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Topics Related to Data Mining
CS 4/59995
Information Retrieval
•
•
•
•
•
•
Relevance Ranking Using Terms
Relevance Using Hyperlinks
Synonyms., Homonyms, and Ontologies
Indexing of Documents
Measuring Retrieval Effectiveness
Information Retrieval and Structured
Data
Information Retrieval Systems
• Information retrieval (IR) systems use a simpler data model
than database systems
– Information organized as a collection of documents
– Documents are unstructured, no schema
• Information retrieval locates relevant documents, on the basis
of user input such as keywords or example documents
– e.g., find documents containing the words “database
systems”
• Can be used even on textual descriptions provided with nontextual data such as images
Keyword Search
• In full text retrieval, all the words in each document are
considered to be keywords.
– We use the word term to refer to the words in a document
• Information-retrieval systems typically allow query expressions
formed using keywords and the logical connectives and, or, and
not
– Ands are implicit, even if not explicitly specified
• Ranking of documents on the basis of estimated relevance to a
query is critical
– Relevance ranking is based on factors such as
• Term frequency
– Frequency of occurrence of query keyword in document
• Inverse document frequency
– How many documents the query keyword occurs in
» Fewer  give more importance to keyword
• Hyperlinks to documents
– More links to a document  document is more important
Relevance Ranking Using Terms
• TF-IDF (Term frequency/Inverse Document frequency)
ranking:
– Let n(d) = number of terms in the document d
– n(d, t) = number of occurrences of term t in the document d.
– Relevance of a document d to a term t
TF (d, t) = log
1 + n(d, t)
n(d)
(d, t)
r (d, Q) =  TFn(t)
tQ
• The log factor is to avoid excessive weight to frequent terms
– Relevance of document to query Q
IDF=1/n(t), n(t) is the number of documents that contain the term t
Relevance Ranking Using Terms (Cont.)
• Most systems add to the above model
– Words that occur in title, author list, section headings, etc. are given
greater importance
– Words whose first occurrence is late in the document are given lower
importance
– Very common words such as “a”, “an”, “the”, “it” etc are eliminated
• Called stop words
– Proximity: if keywords in query occur close together in the document,
the document has higher importance than if they occur far apart
• Documents are returned in decreasing order of relevance score
– Usually only top few documents are returned, not all
Synonyms and Homonyms
• Synonyms
– E.g. document: “motorcycle repair”, query: “motorcycle maintenance”
• need to realize that “maintenance” and “repair” are synonyms
– System can extend query as “motorcycle and (repair or maintenance)”
• Homonyms
– E.g. “object” has different meanings as noun/verb
– Can disambiguate meanings (to some extent) from the context
• Extending queries automatically using synonyms can be
problematic
– Need to understand intended meaning in order to infer synonyms
• Or verify synonyms with user
– Synonyms may have other meanings as well
Indexing of Documents
• An inverted index maps each keyword Ki to a set of documents
Si that contain the keyword
– Documents identified by identifiers
• Inverted index may record
– Keyword locations within document to allow proximity based ranking
– Counts of number of occurrences of keyword to compute TF
• and operation: Finds documents that contain all of K1, K2, ...,
Kn.
– Intersection S1 S2 .....  Sn
• or operation: documents that contain at least one of K1, K2, …,
Kn
– union, S1S2 .....  Sn,.
• Each Si is kept sorted to allow efficient intersection/union by
merging
• “not” can also be efficiently implemented by merging of sorted
lists
Word-Level Inverted File
lexicon
posting
Measuring Retrieval Effectiveness
• Information-retrieval systems save space by using index
structures that support only approximate retrieval. May result in:
– false negative (false drop) - some relevant documents may
not be retrieved.
– false positive - some irrelevant documents may be
retrieved.
– For many applications a good index should not permit any
false drops, but may permit a few false positives.
• Relevant performance metrics:
– precision - what percentage of the retrieved documents are
relevant to the query.
– recall - what percentage of the documents relevant to the
query were retrieved.
Measuring Retrieval Effectiveness (Cont.)
