1. (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. (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. (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. (4) Criteria based on Trade-off of factors Simplicity of Model Ockham’s razor Consistency for Data Coverage for Data Matchable principal Feature general criteria should include these three factors Case-increasing Feature-increasing Accuracy Minimize error

5. (5) “ Simplest model is selected with increasing Coverage for Data ” Deriving Matchable Principal Matchable principal Maximizing Matching Opportunity Powerful predictable Model Empirical based processing based on Matching Model which has large matching opportunity can predict powerfully

6. (6) Situation Decomposition Extracting partial situations which are combination of selected Feature and Case from spread sheet. MS 1 MS 2 MS 3 MS 4 Matchability=This criteria evaluates Matching Opportunity Matchable Situation = Local maximums of Matchability

7. (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,…,d D ) Case selection vector : n = (n 1, n 2,…,n N ) Vector element d i,n i 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 2 D+N partial situation.

8. (8) Case selection using Segment space Segment space is multiplication of separation of each selected features. n ： Number of selected cases → Make Larger S d ： Number of total segments → Make Larger r d ： Number of selected segments → Make Smaller ※ Cases inside the chosen segments are surely chosen. Sd =s1 s2Sd =s1 s2

9. (9) Matchability on Spread sheet form Three factors enlarge a matching opportunity. [Case-increasing in situation] n →Make Larger [Feature-increasing in situation] S d →Make Larger [Simplicity of situation] r d →Make Smaller nn SdSd rdrd rdrd N: Total number of cases, C 1, C ２, C ３ : Positive constant

10. (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. (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 = 2 RdRd rdrd where R d is number of segment that contains one or more cases. ① ②

12. (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 r d Sorting segment and search local maximums. rdrd

13. (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. (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. (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 φ MS1 (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. (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....