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ShiftTree: model based time series classifier (ECML/PKDD 2011 presentation)

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This slideshow is about the time series classifier algorithm, ShiftTree.
ShiftTree is a unique, model-based approach for time series classification. The basic idea is that we assign a cursor (or eye) to each series and move this to certain positions on the time axis. We generate dynamic attributes by answering two questions: (1) Where to look? (2) What to look at?. The answer to the first question tells us where to move the cursor (e.g.: forward 100 steps, to the previous local maxima, etc), while the second answer defines the calculation of the dynamic attributes (e.g.: value at that point, the weighted avarage of the values around the position, the difference in the current and previous cursor position, etc). These dynamic attributes then used in a binary decision tree.
This slideshow was originally presented at ECML/PKDD 2011 in Athens.
Note that for whatever reasons SlideShare doesn't support animations. Therefore the animated slides were split into multiple slides.

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ShiftTree: model based time series classifier (ECML/PKDD 2011 presentation)

  1. 1. SHIFTTREE:AN INTERPRETABLE MODEL-BASED APPROACH FOR TIME SERIES CLASSIFICATION Balázs Hidasi - hidasi@tmit.bme.hu Csaba Gáspár-Papanek - gaspar@tmit.bme.hu Budapest University of Technology and Economics, Hungary ECML/PKDD, 6TH SEPTEMBER 2011, ATHENS
  2. 2. OUTLINE General concept Task & adaptation Labeling & learning Evaluation Forest methods Conclusion 2/17
  3. 3. GENERAL CONCEPT Not limited to time series  Time series  Semi-structured data  Graphs Two questions:  „Where to look at?”  „What to observe?” Operator families  EyeShifter Operator(s) (ESO) F(x)  ConditionBuilder Operators (CBO) Dynamic attributes Model: sequence of simple operatos / rules 3/17
  4. 4. TIME SERIES CLASSIFICATION Time series Learning Model  With one observed variable  Evenly sampled  The algorithm has no such limitations Standard classification task  Focusing on accuracy Model Labeling Goals  Satisfying accuracy  Model-based instead of memory-based 4/17  Interpretable models
  5. 5. EXPLAINING THE GOALS Why model-based?  Labeling is much faster   Can learn more general properties of the classes   Needs more training samples  What is interpretability good for?  Getting user trust   Helping in understanding the data  5/17
  6. 6. CONCEPT APPLIED TO TIME SERIES Dynamic attributes of time series  EyeShifter Operator (ESO): „Where to look at?”  Moves a cursor along the time axis  To a specified point of the series  E.g.: „To the next local minimum”, „100 steps ahead”, etc.  Note: result of operator sequence depens on the order  ConditionBuilder Operator (CBO): „What to observe?” F(x)  Computes the dynamic attribute  E.g.: „Value at the given time”, „Length of the jump”, etc. Decision tree as model Weighted average  Works well with the dynamic attribute concept 6/17  Operator sequence from root to leaf
  7. 7. LABELING Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  8. 8. LABELING Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  9. 9. LABELING Dynamic attribute value: 0,836848 Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  10. 10. LABELING Dynamic attribute value: 0,836848 Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  11. 11. LABELING Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  12. 12. LABELING Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  13. 13. LABELING Dynamic attribute value: 0,767139 Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  14. 14. LABELING Dynamic attribute value: 0,767139 Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  15. 15. LABELING Level 0 ESO: To global max CBO: Value at time Threshold: 1,20775 Level 1 Level 1 ESO: Step forward 100 ESO: To next local max CBO: Value at time CBO: Value at time Threshold : 0,390093 Threshold : -0,700739 Level 2 Level 2 Level 2 Level 2 7/17 Leaf Leaf Leaf Leaf
  16. 16. LEARNING (1/3) Operator pool definition: ESOs, CBOs Root node Cursor starts at the beginning  May be overridden 8/17
  17. 17. F(x)LEARNING (2/3) Available dynamic attributes (CBO pool)  At/around reachable positions Selecting a…  Attribute  Threshold value Minimize weighted child node entropy 9/17
  18. 18. LEARNING (3/3) Best split selected Cursor is moved by ESO  Reachable positions will change  Train set split  Child nodes continue the learning process  Stop: homogenous nodes 10/17
  19. 19. INTERPRETABILITY Depends on the operators Helps undepstanding the data E.g.: CBF dataset  Z-normalized, 3 class: Cylinder, Bell, Funnel  Distinguish cylinder from bell and funnel by global maxima  The data is z-normalized (standardized)  Distinguish bell from funnel by stepping back 25 steps + noise 11/17 filtering through weighted average  On which side is the peak
  20. 20. PERFORMANCE OF THE ALGORITHM Databases  UCR: mostly smaller data sets (20)  Ford: larger data sets (2) No optimizations in the experiments Performance  Better on larger data sets (model-based) 100.00% 94.97% 96.52% 92.94% 90.00% 81.29% 83.19% 80.00% 74.67% 73.33% 69.11% 70.00% 64.93% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 12/17 0.00% Smaller UCR sets (15) Larger UCR sets (5) Ford (largest) sets (2) 1NN Eucledian 1NN DTW ShiftTree
  21. 21. ADVANTAGES AND DRAWBACKS Advantages  Advantages of being model based (fast labeling, etc)  Interpretable (depens on operators)  Can be used independently of application domain  Expert’s knowledge can be built in through operators Disadvantages  Optimization of the operators is not trivial  Learning may take a long time when too many operators used  Disadvantages of the model based methods (larger training set required, etc) 13/17
