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Knn Algorithm

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Kamal Gupta Roy

kNN Algorithm

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Kamal Gupta Roy Kamal Gupta Roy kNN Algorithm
Kamal Gupta Roy What would be the color of new circles? | 2 A B C D Circle Color A Red B Brown C Blue D ???
Kamal Gupta Roy | 3
Kamal Gupta Roy Kamal Gupta Roy Its all about how far and how close you are from others? | 4 A B C D Finding Nearest Neighbors, who they are?
Kamal Gupta Roy Kamal Gupta Roy Different Names for the same algorithm | 5 Memory based Reasoning Example based Reasoning Instance based Learning Lazy Learning K-nearest neighbor (KNN)
Kamal Gupta Roy Kamal Gupta Roy What is k in kNN? | 6 A Dotted Circle Decision k Purple Red 1 Green Red 3 Orange Blue 13
Kamal Gupta Roy Kamal Gupta Roy Choosing the value of k? | 7 Neighborhood may include points from other classes Sensitive to noise points k is too small k is too large
Kamal Gupta Roy Kamal Gupta Roy Optimal k | 8
Kamal Gupta Roy Distance | 9
Kamal Gupta Roy Kamal Gupta Roy Yellow path Red path Blue path Green path | 10 A B
Kamal Gupta Roy Kamal Gupta Roy Manhattan Distance | 11 • The distance between two points measured along axes at right angles. • In a plane with p1 at (x1, y1) and p2 at (x2, y2), it is |x1 - x2| + |y1 - y2|
Kamal Gupta Roy Kamal Gupta Roy Euclidean Distance
Kamal Gupta Roy Kamal Gupta Roy Manhattan vs Euclidien | 13
Kamal Gupta Roy Kamal Gupta Roy New Value = 46 | 14 Age Default distance square(distance) d 25 Y -21 441 21 35 Y -11 121 11 45 Y -1 1 1 20 Y -26 676 26 35 Y -11 121 11 52 Y 6 36 6 23 Y -23 529 23 40 N -6 36 6 60 N 14 196 14 48 N 2 4 2 33 N -13 169 13 27 N -19 361 19 37 N -9 81 9 Default = Yes
Kamal Gupta Roy Kamal Gupta Roy Exercise | 15 Age Loan Default 25 40,000 Y 35 60,000 Y 45 80,000 Y 20 20,000 Y 35 120,000 Y 52 38,000 Y 23 85,000 Y 40 62,000 N 60 98,000 N 48 100,000 N 33 110,000 N 27 130,000 N 37 90,000 N Predict default for a customer with age = 46 and applied loan for 128,000
Kamal Gupta Roy • Age = 46 • loan=128,000 | 16 • Default = No Age Loan Default age dist sq loan dist sq d 25 40,000 Y 441 7,744,000,000 88,000 35 60,000 Y 121 4,624,000,000 68,000 45 80,000 Y 1 2,304,000,000 48,000 20 20,000 Y 676 11,664,000,000 108,000 35 120,000 Y 121 64,000,000 8,000 52 38,000 Y 36 8,100,000,000 90,000 23 85,000 Y 529 1,849,000,000 43,000 40 62,000 N 36 4,356,000,000 66,000 60 98,000 N 196 900,000,000 30,000 48 100,000 N 4 784,000,000 28,000 33 110,000 N 169 324,000,000 18,000 27 130,000 N 361 4,000,000 2,000 37 90,000 N 81 1,444,000,000 38,000
Kamal Gupta Roy • Age = 46 • loan=128 K | 17 • Default = Yes Age Loan Default age dist sq loan dist sq d 25 40 Y 441 7,744 90 35 60 Y 121 4,624 69 45 80 Y 1 2,304 48 20 20 Y 676 11,664 111 35 120 Y 121 64 14 52 38 Y 36 8,100 90 23 85 Y 529 1,849 49 40 62 N 36 4,356 66 60 98 N 196 900 33 48 100 N 4 784 28 33 110 N 169 324 22 27 130 N 361 4 19 37 90 N 81 1,444 39
Kamal Gupta Roy Kamal Gupta Roy Feature Scaling | 18
Kamal Gupta Roy Why scaling? Scaling issues – Attributes may have to be scaled to prevent distance measures from being dominated by one of the attributes Example: height of a person may vary from 1.5m to 1.8m weight of a person may vary from 45 KG to 100KG income of a person may vary from Rs10K to Rs 5 lakh | 19
Kamal Gupta Roy Standardization Also called as Z-score normalization Mean is zero Standard deviation 1 | 20
