Question

K-Nearest Neighbors The given data contains pairs of points and their corresponding class. (2,5), 1 (1,5), 1 (48,35), 2 (42, 12), 2 Use KNN algorithm, determine the class of the points: (15, 16) (30, 40) (0,0) Report results for k-1, 2, 3 Your are required to finish this question using pen and paper. Please include all the details for different k

Answer 1

Here we want to determine the given points class using KNN(K nearest neighbors) algorithm in the given data points.

For different k we predict the class of the point and the answer with explanation are given below,

Given , their connesponding pains of points and 1 and 2. class . There ane tab classes Points class (2,5) C15) (48, 35) 2. (42,12) class of (15,16) ,(30,40), the Find to we Cuant Co, 0) kNN algonithm Notg let humben of taraining Samples T be the be the Let U point to predict the class (le, unknocn Point) Słone the toraining Samples Calculate Eaclidean distance between the training Samples and unknown Point. Select the poi samples 3) we Smallest distance wuith obtained ( k=l /Select one sample with snoallest distance K-2, select tewo samples culth smallest dstane) Retun the majonity class label of Selected Samples

Euclidean Distance Note Euclidean distance between two points A and caleulated by, B Ce - A1 )82-A2) dCA/B) Hene Find paints class of points using kNN (15, 16) Fon k-1 (16,16) Flnd the betaeen distance Guclidean the and given data Points Class Eudidean distance faam (5, 6 (2/5) 1 is-2) tC16-5) 2 15-10+C16-5) 7.029 1 Cu5) =11.804 (48, 35) V5-48)tC16-36) 2 = 38.078 (42,12) 2 (5-42 C 16-12) 21.29 4 the distance Fr1om we Select Smallest 1 Because k 1, we select 1 distance sanople. Sarople) Smallest distance is Connes pooding and 17.029 nabing Sarople is Point (2,5) Cuth class 1

class label ot Selected Sample is 1 So fon k=1, is 1 class C15, 16) polint Fao k-2 Snoallest two Cue Select distance the Fromm Samoples distance ane t they .029 distance C2,5 1 with Cstth distan ce 1.804 / Point the 1, So classes ane The twa points is in class 1 (15, 16) FosT k-3 ,we Select 3 Snoalest euclidean distance the From distance Samoples They ane (2, 5), Cotth distance 13.624 F.804 CI/5),1 Cot distance 27. 294 42,12),2 aurth distante

Here the majority Class label is 1 CI5,16) n the class 1 So point C30,40) calcutate the Guclidean distance fnom (30,40) to training Samoples Point all class Eudidean elistance faomo (30, 40) C2,5) No-2) (40-5) 44 .82 (1,5) J Go-1) C40-5)2 1 45.453 (48,35 J0-4)(t0-35 2 2 = 18.681 C42 12) 50-42 C40-2) 30.463 1 Foo distance. Sroallest Select 1 Frono the distance we Point 48,35), 2 w th distance That Is haysi'g 2. So Selected Poi ot 15 class label Op lass 2 predicted in 3040)

For k2 Fnom the distance Sraallest distance we Select two Samaples They ane C48,35) ,2 distanie 18. 681 aith distance (42,12), 2 30.463 Cith Seleded So the majoRity Class label of Samppla is In class 2 2. So Predicted the point (s0,A0) For k=3 thaee Smallest Select Cwe Fam the distance distance Samples. They ane distance 48,35),2 18. 681 Gorth / (42,12), 2 Cuit, distante 30.463 distance 44 821 2,5), Gstth Selected class label oc So the majonuty 2 . Samples Is class 2 point C30/40) predicted in So the

C0,0) Pro m(0,0) distance Euclidean the Calculate training Sample s to all class Cucli dean distance from Co, 0) Paint 5.385 No-2)+ Co-5)2 11 (2,5) 5.0490 JG- -5 11 C,) O-4 C0-35) 59.405 C44, 35) 2 -42* Co-12) 2 (42,12) 4 3.680 Fon k-1 Fnom the distance Select we Smallest one distance point leie 1t is (175) ,1 Coith distance 5.094 class label of se lected point is 1 So Co,6) Predicted to in class 1

Foon k 2 Fnono the distance select 2 Smallest distance we Point they are, CIus), distance atth 5.049 C2,5), cwith distance 5.38 5 class label of Selected points is 1 class 1 So (0/0) Predtcted 1 Fo7 k-3 thaee Smmallest Select Frono the distance we distance Point They ane distance 5.099 distance 5. 385 aith C2,5),1 distance 4 3 680 C42,12), 2 Cuith Points is 1 elass label of Selected Majonity in dass 1 So (o,0) Pnedicted