• Recall vs. precision tradeoff:
• Can increase recall by retrieving many documents (down to a
low level of relevance ranking), but many irrelevant documents
would be fetched, reducing precision
• Measures of retrieval effectiveness:
– Recall as a function of number of documents fetched, or
– Precision as a function of recall
– Equivalently, as a function of number of documents fetched
– E.g. “precision of 75% at recall of 50%, and 60% at a recall of
75%”
• Problem: which documents are actually relevant, and
which are not
Information Retrieval and Structured Data
• Information retrieval systems originally treated
documents as a collection of words
• Information extraction systems infer structure from
documents, e.g.:
– Extraction of house attributes (size, address, number
of bedrooms, etc.) from a text advertisement
– Extraction of topic and people named from a new
article
• Relations or XML structures used to store extracted data
– System seeks connections among data to answer
queries
– Question answering systems
Probabilities and Statistic
Probabilities
1.
2.
P ( E  G )  P ( E )  P (G )  P ( E  G )
Event E is defined as a any subset of
f(x) is called a probability distribution function (pdf)
P(E )  1  P( X )
P ( E  G )  P ( E )  P (G )  P ( E  G )
Conditional Probabilities
Conditional probability of E, provided that G
occurred is
P(E G )
P(E | G ) 
P (G )
E and G are independent if and only if P ( E  G )  P ( E ) P ( G )
.
Expected Value
Expected value of X is
For continuous function f(x), the E(X) is
E(X+Y) = E(X)+E(Y)
E(aX+b) = aE(X)+b
Variance
• Var(X) = E(X-E(X))2
2
• It indicates how values of random
variable are distributed around its
expected value
• Standard deviation of X is defined as
• VAR(X+Y) = VAR(X) + VAR(Y)
VAR ( X )
• VAR(aX+b) = VAR(X)b2
2
• P(|S - E(S)|  r)  VAR(S)/r (Chebyshev’s Ineequality)
• Example:
• {1,2,3,4,5,6}; p(i) =1/6 E(X)= 1*1/6+2*1/6+3*1/6+4*1/6+5*1/6+6*1/6
• E(X)=1/6*21=3.5
• (1,2,9,16,25,36) VAR(X) = E(X^2-2XE(X)+E^2(X)=E(X^2)-E^2(X)
• E(X^2)=1/6(1+2+9+16+25+36)=1/6*89
• E^2(X)=3.5*3.5=12.25
• VAR(X)=89/6 -12.25=2.58
• Standard deviation = sqrt(2.58)=1.61
Random Distributions
Normal
E(X) = μ
Var(X) = σ
2
Bernoulli
E(X) = np
Var(X) = np(1-p)
Normal Distributions
E(x) =
Random Distributions
Geometric
E(X) = 1/p; VAR(X) =(1-p)/p2
Poisson
E(X)=VAR(X)=m
Uniform
P(X=x) = 1/(b-a)
E(X)=(b-a)/2; VAR(X)= (b-a) 2 /12
Correlation between age and mortality
Systolic Blood Pressure Distribution
Distribution of heart rate by systolic blood
pressure
Data and their characteristics
Types of Attributes
•
There are different types of attributes
– Nominal
• Examples: ID numbers, eye color, zip codes
– Ordinal
• Examples: rankings (e.g., taste of potato chips on a scale
from 1-10), grades, height in {tall, medium, short}
– Interval
• Examples: calendar dates, temperatures in Celsius or
Fahrenheit.
– Ratio
• Examples: temperature in Kelvin, length, time, counts
Properties of Attribute Values
• The type of an attribute depends on which of the following properties
it possesses:
– Distinctness:
= 
– Order:
< >
– Addition:
+ – Multiplication:
*/
–
–
–
–
Nominal attribute: distinctness
Ordinal attribute: distinctness & order
Interval attribute: distinctness, order & addition
Ratio attribute: all 4 properties
Attribute
Type
Description
Examples
Nominal
The values of a nominal attribute are
just different names, i.e., nominal
attributes provide only enough
information to distinguish one object
from another. (=, )
zip codes, employee
ID numbers, eye color,
sex: {male, female}
mode, entropy,
contingency
correlation, 2 test
Ordinal
The values of an ordinal attribute
provide enough information to order
objects. (<, >)
hardness of minerals,
{good, better, best},
grades, street numbers
median, percentiles,
rank correlation,
run tests, sign tests
Interval
For interval attributes, the
differences between values are
meaningful, i.e., a unit of
measurement exists.
