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Transcript of Dbm630 lecture05
DBM630: Data Mining and
Data Warehousing
MS.IT. Rangsit University
1
Semester 2/2011
Lecture 5
Association Rule Mining
by Kritsada Sriphaew (sriphaew.k AT gmail.com)
Topics
2
Association rule mining
Mining single-dimensional association rules
Mining multilevel association rules
Other measurements: interest and conviction
Association rule mining to correlation analysis
Data Warehousing and Data Mining by Kritsada Sriphaew
What is Association Mining?
3
Association rule mining:
Finding frequent patterns, associations, correlations, or causal structures among sets of items or objects in transaction databases, relational databases, and other information repositories.
Applications:
Basket data analysis, cross-marketing, catalog design, clustering, classification, etc.
Ex.: Rule form: “Body Head [support, confidence]” “Antecedent Consequent [support, confidence]” buys(x, “diapers*”) buys(x, “beers”) [0.5%,60%]
major(x, “CS”)^takes(x, “DB”) grade(x, “A”) [1%, 75%]
Data Warehousing and Data Mining by Kritsada Sriphaew
A typical example of association rule mining is market basket analysis.
4 Data Warehousing and Data Mining by Kritsada Sriphaew
Rule Measures: Support/Confidence
5
Find all the rules “Antecedent(s) Consequent(s)” with minimum support and confidence support, s, probability that a transaction contains {A C}
confidence, c, conditional probability that a transaction having A also contains C
Let min. sup. 50%, and min. conf. 50%, A C (s=50%, c=66.7%)
C A (s=50%, c=100%)
Typically association rules are considered interesting if they satisfy both a minimum support threshold and a mininum confidence threshold
Such thresholds can be set by users or domain experts
Transaction ID Items Bought
2000 A,B,C
1000 A,C
4000 A,D
5000 B,E,F
Transactional databases
• Support= 50% means that 50% of all transactions under analysis show that A and C are purchased together
• Confidence=66.7% means that 66.7% of the customers who purchased A also bought C
Data Warehousing and Data Mining by Kritsada Sriphaew
6
Rule Measures: Support/Confidence
TransID Items Bought
T001 A,B,C
T002 A,C
T003 A,D
T004 B,E,F
Rule: A C
support (AC) = P({AC}) = P(AC)
confidence(AC) = P(C|A) = P({AC})/P({A})
• A B (1/4 = 25%, 1/3 = 33.3%)
• B A (1/4 = 25%, 1/2 = 50%)
• A C (2/4 = 50%, 2/3 = 66.7%)
• C A (2/4 = 50%, 2/2 =100%)
• A, B C (1/4 = 25%, 1/1 = 100%)
• A, C B (1/4 = 25%, 1/2 = 50%)
• B, C A (1/4 = 25%, 1/1 = 100%)
Frequency
A = 3
B = 2
C = 2
AB = 1
AC = 2
BC = 1
ABC = 1
Customer buys diaper(C)
Customer buys both (A&C)
Customer buys beer (A)
probability
Data Warehousing and Data Mining by Kritsada Sriphaew
Association Rule: Support/Confidence for Relational Tables
7
In case that each transaction is a row in a relational table
Find: all rules that correlate the presence of one set of attributes with that of another set of attributes
temp. humidity
sunny
sunny
rainy
rainy
overcast
overcast
overcast
rainy
rainy
sunny
hot
hot
hot
mild
cool
hot
cool
mild
mild
hot
high
high
normal
high
low
low
normal
high
low
high
True
False
True
True
False
True
True
True
False
True
play-time play
85
90
63
5
56
25
5
86
78
74
Y
Y
Y
N
Y
N
N
Y
Y
Y
windy Sponsor
Sony
HP
Ford
Ford
HP
Sony
Nokia
Honda
Ford
Sony
outlook • If temperature = hot
then humidity = high (s=3/10,c=3/5)
• If windy=true and play=Y then humidity=high and outlook=overcast
(s=2/10, c=2/4) • If windy=true and play=Y
and humidity=high then outlook=overcast
(s=2/10, c=2/3)
Data Warehousing and Data Mining by Kritsada Sriphaew
Association Rule Mining: Types
8
Boolean vs. quantitative associations (Based on the types of values handled) (Single vs. multiple Dim.)
