Database Management Systems Data Mining - Data Cubes

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Presentation transcript:

15-721 Database Management Systems Data Mining - Data Cubes Anastassia Ailamaki http://www.cs.cmu.edu/~natassa

Copyright: C. Faloutsos (2001) Substitute lecturer Christos Faloutsos christos@cs.cmu.edu www.cs.cmu.edu/~christos 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Outline Problem Getting the data: Data Warehouses, DataCubes, OLAP Supervised learning: decision trees Unsupervised learning association rules (clustering) 15-721 Copyright: C. Faloutsos (2001)

Problem PGH NY ??? SF Given: multiple data sources Find: patterns (classifiers, rules, clusters, outliers...) sales(p-id, c-id, date, $price) customers( c-id, age, income, ...) NY SF ??? PGH 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Data Ware-housing First step: collect the data, in a single place (= Data Warehouse) How? How often? How about discrepancies / non-homegeneities? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Data Ware-housing First step: collect the data, in a single place (= Data Warehouse) How? A: Triggers/Materialized views How often? A: [Art!] How about discrepancies / non-homegeneities? A: Wrappers/Mediators 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Data Ware-housing Step 2: collect counts. (DataCubes/OLAP) Eg.: 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) OLAP Problem: “is it true that shirts in large sizes sell better in dark colors?” sales ... 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes ‘color’, ‘size’: DIMENSIONS ‘count’: MEASURE f color size color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes ‘color’, ‘size’: DIMENSIONS ‘count’: MEASURE f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes ‘color’, ‘size’: DIMENSIONS ‘count’: MEASURE f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes ‘color’, ‘size’: DIMENSIONS ‘count’: MEASURE f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes ‘color’, ‘size’: DIMENSIONS ‘count’: MEASURE f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes ‘color’, ‘size’: DIMENSIONS ‘count’: MEASURE f size color color; size DataCube 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes SQL query to generate DataCube: Naively (and painfully:) select size, color, count(*) from sales where p-id = ‘shirt’ group by size, color select size, count(*) group by size ... 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes SQL query to generate DataCube: with ‘cube by’ keyword: select size, color, count(*) from sales where p-id = ‘shirt’ cube by size, color 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes DataCube issues: Q1: How to store them (and/or materialize portions on demand) Q2: How to index them Q3: Which operations to allow 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes DataCube issues: Q1: How to store them (and/or materialize portions on demand) A: ROLAP/MOLAP Q2: How to index them A: bitmap indices Q3: Which operations to allow A: roll-up, drill down, slice, dice [More details: book by Han+Kamber] 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q1: How to store a dataCube? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q1: How to store a dataCube? A1: Relational (R-OLAP) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q1: How to store a dataCube? A2: Multi-dimensional (M-OLAP) A3: Hybrid (H-OLAP) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Pros/Cons: ROLAP strong points: (DSS, Metacube) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Pros/Cons: ROLAP strong points: (DSS, Metacube) use existing RDBMS technology scale up better with dimensionality 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Pros/Cons: MOLAP strong points: (EssBase/hyperion.com) faster indexing (careful with: high-dimensionality; sparseness) HOLAP: (MS SQL server OLAP services) detail data in ROLAP; summaries in MOLAP 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q1: How to store a dataCube Q2: What operations should we support? Q3: How to index a dataCube? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q2: What operations should we support? f color size color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q2: What operations should we support? Roll-up f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q2: What operations should we support? Drill-down f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q2: What operations should we support? Slice f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q2: What operations should we support? Dice f size color color; size 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q2: What operations should we support? Roll-up Drill-down Slice Dice 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q1: How to store a dataCube Q2: What operations should we support? Q3: How to index a dataCube? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q3: How to index a dataCube? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q3: How to index a dataCube? A1: Bitmaps 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) DataCubes Q3: How to index a dataCube? A2: Join indices (see [Han+Kamber]) 15-721 Copyright: C. Faloutsos (2001)

D/W - OLAP - Conclusions D/W: copy (summarized) data + analyze OLAP - concepts: DataCube R/M/H-OLAP servers ‘dimensions’; ‘measures’ 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Outline Problem Getting the data: Data Warehouses, DataCubes, OLAP Supervised learning: decision trees Unsupervised learning association rules (clustering) 15-721 Copyright: C. Faloutsos (2001)