(+, - )
calendar dates,
temperature in Celsius
or Fahrenheit
mean, standard
deviation, Pearson's
correlation, t and F
tests
For ratio variables, both differences
and ratios are meaningful. (*, /)
temperature in Kelvin,
monetary quantities,
counts, age, mass,
length, electrical
current
geometric mean,
harmonic mean,
percent variation
Ratio
Operations
Discrete and Continuous Attributes
• Discrete Attribute
– Has only a finite or countably infinite set of values
– Examples: zip codes, counts, or the set of words in a collection
of documents
– Often represented as integer variables.
– Note: binary attributes are a special case of discrete attributes
• Continuous Attribute
– Has real numbers as attribute values
– Examples: temperature, height, or weight.
– Practically, real values can only be measured and represented
using a finite number of digits.
– Continuous attributes are typically represented as floating-point
variables.
Data Matrix
• If data objects have the same fixed set of numeric attributes, then
the data objects can be thought of as points in a multi-dimensional
space, where each dimension represents a distinct attribute
• Such data set can be represented by an m by n matrix, where there
are m rows, one for each object, and n columns, one for each
attribute
Projection
of x Load
Projection
of y load
Distance
Load
Thickness
10.23
5.27
15.22
2.7
1.2
12.65
6.25
16.22
2.2
1.1
Data Quality
• What kinds of data quality problems?
• How can we detect problems with the
data?
• What can we do about these problems?
• Examples of data quality problems:
– Noise and outliers
– missing values
– duplicate data
Noise
• Noise refers to modification of original
values
– Examples: distortion of a person’s voice when
talking on a poor phone and “snow” on
television screen
Two Sine Waves
Two Sine Waves + Noise
Outliers
• Outliers are data objects with
characteristics that are considerably
different than most of the other data
objects in the data set
Data Preprocessing
•
•
•
•
•
•
•
Aggregation
Sampling
Dimensionality Reduction
Feature subset selection
Feature creation
Discretization and Binarization
Attribute Transformation
Aggregation
• Combining two or more attributes (or objects) into a single attribute
(or object)
• Purpose
– Data reduction
• Reduce the number of attributes or objects
– Change of scale
• Cities aggregated into regions, states, countries, etc
– More “stable” data
• Aggregated data tends to have less variability
Sampling
• Sampling is the main technique employed for data
selection.
– It is often used for both the preliminary investigation of
the data and the final data analysis.
• Statisticians sample because obtaining the entire set
of data of interest is too expensive or time
consuming.
• Sampling is used in data mining because processing
the entire set of data of interest is too expensive or
time consuming.
Sampling …
• The key principle for effective sampling is
the following:
– using a sample will work almost as well as
using the entire data sets, if the sample is
representative
– A sample is representative if it has
approximately the same property (of interest)
as the original set of data
Types of Sampling
• Simple Random Sampling
– There is an equal probability of selecting any particular item
• Sampling without replacement
– As each item is selected, it is removed from the population
• Sampling with replacement
– Objects are not removed from the population as they are
selected for the sample.
• In sampling with replacement, the same object can be
picked up more than once
• Stratified sampling
– Split the data into several partitions; then draw random samples
from each partition
Curse of Dimensionality
• When dimensionality
increases, data becomes
increasingly sparse in the
space that it occupies
• Definitions of density and
distance between points,
which is critical for
clustering and outlier
detection, become less
meaningful
• Randomly generate 500 points
• Compute difference between max and min
distance between any pair of points
Discretization
• Three types of attributes:
– Nominal — values from an unordered set
– Ordinal — values from an ordered set
– Continuous — real numbers
• Discretization:
divide the range of a continuous attribute into
intervals
– Some classification algorithms only accept
categorical attributes.
– Reduce data size by discretization
– Prepare for further analysis
Discretization and Concept hierarchy
• Discretization
– reduce the number of values for a given continuous
attribute by dividing the range of the attribute into
intervals. Interval labels can then be used to replace
actual data values.
• Concept hierarchies
– reduce the data by collecting and replacing low level
concepts (such as numeric values for the attribute
age) by higher level concepts (such as young,
middle-aged, or senior).