Single level vs. multilevel analysis What brands of beers are associated with what brands of diapers?
Various extensions Maxpatterns and closed itemsets
SQLServer ^ DMBooks DBMiner [0.2%, 60%]
buys(x, “SQLServer”) ^ buys(x, “DMBook”)
buys(x, “DBMiner”) [0.2%, 60%]
age(x, “30..39”) ^ income(x, “42..48K”)
buys(x, “PC”) [1%, 75%]
Data Warehousing and Data Mining by Kritsada Sriphaew
An Example (single dimensional Boolean association Rule Mining)
9
For rule A C: support = support({A, C}) = 50%
confidence = support({A, C})/support({A}) = 66.7%
The Apriori principle:
Any subset of a frequent itemset must be frequent
Transaction ID Items Bought
2000 A,B,C
1000 A,C
4000 A,D
5000 B,E,F
Frequent Itemset Support
{A} 75%
{B} 50%
{C} 50%
{A,C} 50%
Min. support 50%
Min. confidence 50%
Data Warehousing and Data Mining by Kritsada Sriphaew
Two Steps in Mining Association Rules
10
A subset of a frequent itemset must also be a frequent itemset
i.e., if {AB} is a frequent itemset, both {A} and {B} must be a frequent itemset
Iteratively find frequent itemsets with cardinality from 1 to k (k-itemset) Step1: Find the frequent itemsets: the sets of items that
have minimum support
Step2: Use the frequent itemsets to generate association
rules
Data Warehousing and Data Mining by Kritsada Sriphaew
The Apriori Algorithm
11
Join Step: Ck is generated by joining Lk-1with itself
Prune Step: Any (k-1)-itemset that is not frequent cannot be a subset of a frequent k-itemset
Pseudo-code:
Ck: Candidate itemset of size k
Lk : frequent itemset of size k
L1 = {frequent 1-itemsets};
for (k = 1; Lk !=f; k++) do begin
Ck+1 = candidates generated from Lk;
for each transaction t in database do
increment the count of all candidates in Ck+1
that are contained in t
Lk+1 = candidates in Ck+1 with min_support
end
return Uk Lk;
1
2
Find the frequent itemsets
Data Warehousing and Data Mining by Kritsada Sriphaew
The Apriori Algorithm — Example
12
TID Items
100 1 3 4
200 2 3 5
300 1 2 3 5
400 2 5
Database D itemset sup.
{1} 2
{2} 3
{3} 3
{4} 1
{5} 3
itemset sup.
{1} 2
{2} 3
{3} 3
{5} 3
Scan D
C1
L1
itemset
{1 2}
{1 3}
{1 5}
{2 3}
{2 5}
{3 5}
itemset sup
{1 2} 1
{1 3} 2
{1 5} 1
{2 3} 2
{2 5} 3
{3 5} 2
itemset sup
{1 3} 2
{2 3} 2
{2 5} 3
{3 5} 2
L2
C2 C2
Scan D
C3 L3 itemset
{2 3 5}Scan D itemset sup
{2 3 5} 2
How to Generate Candidates?
13
Suppose the items in Lk-1 are listed in an order
Step 1: self-joining Lk-1
INSERT INTO Ck SELECT p.item1, p.item2, …,
p.itemk-1, q.itemk-1 FROM Lk-1 p, Lk-1 q
WHERE p.item1 = q.item1, …,
p.itemk-2 = q.itemk-2,
p.itemk-1 < q.itemk-1
Step 2: pruning ForAll itemsets c IN Ck DO
ForAll (k-1)-subsets s OF c DO
IF (s is not in Lk-1) THEN DELETE c FROM Ck
Example of Generating Candidates
14
Self-joining: L3×L3
abc + abd abcd
acd + ace acde
Pruning: acde is removed because
ade is not in L3
L3={abc, abd, acd, ace, bcd}
C4={abcd}
Data Warehousing and Data Mining by Kritsada Sriphaew
How to Count Supports of Candidates?
15
Why counting supports of candidates a problem?
