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Handling Numeric Attributes in Hoeffding Trees

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Handling Numeric Attributes in Hoeffding Trees Bernhard Pfahringer, Geoff Holmes and Richard Kirkby
Overview ,[object Object],[object Object],[object Object],[object Object]
Data Streams - reminder ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Main assumptions/limitations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Hoeffding Trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Active leaf data structure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Numeric Handling Methods ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Numeric Handling Methods ,[object Object],[object Object],[object Object],[object Object],[object Object]
Handling Numeric Methods ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Gaussian approximation – 2 class problem
Gaussian approximation – 3 class problem
Gaussian approximation – 4 class problem
Empirical Evaluation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Data generators ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Tree Measurements ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sensor Network (100K memory limit) Pred Spd % Train Spd % AvgTree Depth Total Nodes Inactive (hdrds) Active Leaves Train (million) % correct Method 79 64 20 11.7 8.08 0.01 16 85.33 GAUSS100 81 68 12 12.1 8.87 0 20 86.16 GAUSS10 88 60 3 0.13 0.08 0 1 74.65 GK1000 84 71 8 5.03 4.03 0 12 82.92 GK100 89 75 3 0.11 0.07 0 1 74.45 BT 88 81 3 0.14 0.09 0 1 76.06 VF1000 85 76 7 4.5 3.65 0 13 79.47 VF100 82 70 11 10.6 8.13 0 21 87.7 VF10
Handheld Environment (32MB memory limit) Pred Spd % Train Spd % AvgTree Depth Total Nodes Inactive (hdrds) Active Leaves Train (million) % correct Method 69 14 50 1167 639 92.6 853 90.91 GAUSS100 69 15 24 1166 683 93.7 874 91.35 GAUSS10 75 16 27 581 403 2.66 937 90.94 GK1000 73 17 34 777 530 6.89 961 89.96 GK100 73 15 22 540 373 3.68 808 90.48 BT 73 17 27 604 412 4.22 951 90.97 VF1000 73 17 24 704 481 5.99 973 90.97 VF100 72 16 22 1009 675 31.8 909 91.53 VF10
Server Environment (400MB memory limit) 74 4 24 591 80.4 320 293 91.41 VF10 Pred Spd % Train Spd % AvgTree Depth Total Nodes Inactive (hdrds) Active Leaves Train (million) % correct Method 66 6 63 998 38.7 566 538 90.75 GAUSS100 73 6 28 891 26.8 540 518 91.21 GAUSS10 80 3 21 197 122 17.6 91 91.03 GK1000 75 4 32 346 145 84 158 89.88 GK100 81 2 19 147 92.9 13.7 60 90.50 BT 79 3 22 206 127 19 108 91.12 VF1000 75 4 23 316 143 73.9 142 91.19 VF100
Overall results - comments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Remarks – sensor network environment ,[object Object],[object Object]
Remarks – Handheld Environment ,[object Object]
Remarks – Server Environment
VFML10 vs GAUSS10 – Closer Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Data order
Conclusion ,[object Object],[object Object],[object Object],[object Object]
All algorithms available ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Handling Numeric Attributes in Hoeffding Trees

  • 1. Handling Numeric Attributes in Hoeffding Trees Bernhard Pfahringer, Geoff Holmes and Richard Kirkby
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  • 10. Gaussian approximation – 2 class problem
  • 11. Gaussian approximation – 3 class problem
  • 12. Gaussian approximation – 4 class problem
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  • 16. Sensor Network (100K memory limit) Pred Spd % Train Spd % AvgTree Depth Total Nodes Inactive (hdrds) Active Leaves Train (million) % correct Method 79 64 20 11.7 8.08 0.01 16 85.33 GAUSS100 81 68 12 12.1 8.87 0 20 86.16 GAUSS10 88 60 3 0.13 0.08 0 1 74.65 GK1000 84 71 8 5.03 4.03 0 12 82.92 GK100 89 75 3 0.11 0.07 0 1 74.45 BT 88 81 3 0.14 0.09 0 1 76.06 VF1000 85 76 7 4.5 3.65 0 13 79.47 VF100 82 70 11 10.6 8.13 0 21 87.7 VF10
  • 17. Handheld Environment (32MB memory limit) Pred Spd % Train Spd % AvgTree Depth Total Nodes Inactive (hdrds) Active Leaves Train (million) % correct Method 69 14 50 1167 639 92.6 853 90.91 GAUSS100 69 15 24 1166 683 93.7 874 91.35 GAUSS10 75 16 27 581 403 2.66 937 90.94 GK1000 73 17 34 777 530 6.89 961 89.96 GK100 73 15 22 540 373 3.68 808 90.48 BT 73 17 27 604 412 4.22 951 90.97 VF1000 73 17 24 704 481 5.99 973 90.97 VF100 72 16 22 1009 675 31.8 909 91.53 VF10
  • 18. Server Environment (400MB memory limit) 74 4 24 591 80.4 320 293 91.41 VF10 Pred Spd % Train Spd % AvgTree Depth Total Nodes Inactive (hdrds) Active Leaves Train (million) % correct Method 66 6 63 998 38.7 566 538 90.75 GAUSS100 73 6 28 891 26.8 540 518 91.21 GAUSS10 80 3 21 197 122 17.6 91 91.03 GK1000 75 4 32 346 145 84 158 89.88 GK100 81 2 19 147 92.9 13.7 60 90.50 BT 79 3 22 206 127 19 108 91.12 VF1000 75 4 23 316 143 73.9 142 91.19 VF100
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  • 22. Remarks – Server Environment
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