Discretization
• Three types of attributes:
– Nominal — values from an unordered set
– Ordinal — values from an ordered set
– Continuous — real numbers
• Discretization:
divide the range of a continuous attribute into
intervals
– Some classification algorithms only accept
categorical attributes.
– Reduce data size by discretization
– Prepare for further analysis
Discretization and generation for numeric
data
• Binning
• Histogram analysis
• Entropy-based discretization
• Segmentation by natural partitioning
Discretization
Sort Attribute
Select cut Point
Evaluate Measure
NO
NO
Satisfied
Yes
Split/Merge
Stop
DONE
Simple Discretization Methods:
Binning
• Equal-width (distance) partitioning:
– It divides the range into N intervals of equal size:
uniform grid
– if A and B are the lowest and highest values of the
attribute, the width of intervals will be: W = (B-A)/N.
– The most straightforward
– But outliers may dominate presentation
– Skewed data is not handled well.
• Equal-depth (frequency) partitioning:
– It divides the range into N intervals, each containing
approximately same number of samples
– Good data scaling
– Managing categorical attributes can be tricky.
Discretization
• Three types of attributes:
– Nominal — values from an unordered set
– Ordinal — values from an ordered set
– Continuous — real numbers
• Discretization:
divide the range of a continuous attribute into
intervals
– Some classification algorithms only accept
categorical attributes.
– Reduce data size by discretization
– Prepare for further analysis
Entropy-Based Discretization
• Given a set of samples S, if S is partitioned into two intervals S1 and
S2 using boundary T, the entropy after partitioning is
E (S ,T ) 
|S |
|S |
1 E nt (
2 E nt (
)

)
S
S
1
2
|S |
|S |
• The boundary that minimizes the entropy function over all possible
boundaries is selected as a binary discretization.
• The process is recursively applied to partitions obtained until some
stopping criterion is met, e.g.,
Ent ( S )  E ( T , S )  
• Experiments show that it may reduce data size and improve
classification accuracy
Specification of a set of attributes
Concept hierarchy can be automatically generated
based on the number of distinct values per attribute in
the given attribute set. The attribute with the most
distinct values is placed at the lowest level of the
hierarchy.
country
15 distinct values
province_or_ state
65 distinct values
city
3567 distinct values
street
674,339 distinct values
Similarity and Dissimilarity
• Similarity
– Numerical measure of how alike two data objects are.
– Is higher when objects are more alike.
– Often falls in the range [0,1]
• Dissimilarity
– Numerical measure of how different are two data
objects
– Lower when objects are more alike
– Minimum dissimilarity is often 0
– Upper limit varies
• Proximity refers to a similarity or dissimilarity
Similarity/Dissimilarity for Simple
Attributes
p and q are the attribute values for two data objects.
Euclidean
Distance
• Euclidean Distance
dist 
n
 ( pk  qk )
2
k 1
Where n is the number of dimensions (attributes)
and pk and qk are, respectively, the kth attributes
(components) or data objects p and q.
Euclidean Distance
3
point
p1
p2
p3
p4
p1
2
p3
p4
1
p2
0
0
1
2
3
4
5
y
2
0
1
1
6
p1
p1
p2
p3
p4
x
0
2
3
5
0
2.828
3.162
5.099
p2
2.828
0
1.414
3.162
Distance Matrix
p3
3.162
1.414
0
2
p4
5.099
3.162
2
0
Minkowski Distance
Minkowski Distance is a generalization of Euclidean
Distance
n
dist  (  | p k  q k
1
r r
| )
k 1
Where r is a parameter, n is the number of
dimensions (attributes) and pk and qk are,
respectively, the kth attributes (components) or
data objects p and q.
Minkowski Distance
point
p1
p2
p3
p4
x
0
2
3
5
y
2
0
1
1
L1
p1
p2
p3
p4
p1
0
4
4
6
p2
4
0
2
4
p3
4
2
0
2
p4
6
4
2
0
L2
p1
p2
p3
p4
p1
p2
2.828
0
1.414
3.162
p3
3.162
1.414
0
2
p4
5.099
3.162
2
0
0
2.828
3.162
5.099
Distance Matrix
Covariance
• Covariance=E((x-E(x)(y –E(y))
• Describes a some sort of dependency
between variables.
