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Slide 1 © Gerd Stumme 2002 Invited Talk at DEXA ‘2 Efficient Data Mining Based on Formal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany Gerd Stumme Ergänzung zu Kap. 4 der KDD- Vorlesung SS 2005
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Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Mar 11, 2018

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Page 1: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 1© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Efficient Data Mining

Based on

FormalConceptAnalysis

Institute for Applied Informatics (AIFB)

University of Karlsruhe, Germany

Gerd Stumme

Ergänzung zu Kap. 4 der KDD-Vorlesung SS 2005

Page 2: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 2© Gerd Stumme 2002 Invited Talk at DEXA ‘2

1. Motivation: Structuring theFrequent Itemset Space

2. Formal Concept Analysis

3. Conceptual Clusteringwith Iceberg Concept Lattices

4. FCA-Based Miningof Association Rules

5. Other Application(s) of FCA

Page 3: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 3© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Association Rules are a popular data miningtechnique, e.g. for warehousebasket analysis: „Which itemsare frequently boughttogether?“

Association Rules in a Nutshell

#(swimming+hiking parks) / #(swimming parks)

#(swimming+hiking parks) / #(all parks)

Toy Example:Which activities can befrequently performed togetherin National Parks in California?

National Parks in California

{Swimming} → {Hiking}

conf = 100 %, supp = 10/19

Page 4: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 4© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Observation:

The rules

{ Boating } → { Hiking, NPS Guided Tours, Fishing }

{ Boating, Swimming } → { Hiking, NPS Guided Tours, Fishing }

have the same support and the same confidence,

because the two sets

{ Boating } and { Boating, Swimming }

describe exactly the same set of parks.

Conclusion:

It is sufficient to look at one of those sets!

→ faster computation

→ no redundant rules

Page 5: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 5© Gerd Stumme 2002 Invited Talk at DEXA ‘2

123

a b c e

Another ToyExample:

Unique represen-tatives of each class:

the closed itemsets

(or concept intents).

(6 instead of 16)

The space of (potentiallyfrequent) itemsets: the powerset of { a, b, c, e }

Classes of itemsets describing the same sets of objects

Page 6: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 6© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Our task:Find a basis of rules, i.e., a minimal set of rules out of which all other rules can be derived.

Classical Data Mining Task:Find, for given minsupp, minconf ∈[0,1], all rules with support and confidence above these thresholds.

Bases of Association Rules

Two-Step Approach:

1. Compute all frequent itemsets(e.g., Apriori).

2. For each frequent itemset Xand all its subsets Y:

check X → Y.

Two-Step Approach:

1. Compute all frequent closeditemsets.

2. For each frequent closed itemset Xand all its closed subsets Y:

check X → Y.

Page 7: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 7© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Our task:Find a basis of rules, i.e., a minimal set of rules out of which all other rules can be derived.

Two-Step Approach:

1. Compute all frequent closeditemsets.

2. For each frequent closed itemset Xand all its closed subsets Y:

check X → Y.

Association Rules and Formal Concept Analysis

Based on Formal Concept Analysis (FCA).

This relationship was discoveredindependently in 1998/9 at

• Clermont-Ferrand (Lakhal)

• Darmstadt (Stumme)

• New York (Zaki)

with Clermont being the fastest groupdeveloping algorithms (Close).

Page 8: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 8© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Our task:Find a basis of rules, i.e., a minimal set of rules out of which all other rules can be derived.

Two-Step Approach:

1. Compute all frequent closeditemsets.

2. For each frequent closed itemset Xand all its closed subsets Y:

check X → Y.

Association Rules and Formal Concept Analysis

Based on Formal Concept Analysis (FCA).

This relationship was discoveredindependently in 1998/9 at

• Clermont-Ferrand (Lakhal)

• Darmstadt (Stumme)

• New York (Zaki)

with Clermont being the fastest groupdeveloping algorithms (Close).

Structureof the Talk:

• Introduction to FCA

• Conceptual Clustering with FCA

• Mining Association Rules with FCA

• Other Applications of FCA

Page 9: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 9© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Our task:Find a basis of rules, i.e., a minimal set of rules out of which all other rules can be derived.