Kamal Gupta Roy Max-Min Normalization Also called as Min-Max scaling normalization Minimum is zero Maximum is 1 | 21
Kamal Gupta Roy | 22 Raw Data Z Normalized Max-Min
Kamal Gupta Roy • Age = 46; norm age: 0.65 • loan=128,000; norm age: 0.98 | 23 • Default = No Age Loan Default norm age norm loan age dist sq loan dist sq d 25 40,000 Y 0.13 0.18 0.28 0.64 0.96 35 60,000 Y 0.38 0.36 0.08 0.38 0.68 45 80,000 Y 0.63 0.55 0.00 0.19 0.44 20 20,000 Y - - 0.42 0.96 1.18 35 120,000 Y 0.38 0.91 0.08 0.01 0.28 52 38,000 Y 0.80 0.16 0.02 0.67 0.83 23 85,000 Y 0.08 0.59 0.33 0.15 0.70 40 62,000 N 0.50 0.38 0.02 0.36 0.62 60 98,000 N 1.00 0.71 0.12 0.07 0.44 48 100,000 N 0.70 0.73 0.00 0.06 0.26 33 110,000 N 0.33 0.82 0.11 0.03 0.36 27 130,000 N 0.18 1.00 0.23 0.00 0.48 37 90,000 N 0.43 0.64 0.05 0.12 0.41
Kamal Gupta Roy | 24 Age Loan Default age dist sq loan dist sq d 25 40,000 Y 441 7,744,000,000 88,000 35 60,000 Y 121 4,624,000,000 68,000 45 80,000 Y 1 2,304,000,000 48,000 20 20,000 Y 676 11,664,000,000 108,000 35 120,000 Y 121 64,000,000 8,000 52 38,000 Y 36 8,100,000,000 90,000 23 85,000 Y 529 1,849,000,000 43,000 40 62,000 N 36 4,356,000,000 66,000 60 98,000 N 196 900,000,000 30,000 48 100,000 N 4 784,000,000 28,000 33 110,000 N 169 324,000,000 18,000 27 130,000 N 361 4,000,000 2,000 37 90,000 N 81 1,444,000,000 38,000 Age Loan Default age dist sq loan dist sq d 25 40 Y 441 7,744 90 35 60 Y 121 4,624 69 45 80 Y 1 2,304 48 20 20 Y 676 11,664 111 35 120 Y 121 64 14 52 38 Y 36 8,100 90 23 85 Y 529 1,849 49 40 62 N 36 4,356 66 60 98 N 196 900 33 48 100 N 4 784 28 33 110 N 169 324 22 27 130 N 361 4 19 37 90 N 81 1,444 39 Age Loan Default norm age norm loan age dist sq loan dist sq d 25 40,000 Y 0.13 0.18 0.28 0.64 0.96 35 60,000 Y 0.38 0.36 0.08 0.38 0.68 45 80,000 Y 0.63 0.55 0.00 0.19 0.44 20 20,000 Y - - 0.42 0.96 1.18 35 120,000 Y 0.38 0.91 0.08 0.01 0.28 52 38,000 Y 0.80 0.16 0.02 0.67 0.83 23 85,000 Y 0.08 0.59 0.33 0.15 0.70 40 62,000 N 0.50 0.38 0.02 0.36 0.62 60 98,000 N 1.00 0.71 0.12 0.07 0.44 48 100,000 N 0.70 0.73 0.00 0.06 0.26 33 110,000 N 0.33 0.82 0.11 0.03 0.36 27 130,000 N 0.18 1.00 0.23 0.00 0.48 37 90,000 N 0.43 0.64 0.05 0.12 0.41
Kamal Gupta Roy CONFUSION MATRIX | 25
Kamal Gupta Roy Kamal Gupta Roy Hiring Process Example | 26 Matrix Predicted Good Predicted Bad Actual Good Hired Good Candidate Rejected Good Candidate Actual Bad Hired Bad Candidate Rejected Bad Candidate TP TN FN FP Confusion Matrix
Kamal Gupta Roy Confusion Matrix Predicted Yes Predicted No Actual Yes TP FN Actual No FP TN | 27 Accuracy = (TP + TN)/ (TP + FN + FP + TN) Recall = TP / (TP + FN) Precision = TP / (TP + FP) Type 1 Error Type 2 Error
Kamal Gupta Roy Kamal Gupta Roy Precision vs Recall | 28
Kamal Gupta Roy Kamal Gupta Roy Pregnancy Test | 29 Predicted Pregnant Predicted Not Pregnant Actual Pregnant TP FN Actual Not Pregnant FP TN TN TP FP FN
Kamal Gupta Roy Sensitivity & Specificity Predicted Yes Predicted No Actual Yes TP FN Actual No FP TN | 30 True Negative Rate, Specificity = TN / (TN+FP) False Positive Rate = FP / (TN+FP) True Positive Rate, Sensitivity = TP / (TP + FN) False Negative Rate = FN / (TN+FP)

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Knn Algorithm

  • 1. Kamal Gupta Roy Kamal Gupta Roy kNN Algorithm
  • 2. Kamal Gupta Roy What would be the color of new circles? | 2 A B C D Circle Color A Red B Brown C Blue D ???
