Chapter 8: Trends in DBMS8.1 Database Support for Field Entities8.2 Content-based Retrieval8.3 Introduction to Spatial Data Warehouses8.4 Summary

Why Learn about Field Data-sets?

Field data is timely and abundantSensors (e.g. satellite based ones) provide periodic snapshot of EarthMost up-to-date data about current events (e.g. fires, flood)

Field data are usefulIn creating, revising and evaluating vector data setsDigital archival of fragile historical paper mapsTo 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 locationsVector interpretation includes roads, water bodies, elevationWhat other information can aerial imagery reveal for construction planning?

• trees (types and location), buildings, …

What are Field Data-sets?

Field data set examplesSatellite images, aerial photographsDigitized paper mapsEarth Science data-sets, e.g. rainfall, temperature maps

Data types of Spatial field data setsImages

• 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 imagesAudio 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

• 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

Figure 8.1

Computing with Field Data

Field data manipulated using operations of map algebra image algebra

An Algebra is a mathematical structure consisting ofOperands and Operations

Map AlgebraOperand: rastersOperations: Can be classified into four groups• Local, Focal, Zonal and Global

Image AlgebraOperand: imagesOperations: 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 : thresholdingbinary 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 ApproachStore raster data in a file systemUse custom software to retrieve data-items of interestExample: 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?

LimitationsRigid schema• limited ability to add and manage additional attributesCanned Queries only• limited ability to support ad-hoc queriesData quality• limited ability to identify duplicates or similar data-items

Storage and Retrieval of Raster Data in a SDBMS

A database approachDatabase 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 (Q1)• retrieve latest raster data-item within city of Paris (Q2)• retrieve raster data-items similar to a given image (Q3)Pros: • table schema definition allows user defined attributes• improve ability to pose ad-hoc queries (Ex. Q1, Q2)• improve data reliability and quality • example: Query Q3 may be used for duplicate reduction

Storage and Retrieval of Raster Data - Challenges

Challenges in database based approachStorage: size( raster data item) > size (disk blocks)Retrieval: raster has rich content• a picture is worth a thousand word!

Approaches to storage challenge1. Delegate storage to DBMS

Use Binary Large Object (BLOB) data-typecreate 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?

Figure 8.8

• 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

How is Raster Data Queried?

Retrieval challenge of rich content1. Meta-data approach2. Content based retrievalMeta-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-itemAllow SQL queries on the descriptive attributes

Limitation of meta-data approachRestricts queries to content captured by descriptive attributesDoes not support “Similarity” based queries• example: Find all raster data-items similar to a given raster data item

Content Based Retrieval (CBR)

• ExamplesQ1. Find all raster data-items similar to a given raster data item Q2. Locate a photograph of a river in Minnesota with trees nearbyQ3. 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 Q1

• 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?

• P1: (inside, disjoint) or P2: (inside, covered by)• P3: (disjoint, touch) or P4: (disjoint, inside)• P5: (north west, north) or P6: (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

Figure 8.9

• Study Figure 8.9, pp.234• Nodes = topological relationships• Edges = most similar• Similarity measure = path length

• Inference from Model • P2: (inside, covered by) more

similar than P1: (inside, disjoint) • Do you agree?• Review Figure 2.3 (pp.30)

Direction Relationship Similarity

Figure 8.10

• Study Figure 8.10, pp.235• Nodes = topological relationships; Edges = most similar• Similarity measure = path length• Inference: P5 (north-west, north) more similar than P6 (west, east)

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

Figure 8.12

• 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 O3• rectangles O1, O2• edge (O1, O2) 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

Figure 8.13

• Steps:1. Represent each raster data

item by its ARG vector2. Map query raster data item

by its ARG vector3. 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

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• Q1. Rank Regions by total sales.• Q2. Rank years by total sales.• Q3. 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-L0-A, SALES-L1-A, SALES-L1-B and SALES-L2

• 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-L0-A, SALES-L2-A, SALES-L1-B,

SALES-L2, 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-L0-A, SALES-L1-B, SALES-L2• Example 2: R=SALES-Base, S=(Region, Year)

• Output consists of reports SALES-L0-A, SALES-L1-A, SALES-L2• Drill-down

• Inputs: A report R, A dimension D not in R• Output: A reports detailing R on D• Example: R = SALES-L1-B, D = Region in Figure 8.19 (pp.244)

• Output : report SALES-L0-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-L0-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-L0-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.243SELECT Company, Year, Region, Sum(Sales) AS SalesFROM SALESGROUP 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,G1,G2,…,Gn are aggregate functions where n is small• S is a set of values, e.g. S=(1,2,3,4)• P=(S1,S2,…,Sp) is a partition of S, e.g. P=(S1,S2), S1=(1,2), S2=(3,4)

• Distributive (F) if there exists a G such that• F(S) = G(F(S1),F(S2),…,F(Sn))• Example: sum is distributive • Illustration: sum(1,2,3,4) = sum(sum(1,2),sum(3,4))

• Algebraic (F) if there exists G1,…,Gn, (where n is small) and • F(S) = G(G1(S1),…,Gn(S1),G2(S1),…,Gn(S2),…,G1(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

Figure 8.14

• Examples in cross-tabulation scenario (Figure 8.14, pp.238): • Example 1: Min is distributive• Example 2: Count is distributive

Examples: Algebraic Aggregate Functions

Figure 8.15

• Examples in cross-tabulation scenario (Figure 8.15, pp.239): • Average and Variance are algebraic

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 contentRepresented as raster or image Operations can be categorized into local, focal, zonal, and global

Field data storage and retrievalTiling is a preferred way to divide raster data into disk blocksMeta-data based query is often used for retrievalContent based retrieval may be used for similarity searches

Data warehouses support analysis e.g. cross-tabulation reportsSQL CUBE operator support generation of DWH reportsDistributive and Algebraic aggregate functions can be computed easily