Data mining, data warehousing, multimedia databases, and Web databases• 2000s – Stream data management and mining – Data mining and its applications – Web technology (XML, data integration) and global information systems 7
- 8. What is Data Mining?• Knowledge discovery in databases – Extraction of interesting (non-trivial, implicit, previously unknown and potentially useful) patterns or knowledge from huge amount of data.• Alternative names: – Knowledge discovery (mining) in databases (KDD), knowledge extraction, data/pattern analysis, data archeology, data dredging, information harvesting, business intelligence, etc. 8
- 9. Data Mining: On What Kinds of Data?• Database-oriented data sets and applications – Relational database, data warehouse, transactional database• Advanced data sets and advanced applications – Data streams and sensor data – Time-series data, temporal data, sequence data (incl. bio-sequences) – Structure data, graphs, social networks and multi-linked data – Object-relational databases – Heterogeneous databases and legacy databases – Spatial data and spatiotemporal data – Multimedia database – Text databases – The World-Wide Web 9
- 10. Knowledge Discovery (KDD) Process Interpretation / Knowledge! Evaluation Data Mining Selection & Patterns Transformation TransformedData Cleaning data& Integration Data warehouse • This is a view from typical database systems and data warehousing communities. Databases • Data mining plays an essential role in the knowledge discovery process. 10
- 11. Data Mining and Business IntelligenceIncreasing potentialto supportbusiness decisions End User Decision Making Data Presentation Business Analyst Visualization Techniques Data Mining Data Information Discovery Analyst Data Exploration Statistical Summary, Querying, and Reporting Data Preprocessing/Integration, Data Warehouses DBA Data Sources Paper, Files, Web documents, Scientific experiments, Database Systems 11
- 12. Data Mining: Confluence of Multiple Disciplines 12
- 13. Typical Data Mining System Graphical User Interface Pattern Evaluation Knowledge Data Mining Engine Base Database or Data Warehouse Server data cleaning, integration, and selection Data World-Wide Other info.Database warehouse Web repositories 13
- 14. Data Warehousing• A data warehouse is a subject-oriented, integrated, time-variant, and nonvolatile collection of data in support of managements’ decision making process. —W. H. Inmon 14
- 15. Data Warehousing• Subject-oriented: – Provide a simple and concise view around particular subject issues by excluding data that are not useful in the decision support process.• Integrated: – Constructed by integrating multiple, heterogeneous data sources.• Time-variant: – Provide information from a historical perspective (e.g., past 5-10 years.)• Nonvolatile: – Operational update of data does not occur in the data warehouse environment – Usually requires only two operations: load data & access data. 15
- 16. Data Warehousing• The process of constructing and using data warehouses• A decision support database that is maintained separately from the organization’s operational database• Support information processing by providing a solid platform of consolidated, historical data for analysis• Set up stages for effective data mining 16
- 17. Illustration of Data Warehousing clientData source in Taipei Clean Transform Query and Data AnalysisData source in New York Integrate Warehouse Tools . Load . . clientData source in London 17
- 18. OLTP vs. OLAPOLTP(On-line Transaction Processing) Short online transactions: update, insert, delete current & detailed data, Versatile Online-Transaction Processing Tx. database Complex Queries Analytics Data Mining Decision Making Data Warehouse OLAP(On-line Analytical Processing) aggregated & historical data, Static and Low volume 18
- 19. Multi-Dimensional View of Data Mining• Data to be mined – Relational, data warehouse, transactional, stream, object-oriented/relational, active, spatial, time-series, text, multi-media, heterogeneous, legacy, WWW• Knowledge to be mined – Characterization, discrimination, association, classification, clustering, trend/deviation, outlier analysis, etc. – Multiple/integrated functions and mining at multiple levels• Techniques utilized – Database-oriented, data warehouse (OLAP), machine learning, statistics, visualization, etc.• Applications adapted – Retail, telecommunication, banking, fraud analysis, bio-data mining, stock market analysis, text mining, Web mining, etc. 19
- 20. Mining Capabilities (1/4)• Multi-dimensional concept description: Characterization and discrimination – Generalize, summarize, and contrast data characteristics, e.g., dry vs. wet regions• Frequent patterns (or frequent itemsets), association – Diaper Beer [0.5%, 75%] (support, confidence) 20
- 21. Mining Capabilities (2/4)• Classification and prediction – Construct models (functions) that describe and distinguish classes or concepts for future prediction • E.g., classify countries based on (climate), or classify cars based on (gas mileage) – Predict some unknown or missing numerical values 21
- 22. Mining Capabilities (3/4)• Clustering – Class label is unknown: Group data to form new categories (i.e., clusters), e.g., cluster houses to find distribution patterns – Maximizing intra-class similarity & minimizing interclass similarity• Outlier analysis – Outlier: Data object that does not comply with the general behavior of the data – Noise or exception? Useful in fraud detection, rare events analysis 22
- 23. Mining Capabilities (4/4)• Time and ordering, trend and evolution analysis – Trend and deviation: e.g., regression analysis – Sequential pattern mining: e.g., digital camera large SD memory – Periodicity analysis – Motifs and biological sequence analysis • Approximate and consecutive motifs – Similarity-based analysis 23