The total number of candidates can be very huge
One transaction may contain many candidates
Method:
Candidate itemsets are stored in a hash-tree
Leaf node of hash-tree contains a list of itemsets and counts
Interior node contains a hash table
Subset function: finds all the candidates contained in a transaction
Data Warehousing and Data Mining by Kritsada Sriphaew
Subset Function
16
Subset function: finds all the candidates contained in a transaction. (1) Generate Hash Tree (2) Hashing each item in the transactions
f
itemset
{1 2}
{1 3}
{1 5}
{2 3}
{2 5}
{3 5}
C2
TID Items
100 1 3 4
200 2 3 5
300 1 2 3 5
400 2 5
Database 1
2
3
2
3
5
3
5
5
1+1
1+1
1+1+1
1+1
1
1
Data Warehousing and Data Mining by Kritsada Sriphaew
Is Apriori Fast Enough? — Performance Bottlenecks
17
The core of the Apriori algorithm: Use frequent (k – 1)-itemsets to generate candidate frequent
k-itemsets Use database scan and pattern matching to collect counts for
the candidate itemsets
The bottleneck of Apriori: candidate generation Huge candidate sets:
104 frequent 1-itemset will generate 107 candidate 2-itemsets
To discover a frequent pattern of size 100, e.g., {a1, a2, …, a100}, one needs to generate 2100 1030 candidates.
Multiple scans of database: Needs (n +1 ) scans, n is the length of the longest pattern
Data Warehousing and Data Mining by Kritsada Sriphaew
Mining Frequent Patterns Without Candidate Generation
18
Compress a large database into a compact, Frequent-Pattern tree (FP-tree) structure
highly condensed, but complete for frequent pattern mining
avoid costly database scans
Develop an efficient, FP-tree-based frequent pattern mining method
A divide-and-conquer methodology: decompose mining tasks into smaller ones
Avoid candidate generation: sub-database test only!
Data Warehousing and Data Mining by Kritsada Sriphaew
Construct FP-tree from Transaction DB
19
{}
f:4 c:1
b:1
p:1
b:1 c:3
a:3
b:1 m:2
p:2 m:1
Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3
min_support = 0.5
TID Items bought (ordered) frequent items 100 {f, a, c, d, g, i, m, p} {f, c, a, m, p} 200 {a, b, c, f, l, m, o} {f, c, a, b, m} 300 {b, f, h, j, o} {f, b} 400 {b, c, k, s, p} {c, b, p} 500 {a, f, c, e, l, p, m, n} {f, c, a, m, p}
Steps:
1. Scan DB once, find
frequent 1-itemset
(single item pattern)
2. Order frequent items
in frequency
descending order
3. Scan DB again,
construct FP-tree
Data Warehousing and Data Mining by Kritsada Sriphaew
Mining Frequent Patterns using FP-tree
20
General idea (divide-and-conquer) Recursively grow frequent pattern path using the FP-tree
Method For each item, construct its conditional pattern-base, and then its
conditional FP-tree Repeat the process on each newly created conditional FP-tree Until the resulting FP-tree is empty, or it contains only one path (single
path will generate all the combinations of its sub-paths, each of which is a frequent pattern)
Benefit: Completeness & Compactness Completeness: never breaks a long pattern of any transaction and
preserves complete information for frequent pattern mining Compactness: reduces irrelevant information (infrequent items are gone),
orders in frequency descending ordering (more frequent items are likely to be shared), and smaller than the original database.
