Important Neighbors: A Novel Approach to Binary Classification in High Dimensional Data

Table 1

Misclassification rate (MC) of KIN versus KNN in simulation study.

Number of features	Degree of sparsity (%)	Sample size	Ratio of the first class
				KNN	KIN			KNN	KIN
				MC	MC	TC (%)	#FP	MC	MC	TC (%)	#FP
100	98%		0.5	43.2	30.7	66%	2.7	40.0	27.5	69%	2.5
			0.8	21.4	19.1	71%	1.4	21.6	17.9	65%	1.5
			0.5	40.2	27.6	82%	2.5	37.2	25.4	85%	2.1
			0.8	20.1	17.8	79%	1.3	20.2	16.6	83%	1.1
	95%		0.5	39.6	28.0	76%	2.4	35.0	21.0	84%	2.1
			0.8	21.1	19.1	64%	1.7	21.0	16.3	83%	1.7
			0.5	36.8	23.8	87%	3.0	30.8	17.9	88%	2.6
			0.8	20.0	16.5	87%	1.9	19.2	14.2	92%	1.3
	90%		0.5	39.1	33.9	68%	2.1	30.8	20.5	89%	1.5
			0.8	21.6	22.0	59%	1.6	20.8	16.5	89%	1.5
			0.5	36.9	28.0	87%	2.7	28.1	18.5	92%	2.1
			0.8	20.0	18.6	85%	1.9	18.4	14.3	94%	1.6
300	98%		0.5	43.5	35.4	68%	2.8	40.1	20.4	82%	2.6
			0.8	22.1	21.7	60%	2.2	22.9	17.0	80%	2.4
			0.5	41.2	25.3	77%	5.3	36.6	17.4	87%	3.2
			0.8	20.8	18.3	77%	3.1	21.0	14.9	88%	2.7
	95%		0.5	43.6	41.9	57%	2.1	37.6	23.8	85%	2.1
			0.8	22.3	23.3	54%	2.4	23.5	19.5	83%	2.1
			0.5	41.8	33.0	79%	3.6	33.8	19.4	90%	2.8
			0.8	21.1	21.9	70%	3.0	21.2	16.7	90%	2.6
	90%		0.5	43.6	41.8	53%	2.3	36.6	23.7	85%	2.1
			0.8	32.1	29.7	64%	2.1	30.3	22.9	85%	1.9
			0.5	41.5	33.1	76%	3.7	34.1	19.9	91%	2.7
			0.8	28.3	28.0	77%	3.5	26.2	16.9	92%	2.5
500	98%		0.5	44.7	41.3	58%	2.5	39.9	21.6	82%	2.5
			0.8	22.5	22.5	51%	2.3	23.1	17.1	78%	2.5
			0.5	43.5	29.0	75%	4.9	37.9	17.2	87%	4.0
			0.8	20.5	18.9	69%	3.3	21.3	14.8	88%	3.2
	95%		0.5	45.7	44.8	44%	6.2	38.8	29.3	74%	2.3
			0.8	23.2	25.3	40%	2.3	26.6	22.5	74%	2.2
			0.5	44.5	40.5	69%	3.3	35.8	22.3	88%	3.3
			0.8	21.1	24.6	66%	3.1	21.9	18.1	88%	3.0
	90%		0.5	45.7	45.1	46%	2.5	39.3	26.0	83%	2.0
			0.8	28.2	32.2	50%	2.3	29.7	25.4	77%	2.1
			0.5	46.5	45.2	58%	2.8	36.9	29.5	86%	3.3
			0.8	26.1	30.3	59%	3.2	21.8	23.2	86%	2.8