What is OLAP - On-line analytical processing
Vladimir Estivill-Castro
School of Computing and Information Technology With contributions for J. Han
Introduction
u
When a company has received/accumulated data, it often wants a report
u
to get a summary, to visualize, to make decisions Mainframe systems (old and new) SQL, ODBC, JDBC, etc
Vladimir Estivill -Castro 2
This is often done with some IT tools
u u
Problems
u
Report design (making) can take a long time with traditional systems
does not facilitate explorative views on the data u with large data sets and tricky queries many tables may be involved (many locations)
u
Changes in reports can require modifications in legacy applications
Vladimir Estivill -Castro 3
Data Warehousing
u
A data warehouse is a subject-oriented, integrated, timevariant, and nonvolatile collection of data in support of managements decision- making process. --- W. H. Inmon
uA
u
data warehouse is
A decision support database that is maintained separately from the organizations operational databases.
It integrates data from multiple heterogeneous sources to support the continuing need for structured and /or ad-hoc queries, analytical reporting, and decision support.
Vladimir Estivill -Castro
What is OLAP
u
OLAP:On-Line Analytic Processing
u
Starts with summarizing the data before it is possible to execute the queries (to receive a report)
u this u u
is building the cube this can take a long time both more efficient response for analysis queries
Data (summarization) is represented as cubes and subcubes
Vladimir Estivill -Castro 5
OLAP vs Data Mining
u
Data Mining: Finding patterns in data u OLAP: reporting data, visualizing data, interaction with views of the data.
Vladimir Estivill -Castro
Database terminology
A tuple (data value) is a single data field in a database. It can be a date, a name, a number, etc. u A record is a set of tuples. All tuples in a record are information about an entity u A table is a set of records all from the same domain. Each row in a table is a unique record and each column is the specific tuple (or attribute)
u
Vladimir Estivill -Castro
Data Models
u Data
is either denormalized or normalized
u Denormalized: Multiple rows repeat the same
information u Normalized: Only one row has the information u Star Schema u Developed by R. Kimball u A denormalized approach u Starts with a central fact table that corresponds to facts about a business
Vladimir Estivill -Castro 8
Central Fact Table
u
Facts about the business
Each row contains a combination of facts that makes it unique u The keys to make it unique are called dimensions u Each dimension is associated with a dimension table that contains information specific to the dimension.
u
Vladimir Estivill -Castro 9
Example of Star Schema
Time Dimension Table
Many Time Attributes
Sales Fact Table Product Dimension Table
Time_Key Many Product Attributes Product_Key
Store Dimension Table
Many Store Attributes
Store_Key Location_Key unit_sales
Location Dimension Table
Many Location Attributes
Measurements
dollar_sales Yen_sales
Vladimir Estivill -Castro
10
Example of a Snowflake Schema
Supplier_Key
Time Dimension Table
Many Time Attributes
Sales Fact Table
Time_Key Product_Key
Product Dimension Table
Supplier_Key Product_Key
Store Dimension Table
Many Store Attributes
Store_Key Location_Key unit_sales
Location Dimension Table
Location_Key
Measurements
dollar_sales Yen_sales
Country
Location_Key
Region
Location_Key
Vladimir Estivill -Castro 11
General Structure
FACT Table
Vladimir Estivill -Castro
12
A Star -Net Query Model
Shipping Method Customer Orders Customer CONTRACTS AIR-EXPRESS TRUCK Time ANNUALY QTRLY DAILY PRODUCT ITEM DISTRICT SALES PERSON REGION DISTRICT COUNTRY DIVISION Geography Promotion Vladimir Estivill -Castro Organization 13 ORDER PRODUCT LINE Product PRODUCT GROUP
Construction of Data Cubes
Amount Province
B.C. Prairies Ontario sum 0-20K20-40K 40-60K60K- sum
All Amount Comp_Method, B.C.
Comp_Method Database ... sum
Discipline
l l l l l
Each dimension contains a hierarchy of values for one attribute A cube cell stores aggregate values, e.g., count, sum, max, etc. A sum cell stores dimension summation values. Sparse-cube technology and MOLAP/ROLAP integration. Chunk-based multi-way aggregation and single-pass computation.