- 24. More Advanced Mining Techniques• Data stream mining – Mining data that is ordered, time-varying, potentially infinite.• Graph mining – Finding frequent subgraphs (e.g., chemical compounds), trees (XML), substructures (web fragments)• Information network analysis – Social networks: actors (objects, nodes) and relationships (edges) • e.g., author networks in CS, terrorist networks – Multiple heterogeneous networks • A person could be multiple information networks: friends, family, classmates, … – Links carry a lot of semantic information: Link mining• Web mining – Web is a big information network: from PageRank to Google – Analysis of Web information networks • Web community discovery, opinion mining, usage mining, … 24
- 25. Challenges for Data Mining• Handling of different types of data• Efficiency and scalability of mining algorithms• Usefulness and certainty of mining results• Expression of various kinds of mining results• Interactive mining at multiple abstraction levels• Mining information from different source of data• Protection of privacy and data security 25
- 26. Brief Summary• Data mining: Discovering interesting patterns and knowledge from massive amount of data• A natural evolution of database technology, in great demand, with wide applications• A KDD process includes data cleaning, data integration, data selection, transformation, data mining, pattern evaluation, and knowledge presentation• Mining can be performed in a variety of data• Data mining functionalities: characterization, discrimination, association, classification, clustering, outlier and trend analysis, etc. 26
- 27. A Brief History of Data Mining Society • 1989 IJCAI Workshop on Knowledge Discovery in Databases – Knowledge Discovery in Databases (G. Piatetsky-Shapiro and W. Frawley, 1991) • 1991-1994 Workshops on Knowledge Discovery in Databases – Advances in Knowledge Discovery and Data Mining (U. Fayyad, G. Piatetsky- Shapiro, P. Smyth, and R. Uthurusamy, 1996) • 1995-1998 International Conferences on Knowledge Discovery in Databases and Data Mining (KDD’95-98) – Journal of Data Mining and Knowledge Discovery (1997) • ACM SIGKDD conferences since 1998 and SIGKDD Explorations • More conferences on data mining – PAKDD (1997), PKDD (1997), SIAM-Data Mining (2001), (IEEE) ICDM (2001), etc.More details here: http://www.kdnuggets.com/gpspubs/sigkdd-explorations-kdd-10-years.html • ACM Transactions on KDD starting in 2007 27
- 28. Conferences and Journals on Data Mining• KDD Conferences • Other related conferences – ACM SIGKDD Int. Conf. on – DB: ACM SIGMOD, VLDB, Knowledge Discovery in ICDE, EDBT, ICDT Databases and Data Mining (KDD) – WEB & IR: CIKM, WWW, – SIAM Data Mining Conf. (SDM) SIGIR – (IEEE) Int. Conf. on Data Mining – ML & PR: ICML, CVPR, NIPS (ICDM) • Journals – European Conf. on Machine Learning and Principles and – Data Mining and Knowledge practices of Knowledge Discovery Discovery (DAMI or DMKD) and Data Mining (ECML-PKDD) – IEEE Trans. On Knowledge – Pacific-Asia Conf. on Knowledge and Data Eng. (TKDE) Discovery and Data Mining – KDD Explorations (PAKDD) – ACM Trans. on KDD – Int. Conf. on Web Search and Data Mining (WSDM) 28
- 29. CAPABILITIES OF DATA MINING 29
- 30. FREQUENT PATTERNS &ASSOCIATION RULES 30
- 31. Basic Concepts• Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set• First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context of frequent itemsets and association rule mining• Motivation: Finding inherent regularities in data – What products were often purchased together?— Beer and diapers?! – What are the subsequent purchases after buying a PC? – What kinds of DNA are sensitive to this new drug? – Can we automatically classify web documents?• Applications – Basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis 31
- 32. Mining Association Rules• Transaction data analysis. Given: – A database of transactions (Each tx. has a list of items purchased) – Minimum confidence and minimum support• Find all association rules: the presence of one set of items implies the presence of another set of items Diaper Beer [0.5%, 75%] (support, confidence) 32
- 33. Two Parameters• Confidence (how true) – The rule X&Y ⇒Z has 90% confidence: means 90% of customers who bought X and Y also bought Z.• Support (how useful is the rule) – Useful rules should have some minimum transaction support. 33
- 34. Mining Strong Association Rules in Transaction Databases (1/2)• Measurement of rule strength in a transaction database. A→B [support, confidence] # of tx containing all items in A ∪ B support = Pr( A ∪ B ) = total # of tx # of tx containing both A ∪ B confidence = Pr( B | A) = # of tx containing A 34
- 35. Mining Strong Association Rules in Transaction Databases (2/2)• We are often interested in only strong associations, i.e., – support ≥ min_sup – confidence ≥ min_conf• Examples: – milk → bread [5%, 60%] – tire and auto_accessories → auto_services [2%, 80%]. 35
- 36. Example of Association Rules Transaction-id Items bought 1 A, B, D 2 A, C, D 3 A, D, E 4 B, E, F 5 B, C, D, E, F Let min. support = 50%, min. confidence = 50% Frequent patterns: {A:3, B:3, D:3, E:3, AD:3} Association rules: A D (s = 60%, c = 100%) D A (s = 60%, c = 75%) 36
- 37. Two Steps for Mining Association Rules• Determining “large (frequent) itemsets” – The main factor for overall performance – The downward closure property of frequent patterns • Any subset of a frequent itemset must be frequent • If {beer, diaper, nuts} is frequent, so is {beer, diaper} • i.e., every transaction having {beer, diaper, nuts} also contains {beer, diaper}• Generating rules 37