  • 4. Kamal Gupta Roy Kamal Gupta Roy Its all about how far and how close you are from others? | 4 A B C D Finding Nearest Neighbors, who they are?
  • 5. Kamal Gupta Roy Kamal Gupta Roy Different Names for the same algorithm | 5 Memory based Reasoning Example based Reasoning Instance based Learning Lazy Learning K-nearest neighbor (KNN)
  • 6. Kamal Gupta Roy Kamal Gupta Roy What is k in kNN? | 6 A Dotted Circle Decision k Purple Red 1 Green Red 3 Orange Blue 13
  • 7. Kamal Gupta Roy Kamal Gupta Roy Choosing the value of k? | 7 Neighborhood may include points from other classes Sensitive to noise points k is too small k is too large
  • 8. Kamal Gupta Roy Kamal Gupta Roy Optimal k | 8
  • 10. Kamal Gupta Roy Kamal Gupta Roy Yellow path Red path Blue path Green path | 10 A B
  • 11. Kamal Gupta Roy Kamal Gupta Roy Manhattan Distance | 11 • The distance between two points measured along axes at right angles. • In a plane with p1 at (x1, y1) and p2 at (x2, y2), it is |x1 - x2| + |y1 - y2|
  • 12. Kamal Gupta Roy Kamal Gupta Roy Euclidean Distance
  • 13. Kamal Gupta Roy Kamal Gupta Roy Manhattan vs Euclidien | 13
  • 14. Kamal Gupta Roy Kamal Gupta Roy New Value = 46 | 14 Age Default distance square(distance) d 25 Y -21 441 21 35 Y -11 121 11 45 Y -1 1 1 20 Y -26 676 26 35 Y -11 121 11 52 Y 6 36 6 23 Y -23 529 23 40 N -6 36 6 60 N 14 196 14 48 N 2 4 2 33 N -13 169 13 27 N -19 361 19 37 N -9 81 9 Default = Yes
  • 15. Kamal Gupta Roy Kamal Gupta Roy Exercise | 15 Age Loan Default 25 40,000 Y 35 60,000 Y 45 80,000 Y 20 20,000 Y 35 120,000 Y 52 38,000 Y 23 85,000 Y 40 62,000 N 60 98,000 N 48 100,000 N 33 110,000 N 27 130,000 N 37 90,000 N Predict default for a customer with age = 46 and applied loan for 128,000
  • 16. Kamal Gupta Roy • Age = 46 • loan=128,000 | 16 • Default = No Age Loan Default age dist sq loan dist sq d 25 40,000 Y 441 7,744,000,000 88,000 35 60,000 Y 121 4,624,000,000 68,000 45 80,000 Y 1 2,304,000,000 48,000 20 20,000 Y 676 11,664,000,000 108,000 35 120,000 Y 121 64,000,000 8,000 52 38,000 Y 36 8,100,000,000 90,000 23 85,000 Y 529 1,849,000,000 43,000 40 62,000 N 36 4,356,000,000 66,000 60 98,000 N 196 900,000,000 30,000 48 100,000 N 4 784,000,000 28,000 33 110,000 N 169 324,000,000 18,000 27 130,000 N 361 4,000,000 2,000 37 90,000 N 81 1,444,000,000 38,000
  • 17. Kamal Gupta Roy • Age = 46 • loan=128 K | 17 • Default = Yes Age Loan Default age dist sq loan dist sq d 25 40 Y 441 7,744 90 35 60 Y 121 4,624 69 45 80 Y 1 2,304 48 20 20 Y 676 11,664 111 35 120 Y 121 64 14 52 38 Y 36 8,100 90 23 85 Y 529 1,849 49 40 62 N 36 4,356 66 60 98 N 196 900 33 48 100 N 4 784 28 33 110 N 169 324 22 27 130 N 361 4 19 37 90 N 81 1,444 39
  • 18. Kamal Gupta Roy Kamal Gupta Roy Feature Scaling | 18
  • 19. Kamal Gupta Roy Why scaling? Scaling issues – Attributes may have to be scaled to prevent distance measures from being dominated by one of the attributes Example: height of a person may vary from 1.5m to 1.8m weight of a person may vary from 45 KG to 100KG income of a person may vary from Rs10K to Rs 5 lakh | 19
  • 20. Kamal Gupta Roy Standardization Also called as Z-score normalization Mean is zero Standard deviation 1 | 20