Vladimir Estivill -Castro 14
View of Warehouse & Hierarchies
Table browsing Dimension browsing Cube creation
Vladimir Estivill -Castro
15
u Data
Efficient Data Cube Computation Methods
bottom- most cuboid is the base cube. top most cuboid contains only one cell.
cube can be viewed as a lattice of cuboids
u The u The
u Materialization
u Materialize u Algorithms
of data cube
ALL
every (cuboid), none, or some. for selection of which cuboids to
B A C
materialize.
u
Based on size, sharing, and access frequency.
u Efficient
cube computation methods
algorithms.
AB BC AC
u ROLAP u
Array-based cubing algorithm.
Vladimir Estivill -Castro
ABC
OLAP: On- Line Analytical Processing
u u
A multidimensional, LOGICAL view of the data. Interactive analysis of the data: drill, pivot, slice_dice, filter. Summarization and aggregations at every dimension intersection. Retrieval and display of data in 2-D or 3-D crosstabs, charts, and graphs, with easy pivoting of the axes. Analytical modeling: deriving ratios, variance, etc. and involving measurements or numerical data across many dimensions. Forecasting, trend analysis, and statistical analysis. Requirement: Quick response to OLAP queries.
Vladimir Estivill -Castro
u u
OLAP Architecture
u Logical
u u
architecture:
OLAP view: multidimensional and logic presentation of the data in the data warehouse/mart to the business user. Data store technology: The technology options of how and where the data is stored.
u Three
u u u
services components:
data store services OLAP services, and user presentation services.
u Two
u
data store architectures:
u Multidimensional data store: (MOLAP).
Relational data store: Relational OLAP (ROLAP).
Vladimir Estivill -Castro
Cubes for representing data
u
OLAP considers two types of columns in denormalized data:
u Dimensional
u u u
columns
Contain information used for summarization Take a fixed number of values (categorical) Often its value is part of a hierarchy
u
location-code, postal code, state, region
u Aggregate
u
columns
Calculated amounts like counts, averages and sums
Vladimir Estivill -Castro
19
Design of a cube
u
Deciding which columns will be designated as dimensions and which will be designated as aggregates
Vladimir Estivill -Castro
20
An example database
Name Gender Age Source Movie
Amy
27
Oberlin
Independence Day
Andrew
25
Oberlin
!2 Monkeys
Andy
34
Oberlin
The Birdcage
Vladimir Estivill -Castro
21
Examples of questions (online queries)
u
What are the number of people and their ages by source?
Source
1
Number
103
Average Age
31.41
23
39.35
54
35.04
28
33.43
Vladimir Estivill -Castro
22
Examples of questions (online queries)
u
What are the number of people from the two most populated sources by gender?
Source
1 1 2 2
Gender
Female Male Female Male
Count
55 48 16 17
Vladimir Estivill -Castro
23
More examples
u
For what movies is the average age of the viewers over 35?
Movie Id 110 48 30 23 25 107
Average Age 50.00 46.00 46.00 45.13 44.80 44.00
Vladimir Estivill -Castro
24
More examples
u
The number of times each movie was seen for movies seen more than five times
Movie Id 1 13 26 60 32 22
Average Age 34 14 12 11 10 9
Vladimir Estivill -Castro
25
Moviegoers database
u
There are 3 candidates for dimensions
u u u
the movie the gender of movie goers the source of information (branch) the number of times that each movie was seen the average age of the moviegoers
Vladimir Estivill -Castro 26
There are two candidates for aggregations
u u
The moviegoers into a cube
u
Each dimensions corresponds to an axis in the cube
One dimension is the gender which split the axis into half since there are only two types of genders u The source of information is split into four parts since there are four different sources
u
The cube contains S cells where
u S= #ofSources
#ofGender #of MovieIds
Vladimir Estivill -Castro
27
The Moviegoers cube
Source 1 Source 2 Source 3 Source 4 Movie ID Male Female
Source 3, MovieId 2, Gender F, Count 5, SumAge = 215
Vladimir Estivill -Castro 28
Notes on cubes
u
The number of subcubes (cells) will not change unless the number of movies, genders or sources changes
u This makes it possible to have an unlimited number of
people in the cube u Each cell contains aggregate information
u The cell key is its coordinates
u
movie_id, source, gender The sum of the ages, the number of rows with given key
u The aggregate information are statistics
u
Vladimir Estivill -Castro
29
Notes on cubes
u Cubes
have natural subcubes u All the front cells for a sub-cube that correspond to data about all females
Source 1 Source 2 Source 3 Source 4
Vladimir Estivill -Castro
Male Female
30
Movie ID
The Cube Data Model
Each record must land in only one cell. u The Data Model varies when attributes are numerical
u
u
continues values
There is an assumption about hierarchical dimensions
u
Movies: action, comedy, drama
Problems with dimensions that span multiple fields.