- 38. The Apriori Algorithm• Apriori (R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB94.) – Derivation of large 1-itemsets L1: At the first iteration, scan all the transactions and count the number of occurrences for each item. – Level-wise derivation: At the kth iteration, the candidate set Ck are those whose every (k-1)-item subset is in Lk-1. Scan DB and count the # of occurrences for each candidate itemset. 38
- 39. The Apriori Algorithm—An Example min. support =2 tx’s (50%)Database TDB C1 L1 Itemset sup Itemset supTid Items 1st scan {A} 2 {A} 2100 A, C, D {B} 3 {B} 3200 B, C, E {C} 3 {C} 3300 A, B, C, E {D} 1 {E} 3400 B, E {E} 3 C2 C2 Itemset Itemset sup L2 Itemset sup 2 scan nd {A, B} 1 {A, B} {A, C} 2 {A, C} 2 {A, C} {B, C} 2 {A, E} 1 {A, E} {B, E} 3 {B, C} 2 {B, C} {C, E} 2 {B, E} 3 {B, E} {C, E} 2 {C, E} C3 Itemset 3rd scan L3 Itemset sup {B, C, E} {B, C, E} 2 39
- 40. From Large Itemsets to Rules• For each large itemset m – For each subset p of m if ( sup(m) / sup(m-p) ≥ min_conf ) • output the rule (m-p)→p – conf. = sup(m)/sup(m-p) – support = sup(m)• m = {a,c,d,e,f,g} 2000 tx’s, p = {c,e,f,g} m-p = {a,d} 5000 tx’s – conf. = # {a,c,d,e,f,g} / # {a,d} – rule: {a,d} →{c,e,f,g} confidence: 40%, support: 2000 tx’s 40
- 41. Redundant Rules• For the same support and confidence, if we have a rule {a,d} →{c,e,f,g}, do we have [agga98a]: – {a,d} →{c,e,f} ? Yes! – {a} →{c,e,f,g} ? Yes! – {a,d,c} →{e,f,g} ? No! – {a} →{c,d,e,f,g} ? No! 41
- 42. Practice• Suppose we additionally have – 500 ACE – 600 BCD – Support = 3 tx’s (50%), confidence = 66%• Repeat the large itemset generation – Identify all large itemsets• Derive up to 4 rules – Generate rules from the large itemsets with the biggest number of elements (from big to small) 42
- 43. Discussion of The Apriori Algorithm• Apriori (R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB94.) – Derivation of large 1-itemsets L1: At the first iteration, scan all the transactions and count the number of occurrences for each item. – Level-wise derivation: At the kth iteration, the candidate set Ck are those whose every (k-1)-item subset is in Lk-1. Scan DB and count the # of occurrences for each candidate itemset.• The cardinalitiy (number of elements) of C2 is huge.• The execution time for the first 2 iterations is the dominating factor to overall performance!• Database scan is expensive. 43
- 44. Improvement of the Apriori Algorithm• Reduce passes of transaction database scans• Shrink the number of candidates• Facilitate the support counting of candidates 44
- 45. Example Improvement 1- Partition: Scan Database Only Twice• Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB – Scan 1: partition database and find local frequent patterns – Scan 2: consolidate global frequent patterns• A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association in large databases. In VLDB’95 45
- 46. Example Improvement 2- DHP• DHP (direct hashing with pruning): Apriori + hashing – Use hash-based method to reduce the size of C2. – Allow effective reduction on tx database size (tx number and each tx size.) Tid Items 100 A, C, D 200 B, C, E 300 A, B, C, E 400 B, E J. Park, M.-S. Chen, and P. Yu. An effective hash-based algorithm for mining association rules. In SIGMOD’95. 46
- 47. Mining Frequent Patterns w/o Candidate Generation• A highly compact data structure: frequent pattern tree.• An FP-tree-based pattern fragment growth mining method.• Search technique in mining: partitioning- based, divide-and-conquer method.• J. Han, J. Pei, Y. Yin, Mining Frequent Patterns without Candidate Generation, in SIGMOD’2000. 47
- 48. Frequent Patter Tree (FP-tree)• 3 parts: – One root labeled as ‘null’ – A set of item prefix subtrees – Frequent item header table• Each node in the prefix subtree consists of – Item name – Count – Node-link• Each entry in the frequent-item header table consists of – Item-name – Head of node-link 48
- 49. The FP-tree Structurefrequent item header tableItem Head of node-links root f f:4 c c:1 a c:3 b b:1 m b:1 p a:3 p:1 m:2 b:1 p:2 m:1 49
- 50. FP-tree Construction: Step1• Scan the transaction database DB once (the first time), and derives a list of frequent items.• Sort frequent items in frequency descending order.• This ordering is important since each path of a tree will follow this order. 50
- 51. Example (min. support = 3)Tx ID Items Bought (ordered) Frequent Items100 f,a,c,d,g,i,m,p f,c,a,m,p200 a,b,c,f,l,m,o f,c,a,b,m300 b,f,h,j,o f,b frequent item header table400 b,c,k,s,p c,b,p500 a,f,c,e,l,p,m,n f,c,a,m,p Item Head of node-links f List of frequent items: c (f:4), (c:4), (a:3), (b:3), (m:3), (p:3) a b m p 51
- 52. FP-tree Construction: Step 2• Create a root of a tree, label with “null”• Scan the database the second time. The scan of the first tx leads to the construction of the first branch of the tree. Scan of 1st transaction: f,a,c,d,g,i,m,p root The 1st branch of the tree <(f:1),(c:1),(a:1),(m:1),(p:1)> f:1 c:1 a:1 m:1 p:1 52
- 53. FP-tree Construction: Step 2 (cont’d)• Scan of 2nd transaction: root a,b,c,f,l,m,o → f,c,a,b,m f:2 c:2 two new nodes: (b:1) (m:1) a:2 m:1 b:1 p:1 m:1 53
- 54. Tx ID Items Bought (ordered) Frequent Items 100 f,a,c,d,g,i,m,p f,c,a,m,p The FP-tree 200 a,b,c,f,l,m,o f,c,a,b,m 300 b,f,h,j,o f,b 400 b,c,k,s,p c,b,pfrequent item header table 500 a,f,c,e,l,p,m,n f,c,a,m,pItem Head of node-links root f f:4 c c:1 a c:3 b b:1 m b:1 p a:3 p:1 m:2 b:1 p:2 54 m:1
- 55. Mining Process• Starts from the least frequent item p – Mining order: p -> m -> b -> a -> c -> f frequent item header table Item Head of node-links f c a b m p 55