Two-Step Approach:

1. Compute all frequent closeditemsets.

2. For each frequent closed itemset Xand all its closed subsets Y:

check X → Y.

Association Rules and Formal Concept Analysis

Based on Formal Concept Analysis (FCA).

This relationship was discoveredindependently in 1998/9 at

• Clermont-Ferrand (Lakhal)

• Darmstadt (Stumme)

• New York (Zaki)

with Clermont being the fastest groupdeveloping algorithms (Close).

Structureof the Talk:

• Introduction to FCA

• Conceptual Clustering with FCA

• Mining Association Rules with FCA

• Other Applications of FCA

This is joint work withL. Lakhal, Y. Bastide, N. Pasquier, R. Taouil.

Page 10: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 10© Gerd Stumme 2002 Invited Talk at DEXA ‘2

1. Motivation: Structuring theFrequent Itemset Space

2. Formal Concept Analysis

3. Conceptual Clusteringwith Iceberg Concept Lattices

4. FCA-Based Miningof Association Rules

5. Other Application(s) of FCA

Page 11: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 11© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Formal Concept Analysis

arose around 1980 in Darmstadt as a mathematical theory, which formalizes theconcept of ‚concept‘.

Since then, FCA has found many uses in Informatics, e.g. for

• Data Analysis,

• Information Retrieval,

• Knowledge Discovery,

• Software Engineering.

Based on datasets, FCA derives concepthierarchies.

FCA allows to generate and visualizeconcept hierarchies.

Page 12: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 12© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Some typical applications:

• database marketing

• email management system

• developing qualitative theories in music estethics

• analysis of flight movements at Frankfurt airport

FCA models concepts as units of thought, consisting of two parts:

• The extension consists of all objects belonging to the concept.

• The intension consists of all attributes common to all those objects.

Page 13: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 13© Gerd Stumme 2002 Invited Talk at DEXA ‘2

National Parks in California

Formal ConceptAnalysis

Def.: A formal contextis a triple (G,M,I), where

• G is a set of objects,

• M is a set of attributes

• and I is a relationbetween G and M.

• (g,m)∈I is read as „object g has attribute m“.

Page 14: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 14© Gerd Stumme 2002 Invited Talk at DEXA ‘2

National Parks in California

For A ⊆ G, we define

A´:= { m∈M | ∀g∈A: (g,m)∈I }.

For B ⊆ M, we define dually

B´:= { g∈G | ∀m∈B: (g,m)∈I }.

A

Page 15: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 15© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Intent B

National Parks in California

Ext

ent A

Def.: A formal concept

is a pair (A,B) where

• A is a set of objects(the extent of the concept),

• B is a set of attributes(the intent of the concept),

• A‘ = B and B‘ = A.

= closed itemset

Page 16: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 16© Gerd Stumme 2002 Invited Talk at DEXA ‘2

National Parks in California

The blue concept isa subconcept of the yellow one, since its extent iscontained in theyellow one.

( ⇔ the yellow intentis contained in theblue one.)

Page 17: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 17© Gerd Stumme 2002 Invited Talk at DEXA ‘2

National Parks in California

The concept lattice of the National Parks in California

Page 18: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 18© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Def.: An implicationX → Y holds in a context, ifevery object having all attributes in X also has all attributes in Y.

(= Association rule with 100% confidence)

• Examples:

{ Swimming } → { Hiking }

Implications

{ Boating } → { Swimming, Hiking, NPS Guided Tours, Fishing }

{ Bicycle Trail, NPS Guided Tours } → { Swimming, Hiking }

Page 19: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 19© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Attributes areindependent if theyspan a hyper-cube(i.e., if all 2n combi-nations occur).

Example:

• Fishing• Bicycle Trail• Swimming

are independent attributes.