Vladimir Estivill -Castro
31
Core Operations of OLAP Systems:
u u
u u
Rollup: an aggregation on the data cube by either moving up the concept hierarchy or by the reduction of a dimension. Drill Down: the moving from the current data cube to a more detailed data cube by either adding a dimension, or moving down a concept hierarchy. Slice: this is where you select a dimension from the cube and display only it. Dice: creates a sub cube of the current cube by selecting one or more dimensions and the ranges for the values to be included. Pivot: this operation removes a dimension from a cube and replaces it with another.
Vladimir Estivill -Castro 32
Continuous Values
u
They are clustered into ranges (for efficiency)
u u
Ages grouped into
u0
< young <= 22 and 22 < old < 100
Even if age is chosen as a dimension it can still be used as an aggregate
Vladimir Estivill -Castro
33
Hierarchical dimensions
u
A single dimension can some times seem appropriate for more dimensions than one
u
A date potentially represents information along several dimensions
u
day of the week, month, quarter and year break data model and lots of redundancy
u u
One solution is to use different dimensions
u
Second solution, organize into a hierarchy
Vladimir Estivill -Castro 34
Illustration of hierarchies
4: Year
3: Quarter
1: Week
2: Month
0: Day
Vladimir Estivill -Castro
35
Illustration of the lattice of cubes
Vladimir Estivill -Castro
36
Dimensions that span multiple fields
u
If multiple columns correspond to a single dimension, preprocessing is required to merge into one dimension
If month, day and year data detail exists, the time dimension requires to consider these as one dimension u The preprocessing is guided by the interest of users.
u
Vladimir Estivill -Castro 37
Storage architectures
u
ROLAP vs MOLAP
u
ROLAP (relational OLAP) stores the cube inside a RDBMS
u takes
advantage of many established features of the relational database (security, concurrent access, etc.)
MOLAP (multi-dimensional OLAP) stores the cube as multidimensional database (array) that is designed for the features and performance needs of OLAP
Vladimir Estivill -Castro 38
OLAP
u Offer u u u u
a powerful visualization tools It provides fast, interactive response times It is good for analyzing time series It can be useful to find clusters and outliers There are many vendors of OLAP products
Vladimir Estivill -Castro
39
OLAP
u u u u
Setting up a cube can be difficult It does not handle continues values well Cubes can quickly become out of date It is not data mining
u
It may involve dangerous exploration of the data by users.
Vladimir Estivill -Castro
40
Selective Materialization:
An Effective Method for Spatial Data Cube Construction
Jiawei Han, Nebosja Stefanovic and Krysztof Koperski
41
Selective Materialization
u Pre-introduction u Introduction uA
model of spatial data warehouses u Methods for Computing Spatial Measures in Spatial Data Cube Construction u Performance Analysis u Discussion
Vladimir Estivill -Castro
42
Pre-introduction
u Spatial
data are the data related to objects that occupy space. u A spatial database stores spatial objects represented by spatial data types and spatial relationships among such objects.
