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Data Mining
Βάσεις Δεδομένων 2001-2002
Ευαγγελία Πιτουρά
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Introduction
Finding interesting trends or pattern in large datasets
Statistics: exploratory data analysis
Artificial intelligence: knowledge discovery and machine learning
Scalability with respect to data size
An algorithm is scalable if the running time grows (linearly) in
proportion to the dataset size, given the available system resources
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Introduction
Finding interesting trends or pattern in large datasets
SQL queries (based on the relational algebra)
OLAP queries (higher-level query constructs – multidimensional
data model)
Data mining techniques
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Knowledge Discovery (KDD)
The Knowledge Discovery Process
Data Selection
Data Cleaning
Identify the target dataset and relevant attributes
Remove noise and outliers, transform field values to
common units, generate new fields, bring the data into
the relational schema
Data Mining
Evaluation
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Present the patterns in an understandable form to the
end user (e.g., through visualization)
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Overview
Counting Co-occurrences
Frequent Itemsets
Iceberg Queries
Mining for Rules
Association Rules
Sequential Rules
Classification and Regression
Tree-Structures Rules
Clustering
Similarity Search over Sequences
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Counting Co-Occurrences
A market basket is a collection of items purchased by a customer
in a single customer transaction
Identify items that are purchased together
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Example
Transid
custid
date
item
qty
111
201
5/1/99
pen
2
111
201
5/1/99
ink
1
111
201
5/1/99
milk
3
111
201
5/1/99
juice
6
112
105
6/3/99
pen
1
112
105
6/3/99
ink
1
112
105
6/3/99
milk
1
113
106
5/10/99
pen
1
113
106
5/10/99
milk
1
114
201
6/1/99
pen
2
114
201
6/1/99
ink
2
114
201
6/1/99
juice
4
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one transaction
note that there
is redundancy
Observations of the
form:
in 75% of transactions
both pen and ink are
purchased together
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Frequent Itemsets
Itemset: a set of items
Support of an itemset: the fraction of transactions in
the database that contain all items in the itemset
Example:
Itemset {pen, ink} Support 75%
Itemset {milk, juice} Support 25%
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Frequent Itemsets
Frequent Itemsets: itemsets whose support is higher
than a user specified minimum support called minsup
Example:
If minsup = 70%,
Frequent Itemsets
{pen}, {ink}, {milk}, {pen, ink}, {pen, milk}
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Frequent Itemsets
An algorithm for identify (all) frequent itemsets?
The a priory property:
Every subset of a frequent itemset must also be a frequent
itemset
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Frequent Itemsets
An algorithm for identifying frequent itemsets
For each item,
check if it is a frequent itemset
k=1
repeat
for each new frequent itemset Ik with k items
Generate all itemsets Ik+1 with k+1 items, Ik  Ik+1
Scan all transactions once and check if the generated
k+1 itemsets are frequent
k=k+1
Until no new frequent itemsets are identified
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Frequent Itemsets
A refinement of the algorithm for identifying frequent itemsets
For each item,
check if it is a frequent itemset
k=1
repeat
for each new frequent itemset Ik with k items
Generate all itemsets Ik+1 with k+1 items, Ik  Ik+1 whose
subsets are ferquent itemsets
Scan all transactions once and check if the generated
k+1 itemsets are frequent
k=k+1
Until no new frequent itemsets are identified
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Iceberg Queries
Assume we want to find pairs of customers and items such that
the customer has purchased the item at least 5 times
select P.custid, P. item, sum(P.qty)
from Purchases P
group by P.custid, P.item
having sum (P.qty) > 5
Execution plan for the query?
The number of groups is very large but the answer to the query (the
tip of the iceberg) is usually very small
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Iceberg Queries
Iceberg query
select R.A1, R.A2, …, R.Ak, agr(R.B)
from Relation R
group by R.A1, R.A2, …, R.Ak
having agr(R.B) > = constant
A priory property similar to the a priori property for the frequent
itemsets?