- 56. Mining Process for item p• Starts from the least frequent item p root min. support = 3 Two paths: f:4 <f:4, c:3, a:3, m:2, p:2> c:1 <c:1, b:1,p:1> c:3 b:1 Conditional pattern based of ”p”: b:1 <f:2, c:2, a:2, m:2> a:3 <c:1, b:1> p:1 Conditional frequent pattern: m:2 <c:3> b:1 So we have two frequent patterns: p:2 {p:3}, {cp:3} m:1 56
- 57. Mining Process for Item m root min. support = 3 Two paths:f:4 <f:4, c:3, a:3, m:2> c:1 <f:4, c:3, a:3, b:1, m:1>c:3 b:1 Conditional pattern based of ”m”: b:1 <f:2, c:2, a:2>a:3 <f:1, c:1, a:1, b:1> p:1 Conditional frequent pattern:m:2 <f:3, c:3, a:3> b:1p:2 m:1 57
- 58. Mining m’s Conditional FP-tree Mine (<f:3, c:3, a:3> | m) f a c (am:3) (cm:3) (fm:3) Mine (<f:3, c:3> | am) Mine (<f:3> | cm) c f f(cam:3) (fam:3 (fcm:3Mine (<f:3> | cam) ) ) f (fcam:3 ) So we have frequent patterns: {m:3}, {am:3}, {cm:3}, {fm:3}, {cam:3}, {fam:3}, {fcm:3}, {fcam:3} 58
- 59. Analysis of the FP-tree-based method• Find the complete set of frequent itemsets• Efficient because – Works on a reduced set of pattern bases – Performs mining operations less costly than generation & test• Cons: – No advantages if the length of most tx’s are short – The size of FP-tree not always fit into main memory 59
- 60. Generalized Association Rules• Given the class hierarchy (taxonomy), one would like to choose proper data granularities for mining.• Different confidence/support may be considered.• R. Srikant and R. Agrawal, Mining generalized association rules, VLDB’95. 60
- 61. Freq. itemset ItemsetConcept Hierarchy support Clothes Footwear Jacket 2 Outerwear 3 Outerwear Shirts Shoes Hiking Boots Clothes 4 Shoes 2Jackets Ski Pants Hiking Boots 2 Footwear 4Tx ID Items Bought Outerwear, Hiking Boots 2100 Shirt Clothes, Hiking Boots 2200 Jacket, Hiking Boots Outerwear, Footwear 2300 Ski Pants, Hiking Boots Clothes, Footwear 2400 Shoes sup(30% conf(60% ) )500 Shoes Outerwear -> Hiking 33% 66%600 Jacket Boots Outerwear -> Footwear 33% 66% Hiking Boots -> 33% 100% Outerwear Hiking Boots -> Clothes 33% 100% Jacket -> Hiking Boots 16% 50% 61
- 62. Generalized Association Rulesuniform support reduced support Level 1 Milk Level 1 min_sup = 5% [support = 10%] min_sup = 5% min_sup = 3% Level 2 min_sup = 12% Level 1 Level 2 2% Milk Skim Milk Level 2 min_sup = 5% [support = 6%] [support = 4%] min_sup = 3% Not examined level filtering 2% Milk [support = 10% Milk 62 Not Sk
- 63. Other Relevant Topics• Max patterns – R. J. Bayardo. Efficiently mining long patterns from databases. SIGMOD98.• Closed patterns – N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Discovering frequent closed itemsets for association rules. ICDT99.• Sequential Patterns – What items one will purchase if he/she has bought some certain items. – R. Srikant and R. Agrawal, Mining sequential patterns, ICDE’95• Traversal Patterns – Mining path traversal patterns in a web environment where documents or objects are linked together to facilitate interactive access. – M.-S. Chen, J. Park and P. Yu. Efficient Data Mining for Path Traversal Patterns. TKDE’98.and more… 63
- 64. CLASSIFICATION 64
- 65. Classification• Classifying tuples in a database.• Each tuple has some attributes with known values.• In training set E – Each tuple consists of the same set of multiple attributes as the tuples in the large database W. – Additionally, each tuple has a known class identity. 65
- 66. Classification (cont’d)• Derive the classification mechanism from the training set E, and then use this mechanism to classify general data (in testing set.)• A decision tree based approach has been influential in machine learning studies. 66
- 67. Classification – Step 1: Model Construction • Train model from the existing data pool Training Classification algorithm Dataname age income own cars?Sandy <=30 low no Classification rulesBill <=30 low yesFox 31…40 high yesSusan >40 med noClaire >40 med noAndy 31…40 high yes 67
- 68. Classification – Step 2: Model Usage Testing Data Classification rulesname age income own cars? NoJohn >40 hight ? NoSally <=30 low ? YesAnnie 31…40 high ? 68
- 69. What is Prediction?• Prediction is similar to classification – First, construct model – Second, use model to predict future of unknown objects• Prediction is different from classification – Classification refers to predict categorical class label. – Prediction refers to predict continuous values. • Major method: regression 69
- 70. Supervised vs. Unsupervised Learning• Supervised learning (e.g., classification) – Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations.• Unsupervised learning (e.g., clustering) – We are given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data. – No training data, or the “training data” are not accompanied by class labels. 70
- 71. Evaluating Classification Methods• Predictive accuracy• Speed – Time to construct the model and time to use the model• Robustness – Handling noise and missing values• Scalability – Efficiency in large databases (not memory resident data)• Goodness of rules – Decision tree size – The compactness of classification rules 71
- 72. A Decision-Tree Based Classification• A decision tree of whether going to play tennis or not: outlook sunny rainy overcast humidity windy high low P Yes No N P N P• ID-3 and its extended version C4.5 (Quinlan’93): A top-down decision tree generation algorithm 72
- 73. Algorithm for Decision Tree Induction (1/2)• Basic algorithm (a greedy algorithm) – Tree is constructed in a top-down recursive divide-and- conquer manner. – Attributes are categorical. (if an attribute is a continuous number, it needs to be discretized in advance.) E.g. 0 ~ 20 61 ~ 80 0 <= age <= 100 21 ~ 40 81 ~ 100 41 ~ 60 – At start, all the training examples are at the root. – Examples are partitioned recursively based on selected attributes. 73