[http://fas. sfu.ca/cs/people/GradStudents/koperski/personal/research/research.html]
Vladimir Estivill -Castro
43
Introduction
uA
lot of systems collect a huge amount of spatial data
u Satellite
telemetry systems u Remote sensing systems u etc
u We
want to develop efficient methods for analysis and understanding of the data. u In the paper, it is studied how to construct a spatial data warehouse and how to implement efficient Spatial OLAP (OLAP=familiar)
Vladimir Estivill -Castro 44
Introduction - Two examples
u Example 1
u Over
- Regional weather pattern analysis
3000 weather probes recording temperature and precipitation (rain, snow etc) for a designated area. u A user may want to view weather patterns on a map by month, by region or maybe find a specific pattern by himself.
u Example 2
uA
- Overlay of multiple thematic maps
database stores different thematic maps in a database, such as maps of altitude, population and daily temperature. u A user may want to find relationships between population and altitude for example
Vladimir Estivill -Castro 45
Two examples (Cont.)
u To
satisfy the desired user tasks, there are a couple of challenging issues to solve. u The first challenge is to integrate all the data.
u Data
can be stored in different physical locations u Data can have different format u Data can be stored in databases from different vendors u Since this is implementation issues not related to the paper, it is assumed that the issues above are solved.
Vladimir Estivill -Castro
46
More challenges
u The
second challenge is the realisation of fast and flexible OLAP.
u Different
methods for storing and indexing spatial data for efficient storing and accessing has been studied intensively. u These methods cannot alone provide sufficient support for OLAP for spatial data since OLAP operations usually summarises data into dimensions with different levels of abstraction
Vladimir Estivill -Castro
47
A model of spatial data warehouses
uA
data warehouse is often designed for OLAP and usually adopts the star-schema model (central fact table and dimension tables). u For a spatial data warehouse this model is usually a good choice as well. u A spatial data cube can be constructed according to the dimensions and measures modelled in the warehouse.
Vladimir Estivill -Castro
48
Three cases of modelling dimensions in a spatial data cube
u Non-spatial
u From
dimension
first example temperature and precipitation can be generalised as hot and wet
u Spatial
u Starts
to non-spatial dimension
with a high level dimension that is spatial but after generalisation it becomes non-spatial. For example, state can be represented as spatial but can be generalised as north_west or big_state.
u Spatial
u Data
to spatial dimension
that after generalisation still is spatial.
Vladimir Estivill -Castro 49
Modelling measures
uA
computed measure can be used as a dimension in a dimension (measure-folded) u A spatial cube has two cases for modelling measures
u Numerical
measure - contains only numerical data u Spatial measure - contains one or many pointer(s) to spatial objects
u
If temperature and precipitation are grouped into one cell, then the spatial measure will contain pointers to the regions that satisfy those values.
uA
non-spatial cube contains only non-spatial dimensions and numerical measures.
Vladimir Estivill -Castro 50
Star modelling of example 1
u
Four dimensions:
u u u u
temperature precipitation time region_name region_map (spatial) area (numerical) count (numerical)
u
Star model of a spatial DW Hierarchy for temp. dimension
Three measures
u u u
Vladimir Estivill -Castro
51
How OLAP operations perform in a spatial data cube
u Slicing
and dicing
u Selects
a portion of the cube based on the constant(s) in one or a few dimensions. u Can be done with regular queries
u Pivoting
u Presents
the measures in different cross-tabular layouts u Can be implemented in a similar way as in non-spatial cubes
Vladimir Estivill -Castro
52
How OLAP operations perform in a spatial data cube (Cont.)
u Roll-up
u Generalises
one or a few dimensions and performs appropriate aggregations in the corresponding measures u For non spatial measures aggregation is implemented in the same way as in non-spatial data cubes u For spatial measures, the aggregate takes a collection of spatial pointers
u u
Used for map-overlay Performs spatial aggregation operations such as region merge etc.
