Redescription Mining Pauli Miettinen 17 November 2010 An Example - - PowerPoint PPT Presentation

Redescription Mining

Pauli Miettinen 17 November 2010

An Example

Pauli Miettinen 17 Nov 2010

VLDB ∧ ICDM ∧ SDM ∧ SIGMOD ⇔ (J. Han ∧ P .S. Yu)∨ C.-R. Lin ∨ S. Lonardi

Authors Conferences Co-Authors VLDB ∧ ICDM ∧ SDM ∧ SIGMOD ⇔ (J. Han ∧ P .S. Yu)∨ C.-R. Lin ∨ S. Lonardi

Pauli Miettinen 17 Nov 2010

Authors Conferences Co-Authors VLDB ∧ ICDM ∧ SDM ∧ SIGMOD ⇔ (J. Han ∧ P .S. Yu)∨ C.-R. Lin ∨ S. Lonardi

Pauli Miettinen 17 Nov 2010

Dimitrios Gunopulos Charu C. Aggarwal Philip S. Yu Eamonn J. Keogh ...

Definitions

Pauli Miettinen 17 Nov 2010

The Definitions

• Redescription. Given two data sets with a bijection

between the rows, a redescription is a pair of queries (Q1,Q2)

• ver the columns such that (Q1,Q2) satisfies certain

constraints and supp(Q1)≈supp(Q2).

Pauli Miettinen 17 Nov 2010

Redescription mining. Given the data sets as above, find the (k) best redescriptions.

More Concrete Definition

• Data sets: Boolean
• Queries: Arbitrary Boolean formulae
• Similarity function: Jaccard

|supp(Q1)∩supp(Q2)|/|supp(Q1)∪supp(Q2)|

• Constraints: Minimum support σmin,

maximum support σmax, minimum similarity Jmin, maximum size of formula k, maximum p-value pmax (more on this later)

Pauli Miettinen 17 Nov 2010

Special Cases

• Only conjunctive queries
• ”bi-directional” association rule mining

Q1 ⇒ Q2 and Q2 ⇒ Q1

• One query given
• classification task

Pauli Miettinen 17 Nov 2010

p-values

• On-line: assuming independency, what is the

probability of the observed support intersection size given support sizes?

• Binomial distribution
• Off-line: what is the (empirical) probability of

finding as good redescriptions with given column and row margins

• swap randomization

Pauli Miettinen 17 Nov 2010

Algorithms

Pauli Miettinen 17 Nov 2010

Some Algorithms

• CARTwheels [Ramakrishnan et al. 2004,

Kumar 2007]

• Greedy [Gallo, M. & Mannila 2008]
• Both are for Boolean data
• Neither finds arbitrary Boolean formulae

Pauli Miettinen 17 Nov 2010

Generalizations

Pauli Miettinen 17 Nov 2010

Non-Boolean Data

• Queries of type

x1∈ [-0.2, 1.3] ∨ x2 ∈ (-∞, 20]

• ”Standard” way: binarize data via bucketing
• Allows using existing algorithms
• Has many problems
• Bucketing can be done on the fly [Galbrun &

M., submitted]

Pauli Miettinen 17 Nov 2010

Example: Bioclimatic Niche Finding

• Data: (1) Presence/absence data for

mammals in Europe; (2) climatic data (temperature and rainfall)

• Question: Find a description over

climatic variables that describes the area inhabited by (a group of) mammals (and vice versa)

Pauli Miettinen 17 Nov 2010

Bioclimatic Niche Finding: Background

• A.k.a. bioclimatic envelope finding
• Has been done for a long time by biologists
• Only single, hand-selected species
• Methods used include regression, neural

networks, and genetic algorithms

• Niche: realized niche in Grinnellian sense

Pauli Miettinen 17 Nov 2010

Niche Finding: Our Contributions

• Automate niche finding
• Easy-to-understand method (contra

genetic algorithms and neural networks)