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Iceberg Queries
select P.custid, P. item, sum(P.qty)
from Purchases P
group by P.custid, P.item
having sum (P.qty) > 5
select P.custid
from Purchases P
select P.item
Q1
from Purchases P
group by P.custid
group by P.item
having sum (P.qty) > 5
having sum (P.qty) > 5
Q2
Generate (custid, item) pairs only for custid from Q1 and item from Q2
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Overview
Counting Co-occurences
Frequent Itemsets
Iceberg Queries
Mining for Rules
Association Rules
Sequential Rules
Classification and Regression
Tree-Structures Rules
Clustering
Similarity Search over Sequences
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Association Rules
Example
{pen}  {ink}
If a pen is purchased in a transaction, it is likely that ink will also be
purchased in the transaction
In general:
LHS  RHS
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Association Rules
LHS  RHS
Support: support(LHS  RHS)
The percentage of transactions that contain all of these items
Confidence: support(LHS  RHS) / support(LHS)
Is an indication of the strength of the rule
P(RHS | LHS)
An algorithm for finding all rules with minsum and minconf?
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Association Rules
An algorithm for finding all rules with minsup and minconf
Step 1: Find all frequent itemsets with minsup
Step 2: Generate all rules from step 1
Step 2
For each frequent itemset I with support support(I)
Divide I into LHSI and RHSI
confidence = support(I) / support(LHSI)
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Association Rules and ISA Hierarchies
An ISA hierarchy or category hierarchy upon the set of items: a
transaction implicitly contains for each of its items all of the item’s
ancestors
Beverage
Milk
Juice
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Stationery
Pen
Ink
 Detect
relationships
between items at
different levels of
the hierarchy
 In general, the
support
of
an
itemset can only
increase if an item
is replaced by its
ancestor
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Generalized Association Rules
More general: not just customer transactions
Transid
custid
date
item
qty
111
201
5/1/99
pen
2
111
201
5/1/99
ink
1
111
201
5/1/99
milk
3
111
201
5/1/99
juice
6
112
105
6/3/99
pen
1
112
105
6/3/99
ink
1
112
105
6/3/99
milk
1
113
106
5/10/99
pen
1
113
106
5/10/99
milk
1
114
201
6/1/99
pen
2
114
201
6/1/99
ink
2
114
201
6/1/99
juice
4
Βάσεις Δεδομένων 2001-2002
e.g., Group tuples by
custid
Rule {pen}  {milk}: if a
pen is purchased by a
customer, it likely that
milk
will
also
be
purchased
by
the
customer
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Generalized Association Rules
Group tuples by date: Calendric market basket analysis
A calendar is any group of dates; e.g., every first of the month
Given a calendar, compute association rules over the set of tuples whose date
field falls within the calendar
Calendar: every first of the month
Rule {pen}  {juice}: has support
100%
Over the entire: 50%
Rule {pen}  {milk}: has support
50%
Over the entire: 75%
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Transid
custid
date
item
qty
111
201
5/1/99
pen
2
111
201
5/1/99
ink
1
111
201
5/1/99
milk
3
111
201
5/1/99
juice
6
112
105
6/3/99
pen
1
112
105
6/3/99
ink
1
112
105
6/3/99
milk
1
113
106
5/10/99
pen
1
113
106
5/10/99
milk
1
114
201
6/1/99
pen
2
114
201
6/1/99
ink
2
114
201
6/1/99
juice
4
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Sequential Patterns
Sequence of Itemsets:
The sequence of itemsets purchased by the customer:
Example custid 201: {pen, ink, milk, juice}, {pen, ink, juice}
(ordered by date)
A subsequence of a sequence of itemsets is obtained by deleting one
or more itemsets and is also a sequence of itemsets
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Sequential Patterns
A sequence {a1, a2, .., an} is contained in sequence S if S has a
subsequence {bq, .., bm} such that ai  bi for 1  i  m
Example
{pen}, {ink, milk}, {pen, juice} is contained in {pen, ink}, {shirt},
{juice, ink, milk}, {juice, pen, milk}
The order of items within each itemset does not matter but the
order of itemsets does matter
{pen}, {ink, milk}, {pen, juice} is not conatined in {pen, ink}, {shirt},
{juice, pen, milk}, {juice, milk, ink}
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Sequential Patterns
The support for a sequence S of itemsets is the percentage of
customer sequences of which S is a subsequence
Identify all sequences that have a minimum support
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Overview
Counting Co-occurences
Frequent Itemsets
Iceberg Queries
Mining for Rules
Association Rules
Sequential Rules
Classification and Regression
Tree-Structures Rules
Clustering
Similarity Search over Sequences
Βάσεις Δεδομένων 2001-2002
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Classification and Regression Rules
InsuranceInfo(age: integer, cartype: string, highrisk: boolean)
There is one attribute (highrisk) whose value we would like
to predict: dependent attribute
The other attributes are called the predictors
General form of the types of rules we want to discover:
P1(X1)  P2(X2)  …  Pk(Xk)  Y = c
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Classification and Regression Rules
P1(X1)  P2(X2)  …  Pk(Xk)  Y = c
Pi(Xi) are predicates
Two types:
 numerical
Pi(Xi) : li  Xi  hi
 categorical
Pi(Xi) : Xi  {v1, …, vj}
 numerical dependent attribute
regression rule
 categorical dependent attribute
classification rule
(16  age  25)  (cartype  {Sports, Truck})  highrisk = true
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Classification and Regression Rules
P1(X1)  P2(X2)  …  Pk(Xk)  Y = c
Support:
The support for a condition C is the percentage of tuples that
satisfy C.