Data Warehousing and Data Mining by Kritsada Sriphaew
Step 1: From FP-tree to Conditional Pattern Base
Knowledge Management and Discovery © Kritsada Sriphaew 21
Starting at the frequent header table in the FP-tree
Traverse the FP-tree by following the link of each frequent item
Accumulate all of transformed prefix paths of that item to form a conditional pattern base
Conditional pattern bases
item cond. pattn base
c f:3
a fc:3
b fca:1, f:1, c:1
m fca:2, fcab:1
p fcam:2, cb:1
{}
f:4 c:1
b:1
p:1
b:1 c:3
a:3
b:1 m:2
p:2 m:1
Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3
Step 2: Construct Conditional FP-tree
22
For each pattern-base
Accumulate the count for each item in the base
Construct the FP-tree for the frequent items of the pattern base
m-conditional pattern base:
fca:2,
fcab:1
{}
f:3
c:3
a:3
m-conditional FP-tree
All frequent patterns concerning m
m,
fm, cm, am,
fcm, fam, cam,
fcam
{}
f:4 c:1
b:1
p:1
b:1 c:3
a:3
b:1 m:2
p:2 m:1
Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3
Mining Frequent Patterns by
(Creating Conditional Pattern-Bases)
23
Empty Empty f
{(f:3)}|c {(f:3)} c
{(f:3, c:3)}|a {(fc:3)} a
Empty {(fca:1), (f:1), (c:1)} b
{(f:3, c:3, a:3)}|m {(fca:2), (fcab:1)} m
{(c:3)}|p {(fcam:2), (cb:1)} p
Conditional FP-tree Conditional pattern-base Item
Data Warehousing and Data Mining by Kritsada Sriphaew
Step 3: Recursively mine the conditional FP-
tree
24
{}
f:3
c:3
a:3
m-conditional FP-tree
{}
f:3
c:3
am-conditional FP-tree
{}
f:3
cm-conditional FP-tree
{}
f:3
cam-conditional FP-tree
Data Warehousing and Data Mining by Kritsada Sriphaew
Single FP-tree Path Generation
25
Suppose an FP-tree T has a single path P
The complete set of frequent pattern of T can be generated by enumeration of all the combinations of the sub-paths of P
m-conditional pattern base:
fca:2,
fcab:1
{}
f:3
c:3
a:3
m-conditional FP-tree
All frequent patterns concerning m
m,
fm, cm, am,
fcm, fam, cam,
fcam
{}
f:4 c:1
b:1
p:1
b:1 c:3
a:3
b:1 m:2
p:2 m:1
Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3
FP-growth vs. Apriori: Scalability With the
Support Threshold
26
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3Support threshold(%)
Ru
n t
ime
(se
c.)
D1 FP-growth runtime
D1 Apriori runtime
Data set T25I20D10K
Data Warehousing and Data Mining by Kritsada Sriphaew
CHARM - Mining Closed Association Rules
Instead of horizontal DB format, vertical format is used.
Instead of traditional frequent itemsets, closed frequent
itemsets are mined.
Transaction Items
1 ABDE
2 BCE
3 ABDE
4 ABCE
5 ABCDE
6 BCD
Items Transaction
A 1345
B 123456
C 2456
D 1356
E 12345
27
Horizontal DB Vertical DB
Data Warehousing and Data Mining by Kritsada Sriphaew
CHARM – Frequent Itemsets and Their Supports
28
An example database and its frequent itemsets
Items Trans. A 1345 B 123456 C 2456 D 1356 E 12345
Vertical DB
Support Itemsets 1.00 B 0.83 BE, E 0.67 A, C, D, AB,AE, BC, BD, ABE 0.50 AD, CE, DE, ABD, ADE, BCE, BDE, ABDE
Min. support = 0.5
Data Warehousing and Data Mining by Kritsada Sriphaew
CHARM - Closed Itemsets
29
Closed frequent itemsets and their corresponding frequent itemsets
Closed Itemsets Tidsets Sup. Freq. Itemsets
B 123456 1.00 B
BE 12345 0.83 BE, E ABE 1345 0.67 ABE, AB, AE, A BD 1356 0.67 BD, D BC 2456 0.67 BC, C ABDE 135 0.50 ABDE, ABD, ADE, BDE, AD, DE BCE 245 0.50 CE, BCE
Data Warehousing and Data Mining by Kritsada Sriphaew
The CHARM Algorithm
30
CHARM (? I T, minsup);
1. Nodes = { Ij t(Ij) : Ij I |t(Ij )| minsup }
2. CHARM-EXTEND (Nodes, C)
CHARM-EXTEND (Nodes, C)
3. for each Xi t(Xi) in Nodes
4. NewN = f and X = Xi
5. for each Xj t(Xj) in Nodes, with f(j) > f(I)
6. X’ = X Xj and Y = t(Xi) t(Xj)
7. CHARM-PROPERTY(Nodes, NewN)
8. if NewN f then CHARM-EXTEND(NewN)
9. C = C {X} // if X is not subsumed
CHARM-PROPERY(Nodes, NewN)
1. if (|Y| minsup) then
2. if t(Xi) = t(Xj) then // Propery 1
3. Remove Xj from Nodes
4. Replace all Xi with X’
5. else if t(Xj) t(Xj) then // Propery 2
6. Replace all Xi with X’
7. else if t(Xj) t(Xj) then // Propery 3
8. Remove Xj from Nodes
9. Add X Y to NewN
10. else if t(Xj) t(Xj) then // Propery 4
11. Add X Y to NewN
Ax1345 Bx123456 Cx2456 Dx1356 Ex12345
ABx1345
ABEx1345
ABCx45 ABDx135 ABDEx135
BCx2456
BCDx56 BCEx245
BDx1356 BEx12345
BDEx135
f
Data Warehousing and Data Mining by Kritsada Sriphaew
Presentation of Association Rules (Table Form)
31 Data Warehousing and Data Mining by Kritsada Sriphaew
Visualization of Association Rule Using Plane Graph
32
Visualization of Association Rule Using Rule Graph
33
Multiple-Level Association Rules
Items often form hierarchy.
