Chapter 8 Trends in DBMS 8 1 Database

Chapter 8: Trends in DBMS 8. 1 Database Support for Field Entities 8. 2 Content-based Retrieval 8. 3 Introduction to Spatial Data Warehouses 8. 4 Summary

Why Learn about Field Data-sets? Field data is timely and abundant Sensors (e. g. satellite based ones) provide periodic snapshot of Earth Most up-to-date data about current events (e. g. fires, flood) Field data are useful In creating, revising and evaluating vector data sets Digital archival of fragile historical paper maps To manually get details not captured in vector interpretations Example: Location selection for a facility (e. g. a grocery store) Consider a set of Aerial photographs of different locations Vector interpretation includes roads, water bodies, elevation What other information can aerial imagery reveal for construction planning? • trees (types and location), buildings, …

What are Field Data-sets? Field data set examples Satellite images, aerial photographs Digitized paper maps Earth Science data-sets, e. g. rainfall, temperature maps Data types of Spatial field data sets Images • satellite based, e. g. www. terradata. com • aerial photographs • measurements from a Geo-registered sensor networks, e. g. weather Video, i. e. time series of images Audio data Focus: Primarily images though some discussion will apply to other data types

Fields and Rasters: a Sampling of Field Values • Definitions • Field: a mapping from a spatial domain to a value domain • Image: a mapping from a rectangular grid to a value domain • A rectangular grid is a collection of cells called pixels • Raster is geo-registered image, i. e. grid axis have absolute spatial locations Figure 8. 1 • Fields are often approximated as rasters • Example: Figure 8. 1 • Identify spatial domain, field, rectangular grid, raster approximation • Fields can be approximated as images if relative spatial locations are adequate

Computing with Field Data Field data manipulated using operations of map algebra image algebra An Algebra is a mathematical structure consisting of Operands and Operations Map Algebra Operand: rasters Operations: Can be classified into four groups • Local, Focal, Zonal and Global Image Algebra Operand: images Operations: crop, zoom, rotate

Local Operation • A local operation maps a raster into another raster such that the value of a cell in the new raster depends only on the value of that cell in the original raster • Examples: unary operation : thresholding binary operation: point wise addition Figure 8. 2

Focal Operation • In a focal operation, the value of a cell in the new raster is dependent on the values of the cell and its neighboring cells in the original raster • Examples: unary operations: focal sum, gradient, … Neighborhoods: Rook, Bishop and Queen Figure 8. 3

Zonal Operation • In a global operation, the value of a cell in the new raster is a function of the location or values of all cells in the original or another raster • Examples: zonal sum, zonal average, . . . Figure 8. 4

Global Operation • In a zonal operation, the value of a cell in the new raster is a function of the value of that cell in the original layer and the values of other cells which appear in the same zone specified in another raster • Example: distance from nearest facility Figure 8. 5

Image Operations: Trim • Image Operations • Ignore the absolute locations of pixels. • Come from image processing literature • Ex. smoothing, low pass filter, high pass filter • Example: A trim operation extracts an axis-aligned subset of the original raster Figure 8. 6

Storage and Retrieval of Raster Data - 1 Traditional Approach Store raster data in a file system Use custom software to retrieve data-items of interest Example: personal photographs stored on MS Windows • Q? What attributes can one attach to digital photographs ? • Q? Is there an easy way to retrieve all pictures taken in San Francisco? Limitations Rigid schema • limited ability to add and manage additional attributes Canned Queries only • limited ability to support ad-hoc queries Data quality • limited ability to identify duplicates or similar data-items

Storage and Retrieval of Raster Data in a SDBMS A database approach Database tables store • raster data items • attributes (i. e. meta-data), e. g. creation date, geo-location, subject, . . . Use SQL like query language to retrieve desired data-items • retrieve all raster data-items overlapping with city of San Francisco (Q 1) • retrieve latest raster data-item within city of Paris (Q 2) • retrieve raster data-items similar to a given image (Q 3) Pros: • table schema definition allows user defined attributes • improve ability to pose ad-hoc queries (Ex. Q 1, Q 2) • improve data reliability and quality • example: Query Q 3 may be used for duplicate reduction

Storage and Retrieval of Raster Data - Challenges in databased approach Storage: size( raster data item) > size (disk blocks) Retrieval: raster has rich content • a picture is worth a thousand word! Approaches to storage challenge 1. Delegate storage to DBMS Use Binary Large Object (BLOB) data-type create table my_picture( image: BLOB; creation_date: date; place: point; … ) 2. Do-it-yourself • divide a raster data-item into smaller slices • Q? Which way of slicing reduce disk I/Os for common queries?