Independency

Page 20: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 20© Gerd Stumme 2002 Invited Talk at DEXA ‘2

1. Motivation: Structuring theFrequent Itemset Space

2. Formal Concept Analysis

3. Conceptual Clusteringwith Iceberg Concept Lattices

4. FCA-Based Miningof Association Rules

5. Other Application(s) of FCA

Page 21: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 21© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Iceberg Concept Lattices

For minsupp = 85% the seven most generalof the 32.086 concepts of the Mushroomsdatabase http:\\kdd.ics.uci.edu are shown.

minsupp = 85%

Page 22: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 22© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Iceberg Concept Lattices

minsupp = 85%

minsupp = 70%

Page 23: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 23© Gerd Stumme 2002 Invited Talk at DEXA ‘2

minsupp = 55%

With decreasingminimum support theinformation gets richer.

Page 24: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 24© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Iceberg Concept Lattices and Frequent Itemsets

Iceberg concept lattices are a condensed representation of frequent itemsets:

supp(X) = supp(X‘‘)

Difference between frequent concepts and frequent itemsets in the mushrooms database.

Page 25: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 25© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

computes the iceberg concept lattice using the support:

Page 26: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 26© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

tries to optimize the following three questions:

1. How can the closure of an itemset be determined based on supports only?

2. How can the closure system be computed with determining as few closures as possible?

3. How can as many supports as possible be derived from already known supports?

Page 27: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 27© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

Example: { b,c }‘‘ = { b, c, e }, since

supp( { b, c } ) = 1/3

and

supp( { a, b, c } ) = 0/3

supp( { b, c, e } ) = 1/3,

123

a b c e

1. How can the closure of an itemset be determined based on supports only?

X‘‘ = X ∪ { x∈ M \ X | supp(X) = supp(X ∪ x ) }

Page 28: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 28© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

1. How can the closure of an itemset be determined based on supports only?

X‘‘ = X ∪ { x∈ M \ X | supp(X) = supp(X ∪ x ) }

a

bc

e

1

2

3

Page 29: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 29© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

2. How can the closure system be computed with determiningas few closures as possible?

We determine only the closures of the minimal generators.

• If a set is not minimal generator, then none of its supersets is either.

→ Apriori like approach

In the example, TITANIC needs two runs (and Apriori four).

minimal generator

Page 30: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 30© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

1. How can the closure of an itemset be determined based on supports only?

X‘‘ = X ∪ x∈ M \ X | supp(X) = supp(X ∪ x )

2. How can the closure system be computed with determining as few closures as possible?

Approach à la Apriori

3. How can as many supports as possible be derived from already knownsupports?

Page 31: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 31© Gerd Stumme 2002 Invited Talk at DEXA ‘2

3. How can as many supports as possiblebe derived from already known supports?

Theorem: If X is no minimal generator, then

supp(X) = min { supp(K) | K is minimal generator, K ⊆ X } .

123

a b c e

Example: supp( { a, b, c } )

= min { supp({a, b }), supp({ b, c }), supp(a), supp(b), supp(c) }

= min { 0/3, 1/3, 1/3, 2/3, 2/3 } = 0,

Page 32: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 32© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

1. How can the closure of an itemset be determined based on supports only?

X‘‘ = X ∪ { x∈ M \ X | supp(X) = supp(X ∪ x ) }

2. How can the closure system be computed with determining as few closuresas possible?

Approach à la Apriori

3. How can as many supports as possible be derived from already knownsupports?

If X is no minimal generator, then

supp(X) = min { supp(K) | K is minimal generator, K ⊆ X } .

Page 33: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 33© Gerd Stumme 2002 Invited Talk at DEXA ‘2

TITANIC

We only generatecandidates forminimal generators.

If the support is toolow or equal to thesupport of a lowercover, thecandidate is pruned.

comparedwith Apriori

End

i ← 1i ← singletons

Determine support for all C ∈ i

Determine closures for all C ∈ i - 1

Prune non-minimal generators from i

i ← i + 1i ← Generate_Candidates( i - 1 )

i empty?

no

yes

Count only ifnecessary.