• Describes how the X and Y change
together
Common Properties of a Distance
•
Distances, such as the Euclidean distance, have some well
known properties.
d(p, q)  0 for all p and q and d(p, q) = 0 only if
p = q. (Positive definiteness)
2. d(p, q) = d(q, p) for all p and q. (Symmetry)
3. d(p, r)  d(p, q) + d(q, r) for all points p, q, and r.
(Triangle Inequality)
where d(p, q) is the distance (dissimilarity) between points (data
objects), p and q.
1.
•
A distance that satisfies these properties is called a metric
Common Properties of a Similarity
• Similarities, also have some well known
properties.
1. s(p, q) = 1 (or maximum similarity) only if p = q.
2. s(p, q) = s(q, p) for all p and q. (Symmetry)
where s(p, q) is the similarity between points
(data objects), p and q.
Similarity Between Binary Vectors
•
Common situation is that objects, p and q, have only binary
attributes
•
Compute similarities using the following quantities
M01 = the number of attributes where p was 0 and q was 1
M10 = the number of attributes where p was 1 and q was 0
M00 = the number of attributes where p was 0 and q was 0
M11 = the number of attributes where p was 1 and q was 1
•
Simple Matching and Jaccard Coefficients
SMC = number of matches / number of attributes
= (M11 + M00) / (M01 + M10 + M11 + M00)
J = number of 11 matches / number of not-both-zero attributes
values
= (M11) / (M01 + M10 + M11)
SMC versus Jaccard: Example
p= 1000000000
q= 0000001001
M01 = 2
M10 = 1
M00 = 7
M11 = 0
(the number of attributes where p was 0 and q was 1)
(the number of attributes where p was 1 and q was 0)
(the number of attributes where p was 0 and q was 0)
(the number of attributes where p was 1 and q was 1)
SMC = (M11 + M00)/(M01 + M10 + M11 + M00) = (0+7) /
(2+1+0+7) = 0.7
J = (M11) / (M01 + M10 + M11) = 0 / (2 + 1 + 0) = 0
Data Warehousing and OLAP
Technology for Data Mining
• What is a data warehouse?
• Data warehouse architecture
• Data warehouse implementation
• Further development of data cube technology
• From data warehousing to data mining
Data Warehousing
• Large organizations have complex internal organizations, and have
data stored at different locations, on different operational
(transaction processing) systems, under different schemas
• Data sources often store only current data, not historical data
• Corporate decision making requires a unified view of all
organizational data, including historical data
• A data warehouse is a repository (archive) of information gathered
from multiple sources, stored under a unified schema, at a single
site
– Greatly simplifies querying, permits study of historical trends
– Shifts decision support query load away from transaction
processing systems
Data Warehouse vs. Operational DBMS
• OLTP (on-line transaction processing)
– Major task of traditional relational DBMS
– Day-to-day operations: purchasing, inventory, banking,
manufacturing, payroll, registration, accounting, etc.
• OLAP (on-line analytical processing)
– Major task of data warehouse system
– Data analysis and decision making
• Distinct features (OLTP vs. OLAP):
– User and system orientation: customer vs. market
– Data contents: current, detailed vs. historical, consolidated
– Database design: ER + application vs. star + subject
– View: current, local vs. evolutionary, integrated
– Access patterns: update vs. read-only but complex queries
OLTP vs. OLAP
O LTP
O LAP
u sers
clerk, IT professional
know ledge w orker
f u n ction
day to day operations
decision support
D B d esign
application-oriented
subject-oriented
d ata
current, up -to-date
detailed, flat relational
isolated
repetitive
historical,
summarized, multidimensional
integrated, consolidated
ad -hoc
lots of scans
u n it of w ork
read/w rite
index/hash on prim. key
short, simple transaction
# record s accessed
tens
millions
#u sers
thousands
hundreds
D B size
100M B -G B
100G B -T B
m etric
transaction throughput
query throughput, response
u sage
access
complex query
Data Warehousing
Managing of a warehouse
• When and how to gather data
– Source driven architecture: data sources
transmit new information to warehouse, either
continuously or periodically (e.g. at night)
– Destination driven architecture: warehouse
periodically requests new information from
data sources
• What schema to use
– Schema integration
Managing of a warehouse(Cont.)