- 74. Algorithm for Decision Tree Induction (2/2)• Basic algorithm (a greedy algorithm) – Test attributes are selected on the basis of a heuristic or statistical measure (e.g., information gain): maximizing an information gain measure, i.e., favoring the partitioning which makes the majority of examples belong to a single class. – Conditions for stopping partitioning: • All samples for a given node belong to the same class • There are no remaining attributes for further partitioning – majority voting is employed for classifying the leaf • There are no samples left 74
- 75. Decision Tree Induction: Training Dataset age income student credit_rating buys_computer <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no 75
- 76. Age?<= 30 31…40 > 40 76
- 77. Primary Issues in Tree Construction (1/2)• Split criterion: Goodness function – Used to select the attribute to be split at a tree node during the tree generation phase – Different algorithms may use different goodness functions: • Information gain (used in ID3/C4.5) • Gini index (used in CART) 77
- 78. Primary Issues in Tree Construction (2/2)• Branching scheme: – Determining the tree branch to which a sample belongs Income: Income: Income: – Binary vs. k-ary splitting high medium low• When to stop the further splitting of a node? e.g. impurity measure• Labeling rule: a node is labeled as the class to which most samples at the node belongs. 78
- 79. How to Use a Tree?• Directly – Test the attribute value of unknown sample against the tree. – A path is traced from root to a leaf which holds the label.• Indirectly – Decision tree is converted to classification rules. – One rule is created for each path from the root to a leaf. – IF-THEN is easier for humans to understand . 79
- 80. 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: m Info( D) = −∑ pi log 2 ( pi ) i =1 Expected information (entropy): Entropy is a measure of how "mixed up" an attribute is. It is sometimes equated to the purity or impurity of a variable. High Entropy means that we are sampling from a uniform (boring) distribution. 80
- 81. Expected Information (Entropy) Expected information (entropy) needed to classify a tuple in D: m Info( D) = −∑ pi log 2 ( pi ) (m: number of i =1 labels) 3 3 2 2 5 5 0 0Info( D) = I (3,2) = − log 2 ( ) − log 2 ( ) Info( D) = I (5,0) = − log 2 ( ) − log 2 ( ) 5 5 5 5 5 5 5 5 3 2 = 0−0 = 0 ≈ − × (−0.737) − × (−1.322) 5 5 81
- 82. 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: m Info( D) = I ( D ) = −∑ pi log 2 ( pi ) i =1 Information needed (after using A to split D into v partitions) to v |D | classify D: Info A ( D) = ∑ j × I (D j ) j =1 | D | Information gained by branching on attribute A Gain(A) = Info(D) − Info A(D) 82
- 83. Expected Information (Entropy) Information needed (after using A to split D into v partitions) to classify D: v |D | Info A ( D) = ∑ j × I (D j ) j =1 | D | 2 3 2 3 Info( D) = Info(1,1) + Info(2,1) Info( D) = Info(2,0) + Info(3,0) 5 5 5 5 83
- 84. Attribute Selection: Information Gain Class P: buys_computer = “yes” 5 4 Infoage ( D) = I (2,3) + I (4,0) Class N: buys_computer = “no” 14 14 9 9 5 5 5Info( D) = I (9,5) = − log 2 ( ) − log 2 ( ) =0.940 + I (3,2) = 0.694 14 14 14 14 14 5 age pi ni I(pi, ni) I (2,3) means “age <=30” has 5 out of 14 <=30 2 3 0.971 14 samples, with 2 yes’es and 3 31…40 4 0 0 no’s. Hence >40 3 2 0.971 Gain(age) = Info( D) − Infoage ( D) = 0.246 age income student credit_rating buys_computer<=30 high no fair no<=3031…40 high high no no excellent fair no yes Similarly,>40 medium no fair yes>40>40 low low yes yes fair excellent yes no Gain(income) = 0.02931…40<=30 low medium yes no excellent fair yes no Gain( student ) = 0.151<=30>40 low medium yes yes fair fair yes yes Gain(credit _ rating ) = 0.048<=30 medium yes excellent yes31…40 medium no excellent yes31…40 high yes fair yes>40 medium no excellent no 84
- 85. Gain Ratio for Attribute Selection (C4.5)• Information gain measure is biased towards attributes with a large number of values.• C4.5 (a successor of ID3) uses gain ratio to overcome the problem (normalization to information gain.) v | Dj | | Dj | SplitInfo A ( D) = −∑ × log 2 ( ) j =1 |D| |D| – GainRatio(A) = Gain(A)/SplitInfo(A) 4 4 6 6 4 4 SplitInfo A ( D ) = − × log 2 ( ) − × log 2 ( ) − × log 2 ( ) = 0.926 14 14 14 14 14 14 GainRatio(income) = 0.029/0.926 = 0.031• The attribute with the maximum gain ratio is selected as the splitting attribute. 85
- 86. Gini index (CART, IBM IntelligentMiner)• If a data set D contains examples from n classes, gini index, Gini(D) is defined as n Gini( D) = −1 ∑ p2 j j=1 where pj is the relative frequency of class j in D• If a data set D is split on A into two subsets D1 and D2, the gini index Gini(D) is defined as: |D | |D | Gini A ( D) = 1 Gini( D1) + 2 Gini( D 2) | D| |D|• Reduction in Impurity: ∆Gini( A) = Gini(D) − GiniA ( D)• The attribute provides the smallest GiniA(D) (or the largest reduction in impurity) is chosen to split the node (need to enumerate all the possible splitting points for each attribute.) 86
- 87. Gini index (CART, IBM IntelligentMiner)• Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no.” 2 2 9 5 Gini ( D) = 1 − − = 0.459 14 14 • Suppose the attribute income partitions D into 10 in D 1: {low, medium} and 4 in D2: {high}. 10 4 Giniincome∈{low,medium} ( D) = Gini ( D1 ) + Gini ( D1 ) 14 14 10 6 4 4 1 3 = [1 − ( ) 2 − ( ) 2 ] + [1 − ( ) 2 − ( ) 2 ] 14 10 10 14 4 4 = 0.45 = Giniincome∈{high} ( D) But Giniincomeϵ{medium,high} is 0.30 and thus the best since it is the lowest. 87
