Localized Simple Multiple Kernel K-Means Clustering with Matrix-Induced Regularization

Table 3

ACC, NMI, purity, and Rand index data of localized-SimpleMKKM-matrix-induced regularization with nine comparison methods on six benchmark datasets.

Dataset	AVG-KKM	MKKM [10]	LMKKM [12]	ONKC [24]	MKKM-MR [14]	LKAM [22]	LF-MVC [25]	SimpleMKKM [20]	LI-SimpleMKKM [21]	Proposed
ACC (%)
FLO17	51.3 ± 1.4	43.6 ± 1.7	42.7 ± 1.7	43.4 ± 2.0	57.7 ± 1.2	48.9 ± 0.9	56.7 ± 1.5	59.4 ± 1.5	59.1 ± 1.1	61.3 ± 1.5
FLO102	27.1 ± 0.8	22.4 ± 0.8	—	39.5 ± 0.7	40.2 ± 0.9	41.4 ± 0.8	38.4 ± 1.2	42.5 ± 0.8	44.0 ± 1.0	44.1 ± 1.0
PFold	29.1 ± 1.4	27.1 ± 1.0	22.4 ± 0.7	35.4 ± 1.5	34.3 ± 1.6	34.2 ± 1.6	33.3 ± 2.0	34.4 ± 1.9	35.9 ± 1.5	39.0 ± 1.4
DIGIT	88.8 ± 0.1	47.2 ± 0.6	47.2 ± 0.7	89.5 ± 0.1	87.4 ± 0.1	95.0 ± 0.3	89.2 ± 0.1	90.3 ± 0.1	94.6 ± 0.1	94.9 ± 3.0
Cal-25	34.2 ± 1.0	32.8 ± 0.1	22.6 ± 0.7	34.3 ± 1.2	34.0 ± 1.2	37.2 ± 1.1	34.6 ± 1.1	36.2 ± 1.2	36.7 ± 0.9	37.3 ± 1.1
Cal-7	33.7 ± 0.1	33.3 ± 0.2	34.4 ± 0.1	46.0 ± 4.0	43.5 ± 3.9	49.4 ± 1.0	42.3 ± 2.7	39.4 ± 1.5	46.4 ± 0.9	49.8 ± 0.8
NMI (%)
FLO17	49.9 ± 0.9	44.3 ± 1.3	43.8 ± 1.1	42.9 ± 1.3	56.1 ± 0.7	48.1 ± 0.6	54.6 ± 1.0	57.6 ± 0.1	57.7 ± 0.5	58.9 ± 1.0
FLO102	46.0 ± 0.5	42.7 ± 0.2	—	56.1 ± 0.4	56.7 ± 0.5	56.9 ± 0.3	54.9 ± 0.4	58.6 ± 0.5	60.0 ± 0.4	60.1 ± 0.4
PFold	40.3 ± 1.2	38.1 ± 0.6	34.8 ± 0.6	44.1 ± 0.8	43.2 ± 1.1	43.7 ± 1.0	42.3 ± 1.2	44.2 ± 1.2	45.2 ± 1.3	48.0 ± 0.9
DIGIT	80.7 ± 0.2	48.7 ± 0.7	48.3 ± 0.2	81.7 ± 0.1	79.5 ± 0.1	89.4 ± 0.1	81.2 ± 0.2	83.3 ± 0.1	90.0 ± 0.1	90.3 ± 1.6
Cal-25	59.7 ± 0.5	58.6 ± 0.5	51.9 ± 0.3	59.6 ± 0.8	59.3 ± 0.5	62.0 ± 0.6	59.5 ± 0.7	60.7 ± 0.5	61.4 ± 0.4	61.5 ± 0.5
Cal-7	34.9 ± 0.3	30.0 ± 0.3	30.7 ± 0.1	40.0 ± 1.0	43.1 ± 0.8	43.3 ± 0.2	40.0 ± 0.3	40.5 ± 0.4	39.2 ± 1.3	44.9 ± 0.1
Purity (%)
FLO17	52.3 ± 1.2	45.1 ± 1.4	44.6 ± 1.5	45.1 ± 1.8	59.2 ± 1.1	50.1 ± 0.6	57.5 ± 1.6	60.5 ± 1.3	59.7 ± 0.3	62.7 ± 1.6
FLO102	32.3 ± 0.6	27.8 ± 0.4	—	45.6 ± 0.7	46.3 ± 0.8	48.0 ± 0.6	44.6 ± 0.8	48.6 ± 0.7	50.3 ± 0.7	50.5 ± 0.7
PFold	37.3 ± 1.6	33.7 ± 0.9	31.1 ± 1.0	42.0 ± 1.2	41.2 ± 1.4	41.6 ± 1.3	40.6 ± 1.6	41.4 ± 1.6	42.5 ± 1.6	46.2 ± 1.5
DIGIT	88.8 ± 0.1	50.1 ± 0.7	50.2 ± 0.3	89.5 ± 0.1	87.4 ± 0.1	95.0 ± 0.3	89.2 ± 0.1	90.3 ± 0.1	94.6 ± 0.1	94.9 ± 2.0
Cal-25	36.2 ± 1.0	34.9 ± 0.1	24.4 ± 0.6	36.6 ± 1.1	36.1 ± 1.0	39.4 ± 1.1	36.8 ± 1.0	38.2 ± 1.1	39.1 ± 0.8	39.3 ± 1.1
Cal-7	79.0 ± 0.2	76.7 ± 0.2	74.9 ± 0.1	81.2 ± 0.9	82.9 ± 0.4	83.2 ± 0.2	81.6 ± 0.3	83.3 ± 0.3	80.8 ± 0.7	83.4 ± 0.1
Rand Index (%)
FLO17	32.2 ± 1.3	26.3 ± 1.3	20.6 ± 1.1	35.2 ± 1.5	39.9 ± 1.3	31.6 ± 0.8	44.1 ± 0.4	41.5 ± 1.1	40.9 ± 0.8	42.6 ± 1.4
FLO102	15.5 ± 0.5	12.1 ± 0.5	—	24.9 ± 0.5	25.5 ± 0.6	27.2 ± 0.6	25.5 ± 1.0	28.5 ± 0.8	29.9 ± 0.8	30.0 ± 0.8
PFold	14.4 ± 1.8	12.1 ± 0.7	7.8 ± 0.4	18.0 ± 1.1	17.2 ± 1.5	20.1 ± 1.1	16.5 ± 2.0	17.6 ± 1.9	19.8 ± 1.2	20.8 ± 1.5
DIGIT	77.4 ± 0.2	31.4 ± 0.6	31.3 ± 0.2	81.7 ± 0.3	81.3 ± 0.1	90.8 ± 2.3	78.0 ± 0.1	80.6 ± 0.2	88.2 ± 0.1	88.3 ± 2.9
Cal-25	18.5 ± 0.9	17.3 ± 0.1	8.3 ± 0.6	18.6 ± 1.2	18.4 ± 0.8	21.5 ± 1.0	18.9 ± 0.9	20.4 ± 0.1	20.1 ± 0.7	21.1 ± 0.8
Cal-7	26.5 ± 0.3	23.5 ± 0.3	20.3 ± 0.1	30.9 ± 1.7	31.5 ± 2.2	36.6 ± 0.5	29.3 ± 0.8	30.3 ± 0.7	32.2 ± 1.3	37.1 ± 0.3

Bold indicates better results in comparison with other algorithms.