14. Cube: A Lattice of Cuboids all time item location supplier time,item time,location time,supplier item,location item,supplier location,supplier time,item,location time,item,supplier time,location,supplier item,location,supplier time, item, location, supplier 0-D(apex) cuboid 1-D cuboids 2-D cuboids 3-D cuboids 4-D(base) cuboid
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16. Example of Star Schema Sales Fact Table time_key item_key branch_key location_key units_sold dollars_sold avg_sales Measures time_key day day_of_the_week month quarter year time location_key street city state_or_province country location item_key item_name brand type supplier_type item branch_key branch_name branch_type branch
17. Example of Snowflake Schema Sales Fact Table time_key item_key branch_key location_key units_sold dollars_sold avg_sales Measures time_key day day_of_the_week month quarter year time location_key street city_key location item_key item_name brand type supplier_key item branch_key branch_name branch_type branch supplier_key supplier_type supplier city_key city state_or_province country city
18. Example of Fact Constellation Sales Fact Table time_key item_key branch_key location_key units_sold dollars_sold avg_sales Measures Shipping Fact Table time_key item_key shipper_key from_location to_location dollars_cost units_shipped time_key day day_of_the_week month quarter year time location_key street city province_or_state country location item_key item_name brand type supplier_type item branch_key branch_name branch_type branch shipper_key shipper_name location_key shipper_type shipper
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24. A Concept Hierarchy: Dimension (location) all Europe North_America Mexico Canada Spain Germany Vancouver M. Wind L. Chan ... ... ... ... ... ... all region office country Toronto Frankfurt city
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27. A data cube all product quarter country product, quarter product,country quarter, country product, quarter, country 0-D(apex) cuboid 1-D cuboids 2-D cuboids 3-D(base) cuboid
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29. A Sample Data Cube Total annual sales of TV in U.S.A. Quarter Product Country All, All, All sum sum TV VCR PC 1Qtr 2Qtr 3Qtr 4Qtr U.S.A Canada Mexico sum
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35. Multi-Tiered Architecture Data Warehouse OLAP Engine Analysis Query Reports Data mining Monitor & Integrator Metadata Data Sources Front-End Tools Serve Data Marts Data Storage OLAP Server Extract Transform Load Refresh Operational DBs other sources
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37. Data Warehouse Development: A Recommended Approach Define a high-level corporate data model Data Mart Data Mart Distributed Data Marts Multi-Tier Data Warehouse Enterprise Data Warehouse Model refinement Model refinement
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45. Multi-way Array Aggregation for Cube Computation B A B 29 30 31 32 1 2 3 4 5 9 13 14 15 16 64 63 62 61 48 47 46 45 a1 a0 c3 c2 c1 c 0 b3 b2 b1 b0 a2 a3 C 44 28 56 40 24 52 36 20 60
46. Multi-way Array Aggregation for Cube Computation A B 29 30 31 32 1 2 3 4 5 9 13 14 15 16 64 63 62 61 48 47 46 45 a1 a0 c3 c2 c1 c 0 b3 b2 b1 b0 a2 a3 C 44 28 56 40 24 52 36 20 60 B Order: A B C AB: plane AC: line BC: point
59. What we have Can we do better? O(n 2 ) O(1) store prefix-sum O(1) O(n 2 ) store original cube update cost query cost O(n) O(log(n)) dynamic data cube (naïve version)
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69. What we have Can we do better? Can we do better? O(n 2 ) O(1) store prefix-sum O(1) O(n 2 ) store original cube update cost query cost O(n) O(log(n)) dynamic data cube (naïve version) O(log 2 n) O(log 2 n) dynamic data cube
![Data Warehousing ,[object Object],[object Object],[object Object],modified by Donghui Zhang](https://image.slidesharecdn.com/my2dw-1206370408423431-5/85/My2dw-1-320.jpg)
![Chapter 3: Data Warehousing and OLAP Technology for Data Mining ,[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)