How is Raster Data Stored on Secondary Storage? • Slicing approaches • Linear, e. g. one row per disk block (see Figure 8. 8(b)) • Tiling - see Figure 8. 8(c ) • Tiling is preferred • For queries extracting rectangular sub-images • Example - terraserver. com Figure 8. 8

How is Raster Data Queried? Retrieval challenge of rich content 1. Meta-data approach 2. Content based retrieval Meta-data approach Select a set of descriptive attributes • simpler SQL data types, e. g. numeric, string, date, . . . • example: source, location, time stamp, subject, resolution, . . . Store values of descriptive attributes for each raster data-item Allow SQL queries on the descriptive attributes Limitation of meta-data approach Restricts queries to content captured by descriptive attributes Does not support “Similarity” based queries • example: Find all raster data-items similar to a given raster data item

Content Based Retrieval (CBR) • Examples Q 1. Find all raster data-items similar to a given raster data item Q 2. Locate a photograph of a river in Minnesota with trees nearby Q 3. Find all images of state parks which have a lake within them, are within a radius of one hundred miles from Chicago, and are southwest of Chicago • State of the Art • However, few robust implementations of CBR are available as of 2002 • several research prototypes address similarity query Q 1 • Result quality is similar to those of web searches (e. g. www. google. com) • some of the retrieved raster data-item are useful • many similar data item are not retrieved in the result • usable in application domains such as publishing • Our goal is to understand a current approach to similarity queries • involving spatial similarities

Content Based Retrieval (CBR) • Spatial Similarity • Consider a pair of raster images with common objects (e. g. parks, lakes) • Spatial similarity between raster images can be defined based on • similarity of spatial relationships (e. g. topological, directional) • Q? Which pairs exhibit higher similarity? • P 1: (inside, disjoint) • P 3: (disjoint, touch) • P 5: (north west, north) or or or P 2: (inside, covered by) P 4: (disjoint, inside) P 6: (west, east) • A graph framework for comparing spatial relationships • • Nodes = spatial relationships Edges = connect most similar nodes Similarity metric = number of edge on shortest path between 2 nodes See Figures 8. 9 and 8. 10

Topological Relationship Similarity • Study Figure 8. 9, pp. 234 • Nodes = topological relationships • Edges = most similar • Similarity measure = path length • Inference from Model • P 2: (inside, covered by) more similar than P 1: (inside, disjoint) • Do you agree? • Review Figure 2. 3 (pp. 30) Figure 8. 9

Direction Relationship Similarity • Study Figure 8. 10, pp. 235 • Nodes = topological relationships; Edges = most similar • Similarity measure = path length • Inference: P 5 (north-west, north) more similar than P 6 (west, east) Figure 8. 10

Distance Similarity • Distance similarity is based on • Euclidean distance between the centroids of the objects. • Example: Image R is more similar to P than Q in Figure 8. 11 (pp. 235) Figure 8. 11

A Computational Approach to CBR • Attribute Relation Graph (ARG) • • Node = objects in a raster Edges = relationships Example: raster of Figure 8. 12(a) ARG in Figure 8. 12(b) • point object O 3 • rectangles O 1, O 2 • edge (O 1, O 2) shows that they are disjoint, at 61 degree direction and 5. 2 units distant • Vector representation of ARG • Lists objects and edge properties • Example in Figure 8. 12

A Computational Approach to CBR • Steps: 1. Represent each raster data item by its ARG vector 2. Map query raster data item by its ARG vector 3. Find most similar raster data -items in the database by comparing ARG vector representations • use a distance metric • use a multi-dimensional index • Comment: Result quality is similar to those of web searches. Some of the retrieved raster data-item are useful Figure 8. 13

Why are Data Warehouses Interesting? • Data Warehouse facilitate group decision making • Consider a dataset • 1 measure (i. e. Sales) • 3 dimensions (e. g. Company, Year, Region) • Analysis questions • Q 1. Rank Regions by total sales. • Q 2. Rank years by total sales. • Q 3. Where are sales consistently growing? • Cross tabulates summaries reports used to analyze the trends • Example:

Generating Cross-tabulation Summaries • Traditional Approach • Use custom software pulling data out of a DBMS • Limitations: redundant of work, inefficient use of resources • Data Warehouse approach • Cross-tab. Can be generated using a set of simple report • each report is generated from a SQL “Select. . . group by” statement • Example: Fig. 8. 19 (pp. 244) and Table 8. 3 (pp. 245) • cross-tab example in last slide is a union of • SALES-L 0 -A, SALES-L 1 -B and SALES-L 2 • table 8. 3 shows SQL queries to compute each part • Advantage • rest of SQL is available for pre/post processing of data • performance gains by eliminating unnecessary copying of data

Example Data Warehouse Figure 8. 19

Cross-tabulation vs. Report Hierarchy • Spreadsheet view of a report • Views a report a N-dim. Spreadsheet • N = number of dimension attributes • Each cell contains value of “measure” • Cross-tabulation view of a Report hierarchy • Example: report hierarchy for SALES-L 0 -A, SALES-L 2 -A, SALES-L 1 -B, SALES-L 2, Figure 8. 19 (pp. 244)

What is a Data Warehouse? • Data Warehouse is a special purpose database • Primarily used for specialized data analysis purposes • Facilitates generation and navigation of a hierarchy of reports • Special purpose data-sets and queries • Data consists of: • a few measure attributes • a set of dimension attributes • The measure attribute depends on dimension attributes • Queries generate reports • report measure for selected values of dimensions • aggregate measure for given subset of dimensions • What is a spatial data warehouse? • Data warehouses with spatial measures or dimensions • Example: census data - census tract is a spatial dimension • Example: logistics data - route is a spatial dimension