- 88. Other Attribute Selection Measures• CHAID: a popular decision tree algorithm, measure based on χ2 test for independence• C-SEP: performs better than info. gain and gini index in certain cases• G-statistics: has a close approximation to χ2 distribution• MDL (Minimal Description Length) principle (i.e., the simplest solution is preferred): – The best tree as the one that requires the fewest # of bits to both (1) encode the tree, and (2) encode the exceptions to the tree• Multivariate splits (partition based on multiple variable combinations) – CART: finds multivariate splits based on a linear combination of attributes. Which attribute selection measure is the best? Most give good results, none is significantly superior than others 88
- 89. Other Types of Classification Methods• Bayes Classification Methods• Rule-Based Classification• Support Vector Machine (SVM)• Some of these methods will be taught in the following lessons. 89
- 90. CLUSTERING 90
- 91. What is Cluster Analysis?• Cluster: a collection of data objects – Similar to one another within the same cluster – Dissimilar to the objects in other clusters• Cluster Analysis – Grouping a set of data objects into clusters• Typical applications: – As a stand-alone tool to get insight into data distribution – As a preprocessing step for other algorithms 91
- 92. General Applications of Clustering• Spatial data analysis – Create thematic maps in GIS by clustering feature spaces. – Detect spatial clusters and explain them in spatial data mining.• Image Processing• Pattern recognition• Economic Science (especially market research)• WWW – Document classification – Cluster Web-log data to discover groups of similar access patterns 92
- 93. Examples of Clustering Applications• Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs.• Land use: Identification of areas of similar land use in an earth observation database.• Insurance: Identifying groups of motor insurance policy holders with a high average claim cost.• City-planning: Identifying groups of houses according to their house type, value, and geographical location. 93
- 94. What is Good Clustering?• A good clustering method will produce high quality clusters with – High intra-class similarity – Low inter-class similarity• The quality of a clustering result depends on both the similarity measure used by the method and its implementation.• The quality of a clustering method is also measured by its ability to discover hidden patterns. 94
- 95. Requirements of Clustering in Data Mining (1/2)• Scalability• Ability to deal with different types of attributes• Discovery of clusters with arbitrary shape• Minimal requirements of domain knowledge for input• Able to deal with outliers 95
- 96. Requirements of Clustering in Data Mining (2/2)• Insensitive to order of input records• High dimensionality – Curse of dimensionality• Incorporation of user-specified constraints• Interpretability and usability 96
- 97. Clustering Methods (I)• Partitioning Method – Construct various partitions and then evaluate them by some criterion, e.g., minimizing the sum of square errors – K-means, k-medoids, CLARANS• Hierarchical Method – Create a hierarchical decomposition of the set of data (or objects) using some criterion – Diana, Agnes, BIRCH, ROCK, CHAMELEON• Density-based Method – Based on connectivity and density functions – Typical methods: DBSACN, OPTICS, DenClue 97
- 98. Clustering Methods (II)• Grid-based approach – based on a multiple-level granularity structure – Typical methods: STING, WaveCluster, CLIQUE• Model-based approach – A model is hypothesized for each of the clusters and tries to find the best fit of that model to each other – Typical methods: EM, SOM, COBWEB• Frequent pattern-based – Based on the analysis of frequent patterns – Typical methods: pCluster• User-guided or constraint-based – Clustering by considering user-specified or application-specific constraints – Typical methods: cluster-on-demand, constrained clustering 98
- 99. Typical Alternatives to Calculate the Distance between Clusters• Single link: smallest distance between an element in one cluster and an element in the other, i.e., dis(Ki, Kj) = min(tip, tjq)• Complete link: largest distance between an element in one cluster and an element in the other, i.e., dis(Ki, Kj) = max(tip, tjq)• Average: average distance between an element in one cluster and an element in the other, i.e., dis(Ki, Kj) = avg(tip, tjq)• Centroid: distance between the centroids of two clusters, i.e., dis(Ki, Kj) = dis(Ci, Cj)• Medoid: distance between the medoids of two clusters, i.e., dis(Ki, Kj) = dis(Mi, Mj) – Medoid: one chosen, centrally located object in the cluster 99
- 100. Centroid, Radius and Diameter of a Cluster (for numerical data sets)• Centroid: the “middle” of a cluster ΣiN= 1(t ) Cm = N ip• Radius: square root of average mean squared distance from any point of the cluster to its centroid Σ N (t − cm ) 2 Rm = i =1 ip N• Diameter: square root of average mean squared distance between all pairs of points in the cluster Σ N Σ N (t − t ) 2 diameter != 2 * radius i = 1 j = 1 ip jq D = m N ( N − 1) 100
- 101. Partitioning Algorithms: Basic Concept• Partitioning method: construct a partition of a database D of n objects into a set of k clusters.• Given a number k, find a partition of k clusters that optimizes the chosen partitioning criterion. – Global optimal: exhaustively enumerate all partitions. – Heuristic methods: k-means, k-medoids • k-means (MacQueen’67) • k-medoids or PAM, partion around medoids (Kaufman & Rousseeuw’87) 101
- 102. The K-Means Clustering Method • Given k, the k-means algorithm is implemented in four steps: 1. Arbitrarily choose k points as initial cluster centroids. 2. Update Means (Centroids): Compute seed points as the center of the clusters of the current partition.loop (center: mean point of the cluster) 3. Re-assign Points: Assign each object to the cluster with the nearest seed point. 4. Go back to Step 2, stop when no more new assignment. 102