• Data cleansing
– E.g. correct mistakes in addresses
• E.g. misspellings, zip code errors
– Merge address lists from different sources and purge duplicates
• Keep only one address record per household
(“householding”)
• How to propagate updates
– Warehouse schema may be a (materialized) view of schema
from data sources
– Efficient techniques for update of materialized views
• What data to summarize
– Raw data may be too large to store on-line
– Aggregate values (totals/subtotals) often suffice
– Queries on raw data can often be transformed by query
optimizer to use aggregate values
Conceptual Modeling of Data
Warehouses
• Modeling data warehouses: dimensions & measures
– Star schema: A fact table in the middle connected to a set of
dimension tables
– Snowflake schema: A refinement of star schema where some
dimensional hierarchy to snowflake
– Fact constellations is normalized into a set of smaller dimension
tables, forming a shape similar : Multiple fact tables share
dimension tables, viewed as a collection of stars, therefore called
galaxy schema or fact constellation
Star Schema Example
time
Example of Snowflake
Schema
time_key
day
day_of_the_week
month
quarter
year
item
Sales Fact Table
time_key
item_key
branch_key
branch
location_key
branch_key
branch_name
branch_type
units_sold
dollars_sold
avg_sales
Measures
item_key
item_name
brand
type
supplier_key
supplier
supplier_key
supplier_type
location
location_key
street
city_key
city
city_key
city
province_or_street
country
Example of Fact
Constellation
time
time_key
day
day_of_the_week
month
quarter
year
item
Sales Fact Table
time_key
item_key
item_name
brand
type
supplier_type
item_key
location_key
branch_key
branch_name
branch_type
units_sold
dollars_sold
avg_sales
Measures
time_key
item_key
shipper_key
from_location
branch_key
branch
Shipping Fact Table
location
to_location
location_key
street
city
province_or_street
country
dollars_cost
units_shipped
shipper
shipper_key
shipper_name
location_key
shipper_type
Online Analytical Processing
• The operation of changing the dimensions used in a cross-tab is
called pivoting
• Suppose an analyst wishes to see a cross-tab on item-name and
color for a fixed value of size, for example, large, instead of the
sum across all sizes.
– Such an operation is referred to as slicing.
• The operation is sometimes called dicing, particularly
when values for multiple dimensions are fixed.
• The operation of moving from finer-granularity data to a coarser
granularity is called a rollup.
• The opposite operation - that of moving from coarser-granularity
data to finer-granularity data – is called a drill down.
Three-Dimensional Data Cube
 A data cube is a multidimensional generalization of a crosstab
 Cannot view a three-dimensional object in its entirety
 but crosstabs can be used as views on a data cube
Cube: A Lattice of
Cuboids
all
time
time,item
0-D(apex) cuboid
item
time,location
location
item,location
time,supplier
time,item,location
supplier
1-D cuboids
location,supplier
2-D cuboids
item,supplier
time,location,supplier
3-D cuboids
time,item,supplier
item,location,supplier
4-D(base) cuboid
time, item, location, supplier

Hierarchies
on
Dimensions
Hierarchy on dimension attributes: lets dimensions to be viewed
at different levels of detail
 E.g. the dimension DateTime can be used to aggregate by hour of
day, date, day of week, month, quarter or year
OLAP Implementation
• The earliest OLAP systems used multidimensional arrays in
memory to store data cubes, and are referred to as
multidimensional OLAP (MOLAP) systems.
• OLAP implementations using only relational database features are
called relational OLAP (ROLAP) systems
• Hybrid systems, which store some summaries in memory and
store the base data and other summaries in a relational database,
are called hybrid OLAP (HOLAP) systems.
OLAP Implementation (Cont.)