Decision trees - Problem ?? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Decision trees Pictorially, we have num. attr#1 (eg., ‘age’) num. attr#2 (eg., chol-level) + - 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Decision trees and we want to label ‘?’ num. attr#2 (eg., chol-level) ? - - + + + - + - + - + - + num. attr#1 (eg., ‘age’) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Decision trees so we build a decision tree: num. attr#2 (eg., chol-level) ? - - + + + 40 - + - + - + - + 50 num. attr#1 (eg., ‘age’) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Decision trees so we build a decision tree: age<50 N Y chol. <40 + Y N - ... 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Outline Problem Getting the data: Data Warehouses, DataCubes, OLAP Supervised learning: decision trees problem approach scalability enhancements Unsupervised learning association rules (clustering) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Decision trees Typically, two steps: tree building tree pruning (for over-training/over-fitting) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Tree building How? num. attr#1 (eg., ‘age’) num. attr#2 (eg., chol-level) + - 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building How? A: Partition, recursively - pseudocode: Partition ( Dataset S) if all points in S have same label then return evaluate splits along each attribute A pick best split, to divide S into S1 and S2 Partition(S1); Partition(S2) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building Q1: how to introduce splits along attribute Ai Q2: how to evaluate a split? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building Q1: how to introduce splits along attribute Ai A1: for num. attributes: binary split, or multiple split for categorical attributes: compute all subsets (expensive!), or use a greedy algo 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building Q1: how to introduce splits along attribute Ai Q2: how to evaluate a split? 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Tree building Q1: how to introduce splits along attribute Ai Q2: how to evaluate a split? A: by how close to uniform each subset is - ie., we need a measure of uniformity: 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building entropy: H(p+, p-) Any other measure? 1 0.5 1 p+ 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building entropy: H(p+, p-) ‘gini’ index: 1-p+2 - p-2 1 p+ 1 0.5 0.5 1 p+ 15-721 Copyright: C. Faloutsos (2001)

Tree building skip entropy: H(p+, p-) ‘gini’ index: 1-p+2 - p-2 (How about multiple labels?) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree building Intuition: entropy: #bits to encode the class label gini: classification error, if we randomly guess ‘+’ with prob. p+ 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Tree building Thus, we choose the split that reduces entropy/classification-error the most: Eg.: num. attr#1 (eg., ‘age’) num. attr#2 (eg., chol-level) + - 15-721 Copyright: C. Faloutsos (2001)

Tree building skip Before split: we need (n+ + n-) * H( p+, p-) = (7+6) * H(7/13, 6/13) bits total, to encode all the class labels After the split we need: 0 bits for the first half and (2+6) * H(2/8, 6/8) bits for the second half 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Tree pruning What for? ... num. attr#1 (eg., ‘age’) num. attr#2 (eg., chol-level) + - 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Tree pruning Shortcut for scalability: DYNAMIC pruning: stop expanding the tree, if a node is ‘reasonably’ homogeneous ad hoc threshold [Agrawal+, vldb92] Minimum Description Language (MDL) criterion (SLIQ) [Mehta+, edbt96] 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree pruning Q: How to do it? A1: use a ‘training’ and a ‘testing’ set - prune nodes that improve classification in the ‘testing’ set. (Drawbacks?) A2: or, rely on MDL (= Minimum Description Language) - in detail: 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree pruning envision the problem as compression (of what?) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip Tree pruning envision the problem as compression (of what?) and try to min. the # bits to compress (a) the class labels AND (b) the representation of the decision tree 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) skip (MDL) a brilliant idea - eg.: best n-degree polynomial to compress these points: the one that minimizes (sum of errors + n ) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Outline Problem Getting the data: Data Warehouses, DataCubes, OLAP Supervised learning: decision trees problem approach scalability enhancements Unsupervised learning association rules (clustering) 15-721 Copyright: C. Faloutsos (2001)

Scalability enhancements Interval Classifier [Agrawal+,vldb92]: dynamic pruning SLIQ: dynamic pruning with MDL; vertical partitioning of the file (but label column has to fit in core) SPRINT: even more clever partitioning 15-721 Copyright: C. Faloutsos (2001)

Conclusions for classifiers Classification through trees Building phase - splitting policies Pruning phase (to avoid over-fitting) For scalability: dynamic pruning clever data partitioning 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Overall Conclusions Data Mining: of high commercial interest DM = DB+ ML+ Stat Data warehousing / OLAP: to get the data Tree classifiers (SLIQ, SPRINT) Association Rules - ‘a-priori’ algorithm (clustering: BIRCH, CURE, OPTICS) 15-721 Copyright: C. Faloutsos (2001)

Copyright: C. Faloutsos (2001) Reading material Agrawal, R., T. Imielinski, A. Swami, ‘Mining Association Rules between Sets of Items in Large Databases’, SIGMOD 1993. M. Mehta, R. Agrawal and J. Rissanen, `SLIQ: A Fast Scalable Classifier for Data Mining', Proc. of the Fifth Int'l Conference on Extending Database Technology (EDBT), Avignon, France, March 1996 15-721 Copyright: C. Faloutsos (2001)

Additional references Agrawal, R., S. Ghosh, et al. (Aug. 23-27, 1992). An Interval Classifier for Database Mining Applications. VLDB Conf. Proc., Vancouver, BC, Canada. Jiawei Han and Micheline Kamber, Data Mining , Morgan Kaufman, 2001, chapters 2.2-2.3, 6.1-6.2, 7.3.5 15-721 Copyright: C. Faloutsos (2001)