  • 21. Kamal Gupta Roy Max-Min Normalization Also called as Min-Max scaling normalization Minimum is zero Maximum is 1 | 21
  • 22. Kamal Gupta Roy | 22 Raw Data Z Normalized Max-Min
  • 23. Kamal Gupta Roy • Age = 46; norm age: 0.65 • loan=128,000; norm age: 0.98 | 23 • Default = No Age Loan Default norm age norm loan age dist sq loan dist sq d 25 40,000 Y 0.13 0.18 0.28 0.64 0.96 35 60,000 Y 0.38 0.36 0.08 0.38 0.68 45 80,000 Y 0.63 0.55 0.00 0.19 0.44 20 20,000 Y - - 0.42 0.96 1.18 35 120,000 Y 0.38 0.91 0.08 0.01 0.28 52 38,000 Y 0.80 0.16 0.02 0.67 0.83 23 85,000 Y 0.08 0.59 0.33 0.15 0.70 40 62,000 N 0.50 0.38 0.02 0.36 0.62 60 98,000 N 1.00 0.71 0.12 0.07 0.44 48 100,000 N 0.70 0.73 0.00 0.06 0.26 33 110,000 N 0.33 0.82 0.11 0.03 0.36 27 130,000 N 0.18 1.00 0.23 0.00 0.48 37 90,000 N 0.43 0.64 0.05 0.12 0.41
  • 24. Kamal Gupta Roy | 24 Age Loan Default age dist sq loan dist sq d 25 40,000 Y 441 7,744,000,000 88,000 35 60,000 Y 121 4,624,000,000 68,000 45 80,000 Y 1 2,304,000,000 48,000 20 20,000 Y 676 11,664,000,000 108,000 35 120,000 Y 121 64,000,000 8,000 52 38,000 Y 36 8,100,000,000 90,000 23 85,000 Y 529 1,849,000,000 43,000 40 62,000 N 36 4,356,000,000 66,000 60 98,000 N 196 900,000,000 30,000 48 100,000 N 4 784,000,000 28,000 33 110,000 N 169 324,000,000 18,000 27 130,000 N 361 4,000,000 2,000 37 90,000 N 81 1,444,000,000 38,000 Age Loan Default age dist sq loan dist sq d 25 40 Y 441 7,744 90 35 60 Y 121 4,624 69 45 80 Y 1 2,304 48 20 20 Y 676 11,664 111 35 120 Y 121 64 14 52 38 Y 36 8,100 90 23 85 Y 529 1,849 49 40 62 N 36 4,356 66 60 98 N 196 900 33 48 100 N 4 784 28 33 110 N 169 324 22 27 130 N 361 4 19 37 90 N 81 1,444 39 Age Loan Default norm age norm loan age dist sq loan dist sq d 25 40,000 Y 0.13 0.18 0.28 0.64 0.96 35 60,000 Y 0.38 0.36 0.08 0.38 0.68 45 80,000 Y 0.63 0.55 0.00 0.19 0.44 20 20,000 Y - - 0.42 0.96 1.18 35 120,000 Y 0.38 0.91 0.08 0.01 0.28 52 38,000 Y 0.80 0.16 0.02 0.67 0.83 23 85,000 Y 0.08 0.59 0.33 0.15 0.70 40 62,000 N 0.50 0.38 0.02 0.36 0.62 60 98,000 N 1.00 0.71 0.12 0.07 0.44 48 100,000 N 0.70 0.73 0.00 0.06 0.26 33 110,000 N 0.33 0.82 0.11 0.03 0.36 27 130,000 N 0.18 1.00 0.23 0.00 0.48 37 90,000 N 0.43 0.64 0.05 0.12 0.41
  • 26. Kamal Gupta Roy Kamal Gupta Roy Hiring Process Example | 26 Matrix Predicted Good Predicted Bad Actual Good Hired Good Candidate Rejected Good Candidate Actual Bad Hired Bad Candidate Rejected Bad Candidate TP TN FN FP Confusion Matrix
  • 27. Kamal Gupta Roy Confusion Matrix Predicted Yes Predicted No Actual Yes TP FN Actual No FP TN | 27 Accuracy = (TP + TN)/ (TP + FN + FP + TN) Recall = TP / (TP + FN) Precision = TP / (TP + FP) Type 1 Error Type 2 Error
  • 28. Kamal Gupta Roy Kamal Gupta Roy Precision vs Recall | 28
  • 29. Kamal Gupta Roy Kamal Gupta Roy Pregnancy Test | 29 Predicted Pregnant Predicted Not Pregnant Actual Pregnant TP FN Actual Not Pregnant FP TN TN TP FP FN
  • 30. Kamal Gupta Roy Sensitivity & Specificity Predicted Yes Predicted No Actual Yes TP FN Actual No FP TN | 30 True Negative Rate, Specificity = TN / (TN+FP) False Positive Rate = FP / (TN+FP) True Positive Rate, Sensitivity = TP / (TP + FN) False Negative Rate = FN / (TN+FP)