- 103. Example of the K-Means Clustering Method 10 1010 9 99 8 88 7 77 6 66 5 55 Assign 4 44 3 Update 3 each32 2 the 2 objects 1 11 0 cluster 0 to the0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 means most similar Re-assign Re-assign centroid Given k = 2: 10 10 9 9 Arbitrarily choose k 8 8 object as initial 7 7 6 6 cluster centroid 5 Update 5 4 4 3 the 3 cluster 2 2 1 1 0 0 1 2 3 4 5 6 7 8 9 10 means 0 0 1 2 3 4 5 6 7 8 9 10 103
- 104. Comments on the K-Means Clustering• Time Complexity: O(tkn), where n is # of objects, k is # of clusters, and t is # of iterations. Normally, k,t<<n.• Often terminates at a local optimum. (The global optimum may be found using techniques such as: deterministic annealing and genetic algorithms)• Weakness: – Applicable only when mean is defined, how about categorical data? – Need to specify k, the number of clusters, in advance – Unable to handle noisy data and outliers 104
- 105. Why is K-Means Unable to Handle Outliers?• The k-means algorithm is sensitive to outliers – Since an object with an extremely large value may substantially distort the distribution of the data. X• K-Medoids: Instead of taking the mean value of the object in a cluster as a reference point, medoids can be used, which is the most centrally located object in a cluster. 105
- 106. PAM: The K-Medoids Method • PAM: Partition Around Medoids • Use real object to represent the cluster 1. Randomly select k representative objects as medoids. 2. Assign each data point to the closest medoid. 3. For each medoid m,loop a. For each non-medoid data point o b. Swap m and o, and compute the total cost of the configuration. 1. Select the configuration with the lowest cost. 2. Repeat steps 2 to 5 until there is no change in the medoid. 106
- 107. A Typical K-Medoids Algorithm (PAM)10 10 9 9 8 7 8 Assign each 7 6 Arbitrary 6 remaining object to 5 choose k 5 the nearest medoid 4 4 3 object as 3 2 initial 2 1 1 0 medoids 0 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 9k=2 8 7 10 6 m2 9 5 8 4 7 3 6 2 m1 5 1 4 0 3 0 1 2 3 4 5 6 7 8 9 10 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Swap each medoid and each data point, and compute the total cost of the configuration 107
- 108. PAM Clustering: Total swapping cost TCih=∑jCjih 10 10 9 d(j,h)<d(j,t) 9 j- Original 8 t 8 t 7medoid: t, i 7 6 j 6- h: swap with i 5 5 4 i h 4 h- j: any non- 3 3 i 2 j j 2 j jselected object 1 1 0 0 1 2 3 4 5 6 7 8 9 10 i h 0 0 1 2 3 4 5 6 7 8 9 10 t t Cjih = d(j, h) - d(j, i) Cjih = 0 10 10 9 d(j,h)>d(j,t) 9 8 h 8 7 6 j 7 6 5 5 i i h j t 4 4 3 3 2 j j 2 t j j 1 1 0 0 1 2 3 4 5 6 7 8 9 10 i t 0 0 1 2 3 4 5 6 7 8 9 10 t h Cjih = d(j, t) - d(j, i) Cjih = d(j, h) - d(j, t) 108
- 109. What is the Problem with PAM?• PAM is more robust than k-means in the presence of noise and outliers because a medoid is less influenced by outliers or other extreme values than a mean.• PAM works efficiently for small data sets but does not scale well for large data sets. – O( k(n-k)(n-k) ) for each iteration, where n is # of data, k is # of clusters – Improvements: CLARA (uses a sampled set to determine medoids), CLARANS 109
- 110. Hierarchical Clustering• Use distance matrix as clustering criteria.• This method does not require the number of clusters k as an input, but needs a termination condition. Step 0 Step 1 Step 2 Step 3 Step 4 agglomerative (AGNES) a ab b abcde c cde d de e divisive (DIANA) Step 4 Step 3 Step 2 Step 1 Step 0 110
- 111. AGNES (Agglomerative Nesting)• Introduced in Kaufmann and Rousseeuw (1990)• Use the Single-Link method and the dissimilarity matrix.• Merge nodes that have the least dissimilarity• Go on in a non-descending fashion• Eventually all nodes belong to the same cluster 10 10 10 9 9 9 8 8 8 7 7 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 111
- 112. Dendrogram: Shows How the Clusters are Merged Decompose data objects into a several levels of nested partitioning (tree of clusters), called a dendrogram. A clustering of the data objects is obtained by cutting the dendrogram at the desired level, then each connected component forms a cluster. 112
- 113. DIANA (Divisive Analysis)• Introduced in Kaufmann and Rousseeuw (1990)• Inverse order of AGNES• Eventually each node forms a cluster on its own. 10 10 10 9 9 9 8 8 8 7 7 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 9 8 7 6 5 4 10 3 2 1 0 113
- 114. More on Hierarchical Clustering• Major weakness: – Do not scale well: time complexity is at least O(n2), where n is the number of total objects. – Can never undo what was done previously.• Integration of hierarchical with distance-based clustering – BIRCH(1996): uses CF-tree data structure and incrementally adjusts the quality of sub-clusters. – CURE(1998): selects well-scattered points from the cluster and then shrinks them towards the center of the cluster by a specified fraction. 114
- 115. Density-Based Clustering Methods• Clustering based on density (local cluster criterion), such as density-connected points• Major features: – Discover clusters of arbitrary shape – Handle noise – One scan – Need density parameters as termination condition• Several interesting studies: – DBSCAN: Ester, et al. (KDD’96) – OPTICS: Ankerst, et al (SIGMOD’99). – DENCLUE: Hinneburg & D. Keim (KDD’98) – CLIQUE: Agrawal, et al. (SIGMOD’98) (more grid-based) 115
- 116. Density-Based Clustering: Basic Concepts• Two parameters: – Eps: Maximum radius of the neighborhood – MinPts: Minimum number of points in an Eps-neighborhood of that point Eps 116