• Early OLAP systems precomputed all possible aggregates in order
to provide online response
– Space and time requirements for doing so can be very high
• 2n combinations of group by
– It suffices to precompute some aggregates, and compute others
on demand from one of the precomputed aggregates
• Can compute aggregate on (item-name, color) from an
aggregate on (item-name, color, size)
– For all but a few “non-decomposable” aggregates such
as median
– is cheaper than computing it from scratch
• Several optimizations available for computing multiple aggregates
– Can compute aggregate on (item-name, color) from an
aggregate on
(item-name, color, size)
– Can compute aggregates on (item-name, color, size),
(item-name, color) and (item-name) using a single sorting
of the base data
Group By cube
• The cube operation computes union of group by’s on every subset of
the specified attributes
• E.g. consider the query
select item-name, color, size, sum(number)
from sales
group by cube(item-name, color, size)
This computes the union of eight different groupings of the sales
relation:
{ (item-name, color, size), (item-name, color),
(item-name, size),
(color, size),
(item-name),
(color),
(size),
()}
where ( ) denotes an empty group by list.
• For each grouping, the result contains the null value
for attributes not present in the grouping.
Group BY Cube (con’t)
• The function grouping() can be applied on an attribute
– Returns 1 if the value is a null value representing all, and returns
0 in all other cases.
select item-name, color, size, sum(number),
grouping(item-name) as item-name-flag,
grouping(color) as color-flag,
grouping(size) as size-flag,
from sales
group by cube(item-name, color, size)
• Can use the function decode() in the select clause to replace
such nulls by a value such as all
– E.g. replace item-name in first query by
decode( grouping(item-name), 1, ‘all’, item-name)
Alternative: A Data Mining Query
Language - DMQL
• Cube Definition (Fact Table)
define cube <cube_name> [<dimension_list>]:
<measure_list>
• Dimension Definition ( Dimension Table )
define dimension <dimension_name> as
(<attribute_or_subdimension_list>)
• Special Case (Shared Dimension Tables)
– First time as “cube definition”
– define dimension <dimension_name> as
<dimension_name_first_time> in cube
<cube_name_first_time>
Defining a Star Schema in DMQL
define cube sales_star [time, item, branch, location]:
dollars_sold = sum(sales_in_dollars), avg_sales =
avg(sales_in_dollars), units_sold = count(*)
define dimension time as (time_key, day, day_of_week, month, quarter,
year)
define dimension item as (item_key, item_name, brand, type,
supplier_type)
define dimension branch as (branch_key, branch_name, branch_type)
define dimension location as (location_key, street, city,
province_or_state, country)
Defining a Snowflake Schema in DMQL
define cube sales_snowflake [time, item, branch, location]:
dollars_sold = sum(sales_in_dollars), avg_sales =
avg(sales_in_dollars), units_sold = count(*)
define dimension time as (time_key, day, day_of_week, month, quarter,
year)
define dimension item as (item_key, item_name, brand, type,
supplier(supplier_key, supplier_type))
define dimension branch as (branch_key, branch_name, branch_type)
define dimension location as (location_key, street, city(city_key,
province_or_state, country))
Defining a Fact Constellation in DMQL
define cube sales [time, item, branch, location]:
dollars_sold = sum(sales_in_dollars), avg_sales =
avg(sales_in_dollars), units_sold = count(*)
define dimension time as (time_key, day, day_of_week, month, quarter,
year)
define dimension item as (item_key, item_name, brand, type,
supplier_type)
define dimension branch as (branch_key, branch_name, branch_type)
define dimension location as (location_key, street, city, province_or_state,
country)
define cube shipping [time, item, shipper, from_location, to_location]:
dollar_cost = sum(cost_in_dollars), unit_shipped = count(*)
define dimension time as time in cube sales
define dimension item as item in cube sales
define dimension shipper as (shipper_key, shipper_name, location as
location in cube sales, shipper_type)
define dimension from_location as location in cube sales
define dimension to_location as location in cube sales
Measures: Three Categories
• distributive: if the result derived by applying the function to n
aggregate values is the same as that derived by applying the function
on all the data without partitioning.
• E.g., count(), sum(), min(), max().
• algebraic: if it can be computed by an algebraic function with M
arguments (where M is a bounded integer), each of which is obtained
by applying a distributive aggregate function
.
• E.g., avg(), min_M(), standard_deviation().
• holistic: if there is no constant bound on the storage size needed to
describe a subaggregate.
• E.g., median(), mode(), rank().