Items at the lower level are
expected to have lower
support.
Rules regarding itemsets at
the appropriate levels could
be quite useful.
Transaction database can be
encoded based on
dimensions and levels
We can explore shared
multi-level mining
TID ITEMS
T1 {1121, 1122, 1212}
T2 {1222, 1121, 1122, 1213}
T3 {1124, 1213}
T4 {1111, 1211, 1232, 1221, 1223}
34
Food
(1)
Bread
(12)
Milk
(11)
Skim
(111)
Sunset
(1124)
Fraser
(1121)
2%
(112)
White
(122)
Wheat
(121)
Mining multilevel association rules from transactional databases
Wonder (1222)
Wonder (1213)
Data Warehousing and Data Mining by Kritsada Sriphaew
Mining Multi-Level Associations
35
A top_down, progressive deepening approach:
First find high-level strong rules:
Then find their lower-level “weaker” rules:
Variations at mining multiple-level association rules.
Level-crossed association rules:
Association rules with multiple, alternative hierarchies:
milk bread [20%, 60%]
2% milk wheat bread [6%, 50%]
2% milk Wonder wheat bread [3%, 60%]
2% milk Wonder bread [8%, 72%]
Data Warehousing and Data Mining by Kritsada Sriphaew
Multi-level Association: Redundancy Filtering
36
Some rules may be redundant due to “ancestor” relationships between items.
Example
We say the first rule is an ancestor of the second rule.
A rule is redundant if its support is close to the “expected” value, based on the rule’s ancestor.
milk wheat bread [s=8%, c=70%]
2% milk wheat bread [s=2%, c=72%]
Data Warehousing and Data Mining by Kritsada Sriphaew
Multi-Level Mining: Progressive Deepening
37
A top-down, progressive deepening approach: First mine high-level frequent items:
milk (15%), bread (10%) Then mine their lower-level “weaker” frequent itemsets:
2% milk (5%), wheat bread (4%)
Different min_support threshold across multi-levels lead to different algorithms: If adopting the same min_support across multi-levels
then toss t if any of t’s ancestors is infrequent. If adopting reduced min_support at lower levels
then examine only those descendants whose ancestor’s support is frequent/non-negligible.
Data Warehousing and Data Mining by Kritsada Sriphaew
Problem of Confidence
38
Example: (Aggarwal & Yu, PODS98)
Among 5000 students
3000 play basketball
3750 eat cereal
2000 both play basket ball and eat cereal
play basketball eat cereal [40%, 66.7%] is misleading because the overall percentage of students eating cereal is 75% which is higher than 66.7%.
play basketball not eat cereal [20%, 33.3%] is far more accurate, although with lower support and confidence
basketball not basketball sum(row)
cereal 2000 1750 3750
not cereal 1000 250 1250
sum(col.) 3000 2000 5000
Data Warehousing and Data Mining by Kritsada Sriphaew
Interest/Lift/Correlation
Interest (or lift, correlation)
taking both P(A) and P(B) in consideration
P(AB)=P(B)P(A), if A and B are independent
events
A and B negatively correlated, if the value is less
than 1; otherwise A and B positively correlated
Lift(play basketball eat cereal) = 0.89
Lift(play basketball not eat cereal) = 1.33
basketball not basketball sum(row)
cereal 2000 1750 3750
not cereal 1000 250 1250
sum(col.) 3000 2000 5000
39
)()(
)(
BPAP
BAP
889.0
5000
3750
5000
30005000
2000
33.1
5000
1250
5000
30005000
1000
Data Warehousing and Data Mining by Kritsada Sriphaew
Conviction
Conviction (Brin, 1997)
0 <= conv(AB) <=
A and B are statistically independent if and only if
conv(AB) = 1
0 < conv(AB) < 1 if and only if p(B|A) < p(B)
B is negatively correlated with A.