Data Warehouse Operations • Operations on a data warehouse • Roll-up, Drill-down • Slice, Dice • Pivot • Roll-up • Inputs: A report R, A subset S of dimensions in R • Output: A sequence of reports summarizing R • Example 1: R=SALES-Base, S=(Year, Region) in Figure 8. 19 (pp. 244) • Output consists of reports SALES-L 0 -A, SALES-L 1 -B, SALES-L 2 • Example 2: R=SALES-Base, S=(Region, Year) • Output consists of reports SALES-L 0 -A, SALES-L 1 -A, SALES-L 2 • Drill-down • Inputs: A report R, A dimension D not in R • Output: A reports detailing R on D • Example: R = SALES-L 1 -B, D = Region in Figure 8. 19 (pp. 244) • Output : report SALES-L 0 -A

Data Warehouse Operations • Slice, Dice • • Reduce dimensions in a table (Figure 8. 7, pp. 232) Inputs: A report R, A value V for a dimension D in R Output: A subset of R where D=V Example: R=SALES-L 0 -A, D=Year, V=1994 in Figure 8. 19 (pp. 244) • output: Table 8. 5 (pp. 246) • includes tuple (ALL, 1994, America, 35) Figure 8. 7

Data Warehouse Operations • Pivot • For a spreadsheet view of reports • Transposes a spreadsheet • Example • Inputs: A spreadsheet view of a report R • Output: A transposed spreadsheet • Example: R= SALES-L 0 -A, Figure 8. 19 (pp. 244)

Logical Data Model of a DWH • Purpose of a logical data model • Specify a framework to specify computational structure • Allow extension of SQL to model new needs • Cube operation • Input : A fact table • Output: A set of summary reports covering all subsets of dimension columns • equivalent to union of all tables and reports in Figure 8. 19 (pp. 244) • Example: Figure 8. 18, pp. 243 SELECT Company, Year, Region, Sum(Sales) AS Sales FROM SALES GROUP BY CUBE Company, Year, Region

Physical Data Model of a DWH • Purpose: Computationally efficient implementation • Ideas: • Pre-computation • pre-compute some of reports and use those to compute other reports • New indexing methods, e. g. bit-map index • Query Processing Strategies • strategies for aggregate functions • new strategies for multi-table joins • Let us look at strategies for aggregate functions

DWH Physical Model: Aggregate Function Strategies • Aggregate Functions • Compute summary statistics for a given set of values • Examples: sum, average, centroid (Table 8. 1, pp. 238) • Strategies for efficient computation • Characterize easy to compute aggregate functions • 3 categories: • distributive • algebraic • holistic • First 2 categories can be computed easily in one scan of the dataset

Definitions of Aggregate Function Categories • Notation: • F, G, G 1, G 2, …, Gn are aggregate functions where n is small • S is a set of values, e. g. S=(1, 2, 3, 4) • P=(S 1, S 2, …, Sp) is a partition of S, e. g. P=(S 1, S 2), S 1=(1, 2), S 2=(3, 4) • Distributive (F) if there exists a G such that • F(S) = G(F(S 1), F(S 2), …, F(Sn)) • Example: sum is distributive • Illustration: sum(1, 2, 3, 4) = sum(1, 2), sum(3, 4)) • Algebraic (F) if there exists G 1, …, Gn, (where n is small) and • F(S) = G(G 1(S 1), …, Gn(S 1), G 2(S 1), …, Gn(S 2), …, G 1(Sp), …, Gn(Sp)) • Example: average is distributive • Illustration: average(1, 2, 3, 4)= {count(1, 2)*average(1, 2)+count(3, 4)*average} / {count(1, 2)+count(3, 4)}

Example: Distributive Aggregate Function • Examples in cross-tabulation scenario (Figure 8. 14, pp. 238): • Example 1: Min is distributive • Example 2: Count is distributive Figure 8. 14

Examples: Algebraic Aggregate Functions • Examples in cross-tabulation scenario (Figure 8. 15, pp. 239): • Average and Variance are algebraic Figure 8. 15

Discussion - Spatial Data Warehouse • Example • Consider the example in Figure 8. 16, pp. 241 • A map interpretation may be attached to each report • each row has a spatial footprint, which can be aggregated by geometric-union • The collection of maps may be called a mapcube • Issues: • What is needed in OGIS standard to support map-cube operation? • Hierarchical collection of maps in mapcube • what is an appropriate cartography to convey the relationship among maps?

Spatial Data Warehouses and Mapcube Figure 8. 16

Summary Field data Useful in many applications due to rich content Represented as raster or image Operations can be categorized into local, focal, zonal, and global Field data storage and retrieval Tiling is a preferred way to divide raster data into disk blocks Meta-data based query is often used for retrieval Content based retrieval may be used for similarity searches Data warehouses support analysis e. g. cross-tabulation reports SQL CUBE operator support generation of DWH reports Distributive and Algebraic aggregate functions can be computed easily