Vladimir Estivill -Castro 53
How OLAP operations perform in a spatial data cube (Cont.)
u Drill-down
u Specialises
one or a few dimensions and presents lowlevel data u Can be viewed as a reverse operation of roll- up u Can be implemented by saving a low- level cube and performing a generalisation on it when necessary.
u Major
implementation issues
u Efficient
construction of spatial cubes u Implementation of Roll- up and Drill-down operations
Vladimir Estivill -Castro 54
How OLAP performed in the example
u Starts
with a Roll-up on the time dimension from day to month u After this, roll-up the temperature dimension
u It
is measure folded (continuous) u Start with calculating the average temperature grouped by month and by spatial region u Generalise the values to ranges such as cold, mild, warm
u Do
the same as above with the precipitation dimension
Vladimir Estivill -Castro 55
How OLAP performed in the example (Cont.)
u The
result of the roll-ups gives the following structure of the table
u Time in
month u Temperature in monthly average u Precipitation in monthly average u One spatial measure which is a collection of spatial_ids
u Here
the dimension region_name is dropped
Vladimir Estivill -Castro
56
Results from the roll-up
Table roll-up
Generalise regions
Vladimir Estivill -Castro
57
Results from the roll-up (Cont.)
u Response
time for the merging can only be acceptable if appropriate pre-computation is done u Definitions:
uA
high- level view is called a cuboid u A pre-computed (and saved) cuboid is called a materialised view or a computed cuboid
u Some
DW materialise every cuboid, some none, and some only a part of the cube (some cuboids).
u Balancing
is needed
Vladimir Estivill -Castro 58
Methods for computing spatial measures in spatial data cube construction
u There
are (at least) three choices for computation of spatial measures
u Collect
u u
and store the corresponding spatial object without pre-computation
They have to be computed on the fly Good for cubes in view-only mode
u Pre-compute
u u
and store rough approximations
Good for a rough view If higher precision needed, compute on the fly
u Selectively
u
pre-compute spatial measures
Can require a large pre-computation u What to compute???
Vladimir Estivill -Castro
59
Methods for computing spatial measures in spatial data cube construction (Cont.)
u Focus
on how to select a group of mergeable spatial objects for pre-computation is needed u Three factors to consider when judging wether materialisation should be done or not:
u Potential
access frequency of the generated cuboid u The size of the generated cuboid u How the materialisation of one cuboid may benefit computation of other cuboids
Vladimir Estivill -Castro
60
Methods for computing spatial measures in spatial data cube construction (Cont.)
u There
are two algorithms studied for this purpose
u Pointer
Intersection algorithm u Object Connection algorithm
u Both
algorithms are similar in the way that
u Given
a set of cuboids associated with an estimated access frequency (eaf) and a minimum access frequency (min_freq) threshold u A set of objects should be pre-computed if and only if eaf >=maf
Vladimir Estivill -Castro 61
The algorithms (Cont.)
u The
pointer intersection algorithm
First computes the intersections among the objects u Secondly it performs the (threshold) filtering and examines the objects corresponding spatial objects connections
u
u The
object connection algorithm
Starts with examining the corresponding objects connections u At last it performs the threshold filtering
u
Vladimir Estivill -Castro
62
The pointer intersection algorithm
Vladimir Estivill -Castro
63
The object connection algorithm
Vladimir Estivill -Castro
64
Performance analysis
Vladimir Estivill -Castro
65
Performance analysis (Cont.)
u The
benefit of the materialised groups is studied
u The
number of pre- merged cuboids gets smaller with the increase of frequency threshold u Only a slight difference between effectiveness (between the two algorithms)
u The
algorithms were tested with self- and nonself-intersection
u With
self- intersection, the benefit increased, but without the disk-accesses decreased
Vladimir Estivill -Castro 66
Performance analysis (Cont.)
u Execution
u Maybe
time was also examined (for precomputation)
not as crucial as on- line running time, but it is concerned because the need to DW maintenance.
u For
the object connection algorithm execution time was independent of the frequency threshold
u Since
frequency filtering is the last step in the algorithm u But, pointer frequency algorithm shows better performance when the frequency threshold increases due to fewer groups tested for spatial connectivity.
Vladimir Estivill -Castro 67
Discussion
u What
if the eaf does not exists
u One
solution is to assign an initial access frequency only to a level in the lattice (less work), based on assumption. u For example, assuming that medium level (county level in a province map) are accessed most frequently. u A frequency estimate can be adjusted based on later accessing records
Vladimir Estivill -Castro
68