- 117. Density-Based Clustering: Basic Concepts• Two parameters: – Eps: Maximum radius of the neighborhood – MinPts: Minimum number of points in an Eps-neighborhood of that point• NEps(q): {p | dist(p,q) <= Eps} // p, q are two data points• Directly density-reachable: A point p is directly density- reachable from a point q w.r.t. Eps, MinPts if – p belongs to NEps(q) p MinPts = 5 – core point condition: q Eps = 1 cm |NEps (q)| >= MinPts 117
- 118. Density-Reachable and Density-Connected• Density-reachable: – A point p is density-reachable from a p point q w.r.t. Eps, MinPts if there is a p2 chain of points p1, …, pn, p1 q = q, pn = p such that pi+1 is directly density-reachable from pi.• Density-connected: – A point p is density-connected to a p q point q w.r.t. Eps, MinPts if there is a point o such that both, p and q are o density-reachable from o w.r.t. Eps and MinPts. 118
- 119. DBSCAN: Density Based Spatial Clustering of Applications with Noise• Relies on a density-based notion of cluster: A cluster is defined as a maximal set of density-connected points.• Discovers clusters of arbitrary shape in spatial databases with noise. Border Border Eps = 1cm MinPts = 5 Core 119
- 120. DBSCAN: The Algorithm• Arbitrary select an unvisited point p.• Retrieve all points density-reachable from p w.r.t. Eps and MinPts.• If p is a core point, a cluster is formed. Mark all these points as visited.• If p is a border point (no points are density-reachable from p), mark p as visited and DBSCAN visits the next point of the database.• Continue the process until all of the points have been visited. 120
- 121. References (1)• R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan. Automatic subspace clustering of high dimensional data for data mining applications. SIGMOD98• M. R. Anderberg. Cluster Analysis for Applications. Academic Press, 1973.• M. Ankerst, M. Breunig, H.-P. Kriegel, and J. Sander. Optics: Ordering points to identify the clustering structure, SIGMOD’99.• P. Arabie, L. J. Hubert, and G. De Soete. Clustering and Classification. World Scientific, 1996• Beil F., Ester M., Xu X.: "Frequent Term-Based Text Clustering", KDD02• M. M. Breunig, H.-P. Kriegel, R. Ng, J. Sander. LOF: Identifying Density-Based Local Outliers. SIGMOD 2000.• M. Ester, H.-P. Kriegel, J. Sander, and X. Xu. A density-based algorithm for discovering clusters in large spatial databases. KDD96.• M. Ester, H.-P. Kriegel, and X. Xu. Knowledge discovery in large spatial databases: Focusing techniques for efficient class identification. SSD95.• D. Fisher. Knowledge acquisition via incremental conceptual clustering. Machine Learning, 2:139-172, 1987.• D. Gibson, J. Kleinberg, and P. Raghavan. Clustering categorical data: An approach based on dynamic systems. VLDB’98. 121
- 122. References (2)• V. Ganti, J. Gehrke, R. Ramakrishan. CACTUS Clustering Categorical Data Using Summaries. KDD99.• D. Gibson, J. Kleinberg, and P. Raghavan. Clustering categorical data: An approach based on dynamic systems. In Proc. VLDB’98.• S. Guha, R. Rastogi, and K. Shim. Cure: An efficient clustering algorithm for large databases. SIGMOD98.• S. Guha, R. Rastogi, and K. Shim. ROCK: A robust clustering algorithm for categorical attributes. In ICDE99, pp. 512- 521, Sydney, Australia, March 1999.• A. Hinneburg, D.l A. Keim: An Efficient Approach to Clustering in Large Multimedia Databases with Noise. KDD’98.• A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Printice Hall, 1988.• G. Karypis, E.-H. Han, and V. Kumar. CHAMELEON: A Hierarchical Clustering Algorithm Using Dynamic Modeling. COMPUTER, 32(8): 68-75, 1999.• L. Kaufman and P. J. Rousseeuw, 1987. Clustering by Means of Medoids. In: Dodge, Y. (Ed.), Statistical Data Analysis Based on the L1 Norm, North Holland, Amsterdam. pp. 405-416.• L. Kaufman and P. J. Rousseeuw. Finding Groups in Data: an Introduction to Cluster Analysis. John Wiley & Sons, 1990.• E. Knorr and R. Ng. Algorithms for mining distance-based outliers in large datasets. VLDB’98.• J. B. MacQueen (1967): "Some Methods for classification and Analysis of Multivariate Observations", Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, University of California Press, 1:281-297• G. J. McLachlan and K.E. Bkasford. Mixture Models: Inference and Applications to Clustering. John Wiley and Sons, 1988.• P. Michaud. Clustering techniques. Future Generation Computer systems, 13, 1997.• R. Ng and J. Han. Efficient and effective clustering method for spatial data mining. VLDB94. 122
- 123. References (3)• L. Parsons, E. Haque and H. Liu, Subspace Clustering for High Dimensional Data: A Review , SIGKDD Explorations, 6(1), June 2004• E. Schikuta. Grid clustering: An efficient hierarchical clustering method for very large data sets. Proc. 1996 Int. Conf. on Pattern Recognition,.• G. Sheikholeslami, S. Chatterjee, and A. Zhang. WaveCluster: A multi-resolution clustering approach for very large spatial databases. VLDB’98.• A. K. H. Tung, J. Han, L. V. S. Lakshmanan, and R. T. Ng. Constraint-Based Clustering in Large Databases, ICDT01.• A. K. H. Tung, J. Hou, and J. Han. Spatial Clustering in the Presence of Obstacles , ICDE01• H. Wang, W. Wang, J. Yang, and P.S. Yu. Clustering by pattern similarity in large data sets, SIGMOD’ 02.• W. Wang, Yang, R. Muntz, STING: A Statistical Information grid Approach to Spatial Data Mining, VLDB’97.• T. Zhang, R. Ramakrishnan, and M. Livny. BIRCH : an efficient data clustering method for very large databases. SIGMOD96.• Wikipedia: DBSCAN. http://en.wikipedia.org/wiki/DBSCAN. 123
- 124. MORE ABOUT DATA MINING 124
- 125. http://www.cs.uvm.edu/~xwu/PPT/ICDM10-Sydney/ICDM10-Keynote.pdfICDM ’10 KEYNOTE SPEECH“10 YEARS OF DATA MININGRESEARCH: RETROSPECT ANDPROSPECT” Xindong Wu, University of Vermont, USA 125

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