Data Warehouse Design Process
• Top-down, bottom-up approaches or a combination of both
– Top-down: Starts with overall design and planning (mature)
– Bottom-up: Starts with experiments and prototypes (rapid)
• From software engineering point of view
– Waterfall: structured and systematic analysis at each step before
proceeding to the next
– Spiral: rapid generation of increasingly functional systems, short
turn around time, quick turn around
• Typical data warehouse design process
– Choose a business process to model, e.g., orders, invoices, etc.
– Choose the grain (atomic level of data) of the business process
– Choose the dimensions that will apply to each fact table record
– Choose the measure that will populate each fact table record
Multi-Tiered Architecture
other
Metadata
sources
Operational
DBs
Extract
Transform
Load
Refresh
Monitor
&
Integrator
Data
Warehouse
OLAP Server
Serve
Analysis
Query
Reports
Data mining
Data Marts
Data Sources
Data Storage
OLAP Engine Front-End Tools
Efficient Processing OLAP Queries
•
Determine which operations should be performed on the available cuboids:
– transform drill, roll, etc. into corresponding SQL and/or OLAP operations,
e.g, dice = selection + projection
•
Determine to which materialized cuboid(s) the relevant operations should be
applied.
•
Exploring indexing structures and compressed vs. dense array structures in
MOLAP
Metadata Repository
• Meta data is the data defining warehouse objects. It has the following
kinds
– Description of the structure of the warehouse
• schema, view, dimensions, hierarchies, derived data defn, data
mart locations and contents
– Operational meta-data
• data lineage (history of migrated data and transformation path),
currency of data (active, archived, or purged), monitoring
information (warehouse usage statistics, error reports, audit
trails)
– The algorithms used for summarization
– The mapping from operational environment to the data warehouse
– Data related to system performance
• warehouse schema, view and derived data definitions
– Business data
• business terms and definitions, ownership of data, charging
policies
Data Warehouse Back-End Tools and
Utilities
• Data extraction:
– get data from multiple, heterogeneous, and external sources
• Data cleaning:
– detect errors in the data and rectify them when possible
• Data transformation:
– convert data from legacy or host format to warehouse format
• Load:
– sort, summarize, consolidate, compute views, check integrity, and
build indicies and partitions
• Refresh
– propagate the updates from the data sources to the warehouse
Discovery-Driven Exploration of Data
Cubes
• Hypothesis-driven: exploration by user, huge search space
• Discovery-driven (Sarawagi et al.’98)
– pre-compute measures indicating exceptions, guide user in the
data analysis, at all levels of aggregation
– Exception: significantly different from the value anticipated,
based on a statistical model
– Visual cues such as background color are used to reflect the
degree of exception of each cell
– Computation of exception indicator (modeling fitting and
computing SelfExp, InExp, and PathExp values) can be
overlapped with cube construction
Examples: Discovery-Driven
Data Cubes
Data Warehouse Usage
• Three kinds of data warehouse applications
– Information processing
• supports querying, basic statistical analysis, and reporting
using crosstabs, tables, charts and graphs
– Analytical processing
• multidimensional analysis of data warehouse data
• supports basic OLAP operations, slice-dice, drilling, pivoting
– Data mining
• knowledge discovery from hidden patterns
• supports associations, constructing analytical models,
performing classification and prediction, and presenting the
mining results using visualization tools.
• Differences among the three tasks
From On-Line Analytical Processing to On Line
Analytical Mining (OLAM)
• Why online analytical mining?
– High quality of data in data warehouses
• DW contains integrated, consistent, cleaned data
– Available information processing structure surrounding data
warehouses
• ODBC, OLEDB, Web accessing, service facilities, reporting
and OLAP tools
– OLAP-based exploratory data analysis
• mining with drilling, dicing, pivoting, etc.
– On-line selection of data mining functions
• integration and swapping of multiple mining functions,
algorithms, and tasks.
• Architecture of OLAM
An OLAM Architecture
Mining query
Mining result
Layer4
User Interface
User GUI API
OLAM
Engine
OLAP
Engine
Layer3
OLAP/OLAM
Data Cube API
Layer2
MDDB
MDDB
Meta Data
Filtering&Integration
Database API
Filtering
Layer1
Data cleaning
Databases
Data
Warehouse
Data integration
Data
Repository
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