• Allow for more complex sets of species
• Can be generalized from species to traits
• Traits are more stable on

palaeontological scale

Pauli Miettinen 17 Nov 2010

Niche Finding: Example Results

European Elk ⇔ ([−9.80 ≤ tmax(Feb) ≤ 0.40] ∧ [12.20 ≤ tmax(Jul) ≤ 24.60] ∧[56.852 ≤ pavg(Aug) ≤ 136.46])∨[183.27 ≤ pavg(Sep)≤ 238.78] Jaccard = 0.814; support = 582 Wood Mouse ∧ Natterer’s Bat ∧ Eurasian Pygmy Shrew ⇔ ([3.20 ≤ tmax(Mar) ≤ 14.50] ∧ [17.30 ≤ tmax(Aug) ≤ 25.20] ∧ [14.90 ≤ tmax(Sep) ≤ 22.80]) ∨ [19.60 ≤ tavg(Jul) ≤ 19.956] Jaccard = 0.623; support = 681

Pauli Miettinen 17 Nov 2010

European Elk ⇔ ([−9.80 ≤ tmax(Feb) ≤ 0.40] ∧ [12.20 ≤ tmax(Jul) ≤ 24.60] ∧[56.852 ≤ pavg(Aug) ≤ 136.46])∨[183.27 ≤ pavg(Sep)≤ 238.78]

Pauli Miettinen 17 Nov 2010

Niche Finding: Example Results

European Elk ⇔ ([−9.80 ≤ tmax(Feb) ≤ 0.40] ∧ [12.20 ≤ tmax(Jul) ≤ 24.60] ∧[56.852 ≤ pavg(Aug) ≤ 136.46])∨[183.27 ≤ pavg(Sep)≤ 238.78] Jaccard = 0.814; support = 582 Wood Mouse ∧ Natterer’s Bat ∧ Eurasian Pygmy Shrew ⇔ ([3.20 ≤ tmax(Mar) ≤ 14.50] ∧ [17.30 ≤ tmax(Aug) ≤ 25.20] ∧ [14.90 ≤ tmax(Sep) ≤ 22.80]) ∨ [19.60 ≤ tavg(Jul) ≤ 19.956] Jaccard = 0.623; support = 681

Pauli Miettinen 17 Nov 2010

Wood Mouse ∧ Natterer’s Bat ∧ Eurasian Pygmy Shrew ⇔ ([3.20 ≤ tmax(Mar) ≤ 14.50] ∧ [17.30 ≤ tmax(Aug) ≤ 25.20] ∧ [14.90 ≤ tmax(Sep) ≤ 22.80]) ∨ [19.60 ≤ tavg(Jul) ≤ 19.956]

Pauli Miettinen 17 Nov 2010

Discussion

Pauli Miettinen 17 Nov 2010

Pattern Mining or Subgroup Discovery?

Pauli Miettinen 17 Nov 2010

PM Binary data Unsupervised Frequency Exhaustive Reconstructive SD Numerical data Supervised Interestingness Heuristic Descriptive

Pattern Mining or Subgroup Discovery?

Pauli Miettinen 17 Nov 2010

PM Binary data Unsupervised Frequency Exhaustive Reconstructive SD Numerical data Supervised Interestingness Heuristic Descriptive

Conclusions

• Redescription mining is a promising

research direction

• (SD ∩ PM) ∩ RDM ≠ ∅
• Still a new direction
• There are nails for this hammer

CARTwheels

• Grows two classification and regression trees

(CARTs)

• Fix one tree and grow other to match; alternate
• Leaves are matched and paths are the

descriptions:

(ICDM ) ∨ (¬ICDM ∧¬STOC) ⇔ (C. Olston ∧¬C. Chekuri ) ∨ (¬C. Olston ∧ ¬A. Wigderson)

Pauli Miettinen 17 Nov 2010

(ICDM ) ∨ (¬ICDM ∧¬STOC) ⇔ (C. Olston ∧¬C. Chekuri ) ∨ (¬C. Olston ∧ ¬A. Wigderson)

ICDM STOC

Yes No No

• C. Olston
• C. Chekuri
• A. Wigderson

Yes No No No

Greedy

• Grows formulae in a greedy fashion using

beam search

• Prunes search space as if monotonicity

would hold

• If adding a variable does not help now, it

will not help later, either

• False in general

Pauli Miettinen 17 Nov 2010