The support for a rule C1  C2 is the support of the condition
C1  C2
Confidence
Consider the tuples that satisfy condition C1. The confidence
for a rule C1  C2 is the percentage of such tuples that also
satisfy condition C2
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Classification and Regression Rules
Differ from association rules by considering continuous and
categorical attributes, rather than one field that is set-valued
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Overview
Counting Co-occurences
Frequent Itemsets
Iceberg Queries
Mining for Rules
Association Rules
Sequential Rules
Classification and Regression
Tree-Structures Rules
Clustering
Similarity Search over Sequences
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Tree-Structured Rules
Classification or decision trees
Regression trees
Typically the tree itself is the output of data mining
Easy to understand
Efficient algorithms to construct them
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Decision Trees
A graphical representation of a collection of classification rules.
Given a data record, the tree directs the record from the root
to a leaf.
• Internal nodes: labeled with a predictor attribute (called a
splitting attribute)
• Outgoing edges: labeled with predicates that involve the
splitting attribute of the node (splitting criterion)
• Leaf nodes: labeled with a value of a dependent attribute
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Decision Trees
Example
Age
> 25
<= 25
No
Car Type
Other
Sports, Truck
No
Construct classification
rules from the paths
from the root to the
leaf:
LHS
conjuction
predicates; RHS
value of the leaf
of
the
Yes
(16  age  25)  (cartype  {Sports, Truck})  highrisk = true
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Decision Trees
Constructed into two phases
Phase 1: growth phase
construct a vary large tree (e.g., leaf nodes for
individual records in the database
Phase 2: pruning phase
Build the tree greedily top down:
At the root node, examine the database and compute the locally best
splitting criterion
Partition the database into two parts
Recurse on each child
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Decision Trees
Input: node n partition D split selection method S
Output: decision tree for D rooted at node n
Top down Decision Tree Induction Schema
BuildTree(node n, partition D, method S)
Apply S to D to find the splitting criterion
If (a good splitting criterion is found)
create two children nodes n1 and n2 of n
partition D into D1 and D2
BuildTree(n1, D1, S)
Build Tree(n2, D2, S)
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Decision Trees
Split selection method
An algorithm that takes as input (part of) a relation and outputs
the locally best spliting criterion
Example: examine the attributes cartype and age, select one of
them as a splitting attribute and then select the splitting
predicates
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Decision Trees
How can we construct decision trees when the input database is
larger than main memory?
Provide the split selection method with aggregated information
about the database instead of loading the complete database
into main memory
We need aggregated information for each predictor attribute
AVC set of the predictor attribute X at node n is the projection
of n’s database partition onto X and the dependent attribute
where counts of the individual values in the domain of the
dependent attribute are aggregated
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Decision Trees
age
cartype highrisk
23
Sedan
false
30
Sports
false
36
Sedan
false
25
Truck
true
30
Sedan
false
23
Truck
true
30
Truck
false
25
Sports
true
18
Sedan
false
AVC set of the predictor attribute age at
the root node
select R.age, R.highrisk, count(*)
from InsuranceInfo R
group by R.age, R.highrisk
AVC set of the predictor attribute cartype
at the left child of the root node
select R.cartype, R.highrisk, count(*)
from InsuranceInfo R
where R.age <=25
group by R.age, R.highrisk
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Decision Trees
age
cartype highrisk
23
Sedan
false
30
Sports
false
36
Sedan
false
25
Truck
true
30
Sedan
false
23
Truck
true
30
Truck
false
25
Sports
true
18
Sedan
false
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AVC set of the predictor attribute age at
the root node
select R.age, R.highrisk, count(*)
from InsuranceInfo R
group by R.age, R.highrisk
True
Sedan 0
Sports 1
Truck 2
False
4
1
1
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Decision Trees
AVC group of a node n: the set of the AVC sets of all predictors
attributes at node n
Size of the AVC set?