Page 34: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 34© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Pascal/Titanic compared with Apriori

Weakly correlated data:similar performance ofPascal, Apriori and Max-Miner

Strongly correlated data:Pascal (and Close) are very efficient

Page 35: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 35© Gerd Stumme 2002 Invited Talk at DEXA ‘2

1. Motivation: Structuring theFrequent Itemset Space

2. Formal Concept Analysis

3. Conceptual Clusteringwith Iceberg Concept Lattices

4. FCA-Based Miningof Association Rules

5. Other Application(s) of FCA

Page 36: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 36© Gerd Stumme 2002 Invited Talk at DEXA ‘2

→ more efficient computation (e.g. TITANIC)

→ fewer rules (without information loss!)

32 frequent itemsets arerepresented by 12 frequent concept intents

minsupp = 70%

Advantage of the use of iceberg concept lattices(compared to frequent itemsets)

Page 37: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 37© Gerd Stumme 2002 Invited Talk at DEXA ‘2

• From supp(B) = supp (B´´ ) follows:

Theorem: X → Y and X ´´ → Y ´´ have the same support and the sameconfidence.

Hence for computing association rules, it is sufficient to compute the supports of all frequent sets with B = B´´ (i.e., the intents of the iceberg concept lattice).

Association rules can be visualizedin the iceberg concept lattice:

• exact rules

• approximate rules

conf = 100 %

conf < 100 %

Page 38: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 38© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Association rules can be visualizedin the iceberg concept lattice:

• exact rules

• approximate rules

conf = 100 %

conf < 100 %

Exact association rules

Page 39: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 39© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Exact association rules

supp = 89.92 %

{ring number: one, veil color: white} → {gill attachment: free}

supp = 89.92 % conf = 100 %.

Page 40: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 40© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Association rules can be visualizedin the iceberg concept lattice:

• exact rules

• approximate rules

conf = 100 %

conf < 100 %

Luxenburger Basis for approximate association rules

Page 41: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 41© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Luxenburger Basis for approximate association rules

supp = 89.92 %

{ring number: one} → {veil color: white}

supp = 89.92 % conf = 97.5 % × 99.9 % ≈ 97.4 %.

Page 42: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 42© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Some experimental results

Page 43: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 43© Gerd Stumme 2002 Invited Talk at DEXA ‘2

1. Motivation: Structuring theFrequent Itemset Space

2. Formal Concept Analysis

3. Conceptual Clusteringwith Iceberg Concept Lattices

4. FCA-Based Miningof Association Rules

5. Other Application(s) of FCA

Page 44: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Conceptual Email Manager

Page 45: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 45© Gerd Stumme 2002 Invited Talk at DEXA ‘2

The End

1. Motivation: Structuring theFrequent Itemset Space

2. Formal Concept Analysis

3. Conceptual Clusteringwith Iceberg Concept Lattices

4. FCA-Based Miningof Association Rules

5. Other Application(s) of FCA

Page 46: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 46© Gerd Stumme 2002 Invited Talk at DEXA ‘2

IT-Security Management

8 Supports the analysis of security risks in IT units8 status quo test for establishing guidelines and checklists

Page 47: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 47© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Database Marketing at Jelmoli AG, Zürich

8 Analysis of the user behavior of customers using the Shopping Bonus Card

8 Supporting of Cross-Selling via Direct Mailing

Page 48: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

Slide 48© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Analysis of flight movements at Frankfurt Airport

8Allowing for ad-hoc queries in the database

8 Visualization of dependencies

Page 49: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Conceptual Email Manager

In CEM an email can beassigned to several „folders“.

Page 50: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Conceptual Email Manager

This allows for multiple searchpaths:

• Darmstadt/KVO/KVO_Members

• KVO/Darmstadt/KVO_Members

• KVO/KVO_Members/Darmstadt

Conceptual Email Manager

Page 51: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Mails from subfolders can als befound in the more generalfolders.

Conceptual Email Manager

This allows for multiple searchpaths:

• Darmstadt/KVO/KVO_Members

• KVO/Darmstadt/KVO_Members

• KVO/KVO_Members/Darmstadt

Page 52: Formal Concept Analysis - Universität Kassel · PDF fileFormal Concept Analysis Institute for Applied Informatics (AIFB) University of Karlsruhe, Germany ... In the example, TITANIC

© Gerd Stumme 2002 Invited Talk at DEXA ‘2

Conceptual Email Manager

Nested line diagrams allow thecombination of views.