  22. 22. SHIFTFOREST: COMBINING MULTIPLE MODELS Combining models enhances accuracy Boosting  Some issues on smaller datasets The „XV” method  Splitting training set (random splits)  Building model on the first part, evaluating on the second  Model weight: the measured accuracy 14/17
  23. 23. SHIFTFOREST RESULTS Accuracy increases Interpretability is often lost  May the intersection of the trees can be interpreted 100.00% 96.52%97.77% 92.94%94.97% 88.87% 90.00% 85.93% 81.29% 83.19% 80.00% 74.67% 73.33% 69.11% 70.00% 64.93% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Smaller UCR sets (15) Larger UCR sets (5) Ford (largest) sets (2) 15/17 1NN Eucledian 1NN DTW ShiftTree ShiftForest
  24. 24. CONCLUSION Novel model-based algorithm Uses cursors and operators  Cursor movement  Attribute computation Sequence of simple operators as the model  Decision tree Base of a whole algorithm family 16/17
  25. 25. THANK YOU FOR YOUR ATTENTION! Balázs Hidasi Csaba Gáspár-Papanek (hidasi@tmit.bme.hu) (gaspar@tmit.bme.hu) 17/17 For more ShiftTree related research visit my side: http://www.hidasi.eu
  26. 26. TIME OF MODEL BUILDING, SCALABILITY O(N*log(N)) per node (ordering) Time of model building  Depends on tree structure 200  Acceptable 180 160 140 Scales linearly 120 Time (s)  Experiments 100 80 60 40 20 0 Size of training set Min of 20 Max of 20 Mean of 20
  27. 27. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 27
  28. 28. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 28
  29. 29. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 29
  30. 30. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 30
  31. 31. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 31
  32. 32. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 32
  33. 33. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,332858 -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,985078 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 33
  34. 34. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 34
  35. 35. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 35
  36. 36. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 -1,16155 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,983634 0,600131 1,32624 Inf 0 Best score in the node (so far): 0,985078 0,983634 0,805777 Inf 0 Best ordering: 36
  37. 37. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,332858 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,983634 0,600131 Inf 0 Best score in the node (so far): 0,983634 0,805777 Inf 0 Best ordering: 37
  38. 38. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 ESOMax - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 1,02775 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,983634 0,600131 Inf 0 Best score in the node (so far): 0,983634 0,805777 Inf 0 Best ordering: 38
  39. 39. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 1,02775 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,983634 0,600131 Inf 0 Best score in the node (so far): 0,983634 0,805777 Inf 0 Best ordering: 39
  40. 40. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 40
  41. 41. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 41
  42. 42. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 42
  43. 43. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: CBOSimple - Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 43
  44. 44. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 44
  45. 45. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 45
  46. 46. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,739969 -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,805777 0,600131 Inf 0 Best score in the node (so far): 0,805777 Inf 0 Best ordering: 46
  47. 47. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,739969 -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,600131 Inf 0 Best score in the node (so far): Inf 0 Best ordering: 47
  48. 48. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax ESONext100 - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 0,390093 - Best threshold by current dynamic attribute: -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,600131 Inf 0 Best score in the node (so far): Inf 0 Best ordering: 48
  49. 49. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 - Best threshold by current dynamic attribute: -0,700739 0,390093 0,369887 0,77183 2,48622 - Score of the best split by current dyn. attribute : 0,600131 Inf 0 Best score in the node (so far): Inf 0 Best ordering: 49
  50. 50. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 - Best threshold by current dynamic attribute: -0,700739 0,369887 2,48622 - Score of the best split by current dyn. attribute : Inf 0 Best score in the node (so far): Inf 0 Best ordering: 50
  51. 51. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 - Best threshold by current dynamic attribute: -0,700739 0,369887 2,48622 - Score of the best split by current dyn. attribute : Inf 0 Best score in the node (so far): Inf 0 Best ordering: 51
  52. 52. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 - Best threshold by current dynamic attribute: -0,700739 0,369887 2,48622 - Score of the best split by current dyn. attribute : Inf 0 Best score in the node (so far): Inf 0 Best ordering: 52
  53. 53. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 - Best threshold by current dynamic attribute: -0,700739 0,369887 2,48622 Score of the best split by current dyn. attribute : 0 Best score in the node (so far): 0 Best ordering: 53
  54. 54. LEARNING THE MODEL Defined operators EyeShifter – Cursor position ESONextMax ESONextMax To the next local maximaESO ESONext100 ESONext100 Step forward 100 ESOMax ESOMax To the global maximaCBO CBSimple CBOSimple Value at cursor position ShiftTree F(x) ConditionBuilder - Ordering Best split in node (so far) ESO: ESONextMax - CBO: - CBOSimple Dynamic attribute selection M Threshold: -0,700739 - Best threshold by current dynamic attribute: -0,700739 0,369887 2,48622 Score of the best split by current dyn. attribute : 0 Best score in the node (so far): 0 Best ordering: 54

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