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Decision Trees
Input: node n partition D split selection method S
Output: decision tree for D rooted at node n
Top down Decision Tree Induction Schema
BuildTree(node n, partition D, method S)
Make a scan over D and construct the AVC group of node n in memory
Apply S to AVC group to find the splitting criterion
If (a good splitting criterion is found)
create two children nodes n1 and n2 of n
partition D into D1 and D2
BuildTree(n1, D1, S)
Build Tree(n2, D2, S)
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Overview
Counting Co-occurences
Frequent Itemsets
Iceberg Queries
Mining for Rules
Association Rules
Sequential Rules
Classification and Regression
Tree-Structures Rules
Clustering
Similarity Search over Sequences
Βάσεις Δεδομένων 2001-2002
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Clustering
Partition a set of records into groups (clusters) such that all
records within a group are similar to each other and records
that belong to two different groups are disimilar.
Similarity between records measured computationally by a
distance function.
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Clustering
CustomerInfo(age: integer, salary:real)
Salary
20
40
60
Age
• Visually identify three clusters - shape of clusters: spherical spheres
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Clustering
The output of a clustering algorithm consists of a summarized
representation of each cluster.
Type of output depends on type and shape of clusters.
For example if spherical clusters: center C (mean) and
radius R:
given a collection of records r1, r2, .., rn
C =  ri
R=
 (ri - C)
n
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Clustering
Two types of clustering algorithms:
• Partitional clustering: partitions the data into k groups
such that some criterion that evaluates the clustering
quality is optimized
• Hierarchical clustering generates a sequence of partitions
of the records. Starting with a partition in which each
cluster consists of a single record, merges two partitions in
each step
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Clustering
The BIRCH algorithm:
Assumptions
• Large number of records, just one scan of them
• A limited amount of main memory
Two parameters
• k: main memory threshold: maximum number of clusters that can be
maintained in memory
• e: initial threshold of the radius of each cluster. A cluster is compact
if its radius is smaller than e.
Always maintain in main memory k or fewer compact cluster summaries
(Ci, Ri)
(If this is no possible adjust e)
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Clustering
The BIRCH algorithm:
Read a record r from the database
Compute the distance of r and each of the existing cluster centers
Let i be the cluster (index) such that the distance between r and Ci is the
smallest
Compute R’i assuming r is inserted in the ith cluster
If R’i  e,
insert r in the ith cluster
recompute Ri and Ci
else
start a new cluster containing only r
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Overview
Counting Co-occurences
Frequent Itemsets
Iceberg Queries
Mining for Rules
Association Rules
Sequential Rules
Classification and Regression
Tree-Structures Rules
Clustering
Similarity Search over Sequences
Βάσεις Δεδομένων 2001-2002
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Similarity Search over Sequences
A user specifies a query sequence and wants to retrieve all data
sequences that are similar to the query sequence
Not exact matches
A data sequence X is a sequence of numbers X = <x1, x2, .., xk>
Also called a time series
k length of the sequence
A subsequence Z = <z1, z2, …, zj> is deleting from another sequence by
deleting numbers from the front and back of the sequence
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Similarity Search over Sequences
Given two sequences X and Y we can define the distance of the two
sequences as the Euclidean norm
Given a user-specified query sequence and a threshold parameter
e, retrieve all data sequences within e-distance to the query
sequence
 Complete sequence matching (the query sequence and the
sequence in the database have the same length)
 Subsequence matching (the query is shorter)
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Similarity Search over Sequences
Given a user-specified query sequence and a threshold parameter
e, retrieve all data sequences within e-distance to the query
sequence
Brute-force method?
Each data sequence and the query sequence of length k may be
represented as a point in a k-dimensional space
Construct a multidimensional index
Non-exact matches? Query the index with a hyper-rectangle with
side length 2-e and the query sentence as the center
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