1 < conv(AB) < if and only if p(B|A) > p(B)
B is positively correlated with A.
)(1(
))(1()(
BAConfidence
BSupportBAConviction
40
basketball not basketball sum(row)
cereal 2000 1750 3750
not cereal 1000 250 1250
sum(col.) 3000 2000 5000
375.0667.01
5000
37501
25.2333.01
5000
12501
conviction(play basketball eat cereal) = 0.375
conviction(play basketball not eat cereal) = 2.25
Data Warehousing and Data Mining by Kritsada Sriphaew
From Association Mining to Correlation Analysis
Ex. Strong rules are not necessarily interesting
41
Of 10000 transactions
• 6000 customer transactions include computer games
• 7500 customer transactions include videos • 4000 customer transactions include both computer game and video
• Suppose that data mining program for
discovering association rules is run on
the data, using min_sup of 30% and
min_conf. of 60%
• The following association rule is
discovered:
buys(X, “computer games”) buys(X, “videos”) [s=40%, c=66%]
=4000/10000 =4000/6000
4,000
videos games
This rule is misleading because the probability of purchasing video is 75% (>66%)
In fact, computer games and videos are negatively associated because the purchase of one of these items actually decreases the likelihood of purchasing the other. Therefore, we could easily make unwise business decisions based on this rule
42
buys(X, “computer games”) buys(X, “videos”) [support=40%, confidence=66%]
A misleading “strong” association rule
Data Warehousing and Data Mining by Kritsada Sriphaew
From Association Analysis to Correlation Analysis
To help filter out misleading “strong” association
Correlation rules
A B [support, confidence, correlation]
Lift is a simple correlation measure that is given as follows
The occurrence of itemset A is independent of the occurrence of itemset B if
P(AB) = P(A)P(B);
Otherwise, itemset A and B are dependent and correlated
lift(A,B) = P(AB) / P(A)P(B) = P(B|A) / P(B) = conf(AB) / sup(B)
If lift(A,B) < 1, then the occurrence of A is negatively correlated with the occurrence of B
If lift(A,B) > 1, then A and B is positively correlated, meaning that the occurrence of one implies the occurrence of the other.
43 Data Warehousing and Data Mining by Kritsada Sriphaew
From Association Analysis to Correlation Analysis (Cont.)
Ex. Correlation analysis using lift
The lift of this rule is P{game,video} / (P{game} × P{video}) = 0.40/(0.6 ×0.75) = 0.89
There is a negative correlation between the occurrence of {game} and {video}
Ex. Is this following rule misleading?
Buy walnuts Buy milk [1%, 80%]”
if 85% of customers buy milk
44
buys(X, “computer games”) buys(X, “videos”) [support=40%, confidence=66%]
Data Warehousing and Data Mining by Kritsada Sriphaew
Homework
45
ให transactional database ซงเปน LOG ไฟลบนทกการเขาเยยมชมเวบเพจของปใชแตละคน
ในชวงระยะเวลาหนง จงหากฎสมพนธทนาเชอถอ โดยสมมตวาเราเปนปวเคราะหขอมล ม
สทธตง minimum support และ minimum confidence ดวยตวเอง พรอมอธบายเหตปล
ประกอบวาท าไมถงตงคานน และตรวจสอบดวยวากฎเหลานนเปน misleading หรอไม ถามให
แกไขอยางไร
TID List of items
T001 P1, P2, P3, P4
T002 P3, P6
T003 P2, P5, P1
T004 P5, P4, P3,P6
T005 P1, P3, P4, P2
P1 P2 P3 P4 P5
P6
Feb 26, 2011 (14:00)
Data Warehousing and Data Mining by Kritsada Sriphaew 46
Quiz I
Star-net Query (Multidimensional Table)
Data Cube Computation (Memory Calculation)
Data Preprocessing (Normalization, Smoothing by binning)
Association Rule Mining