(1) abstract and contents new model selection criteria called matchability which is based on...

(1) Abstract and Contents

New model selection criteria called Matchability which is based on maximizing matching opportunity is proposed. Given data set is decomposed into set of reusable partial situations for powerful prediction. This technology is effective

for pre-processing of data analysis and pattern recognition.

Contents:

1. Matchable principle for Prediction (2)-(5)

2. Formalization and Matchability (6)-(9)

3. Search algorithm (10)-(13)

4. Simulation and Results (14)-(15)

(2) Models for Prediction

(1)Memory based reasoning• Weak prediction ability

• No model

(2)Model based reasoning• Powerful prediction ability

• Needs Model Selection Criteria

Our approach Prediction based on informational Scrap&Build. Set of Small Situation is one kind of Models.

(3) Origin of Model Selection Criteria

It is the preconception that model is selected from the hypothesis space which can explain data.

Three Origin

･ Simplicity of Model

･ Consistency for Data: Accuracy, Minimize Error

･ Coverage for Data: Increasing covering case/feature

Ockham’s razor → MDL ､ AIC“Simplest model is selected with increasing Consistency for Data”

Matchable principal (maximizing Matching Opportunity)

“Simplest model is selected with increasing Coverage for Data”

(4) Criteria based on Trade-off of factors

Simplicityof Model

Ockham’s razor

Consistencyfor Data

Coveragefor Data

Matchable principal

Feature general criteria should include these three factors

Case-increasingFeature-increasing Accuracy

Minimize error

(5)

“Simplest model is selected with increasing Coverage for Data”

Deriving Matchable Principal

Matchable principal

Maximizing Matching Opportunity

Powerful predictable ModelEmpirical based processing

based on Matching

Model which has large matching opportunity can predict powerfully

(6) Situation Decomposition

Extracting partial situations which are combination of selected Feature and Case from spread sheet.

MS1

MS2

MS3 MS4

Matchability=This criteria evaluates Matching Opportunity

Matchable Situation = Local maximums of Matchability

(7) Whole situation and Partial situations

Whole situation J=(D, N) : Contains N features and D cases.

Feature selection vector: d = (d １ , d ２ ,…,dD)

Case selection vector : n = (n1, n2,…,nN)

Vector element di,ni are binary indicator of

selection/unselection.

Number of selected features: d

Number of selected cases : n

Selecting all features: D

Selecting all cases: N

Situation decomposition extracts some matchable situations from whole situation J=(D, N) which potentially contains 2D+N partial situation.

(8) Case selection using Segment space

Segment space is multiplication of separation of each selected features.

n ： Number of selected cases

→ Make Larger

Sd ： Number of total segments

→ Make Larger

rd ： Number of selected

segments

→ Make Smaller

※ Cases inside the chosen segments are surely chosen.

Sd =s1 s2

(9)

dd SC

rC

NCNSrnM logloglog),,,( 321 dd

Matchability on Spread sheet form

Three factors enlarge a matching opportunity.[Case-increasing in situation]

n →Make Larger

[Feature-increasing in situation]

Sd →Make Larger

[Simplicity of situation]

rd →Make Smaller

nn

Sd

rd

rdN: Total number of cases, C1, C ２ , C ３ : Positive

constant

(10) Algorithm Overview

for each subset of d of D Search Local maximums

(procedure 2) Reject saddle point (procedure 3) end

Time complexity 2∝

D

(11) Segment selecting space without no-case

① We don’t take care of the segment which contains no case from Matchability nature.

Size of this searching space

= 2Rd

rd

where Rd is number ofsegment that contains

one or more cases.

①

②

(12) Searching on Sorted segments

② Many case containing segment are selected prior to the less containing segment from Matchability nature.

Only one set of segment could be local maximum for one

number of selecting segments rd

Sorting segment and search local maximums.

rd

(13) Reject Saddle point

Local maximums for feature selecting vector d is tested by changing selecting features.

If superior to every that is not saddle point.

Then is local

maximum

→ Matchable situation

(14) Simulation and Result

Input situation 11×11 cases are arranged to notches at a

regular interval of 0.1 on a plane• Situation A: plane x + z = 1• Situation B: plane y +z = 1

Extracted situation Input Situations

• MS １＝ Input Situation A• MS ２＝ Input Situation B

A New Situation

• MS ３ :

line x = y, x + z = 1

(15) Powerful prediction using Matchable situations

Multi-valued function φ:(x,y)→z

1. Generalization ability• Even if the input situation A (x+z=1) lacks half of its parts, such that

no data exists in the range y>0.5, our method outputs φMS1(0,1)=1.0.

2. The output of every situation• Output is generated depending on situations.

Output could be average value (φ(0,1)=0.5 ), without decomposed situation.

(16) Conclusions & Future work

Matchability is new model selection criterion maximizing matching opportunity, which emphasize Coverage for data. In opposition ockham’s razor emphasize the Consistency for data. Decomposed situations by matchability criterion has powerful prediction ability. Situation decomposition method can be applied to pre-processing of data analysis, self-organization, pattern recognition and so on.

Future work Needs theoretical studies on Matchabilty criterion.

• This criteria is delivered intuitively.

Needs speed up for large-scale problem.• Exponential time complexity for number of future is awful.

Combing this method to other data analyses method• This method could be the pre-processing for neural network, liner

regression etc....