A New Fuzzy Logic-Based Similarity Measure Applied to Large Gap Imputation for Uncorrelated Multivariate Time Series

Table 2

Average imputation performance indices of various imputation algorithms on simulated dataset (32,000 collected points).

Gap size	Method	Accuracy indices			Shape indices
		1-Sim	1-	RMSE	FSD	FB	1-FA2
1%	FSMUMI	0.083	0.515	1.033	0.159	2.51	0.574
	Amelia	0.157	1	2.206	0.232	3.619	0.794
	FcM	0.118	0.998	1.483	1.98	2.015	0.998
	MI	0.16	0.999	2.241	0.2	0.915	0.799
	MICE	0.159	0.998	2.201	0.214	1.449	0.801
	missForest	0.127	0.998	1.608	0.836	12.034	0.861
	na.approx	0.146	0.992	1.901	0.393	18.997	0.777
	DTWUMI	0.09	0.552	1.156	0.007	6.022	0.562
2%	FSMUMI	0.068	0.487	1.166	0.194	1.971	0.611
	Amelia	0.12	0.998	2.312	0.107	2.191	0.794
	FcM	0.093	0.999	1.672	1.985	1.96	0.998
	MI	0.12	1	2.307	0.123	3.949	0.789
	MICE	0.119	0.999	2.282	0.114	8.881	0.789
	missForest	0.096	1	1.769	0.941	2.777	0.858
	na.approx	0.118	1	2.261	0.721	2.059	0.786
	DTWUMI	0.074	0.523	1.545	0.008	3.686	0.583
3%	FSMUMI	0.068	0.453	1.053	0.076	10.649	0.582
	Amelia	0.13	0.999	2.212	0.062	3.779	0.794
	FcM	0.098	0.999	1.526	1.984	2.22	0.997
	MI	0.13	0.999	2.197	0.078	9.374	0.795
	MICE	0.129	1	2.19	0.067	1.938	0.792
	missForest	0.102	0.999	1.626	0.855	2.407	0.851
	na.approx	0.116	0.997	1.938	0.518	1.974	0.818
	DTWUMI	0.073	0.526	1.189	0.01	8.725	0.567
4%	FSMUMI	0.064	0.412	1.067	0.061	1.374	0.568
	Amelia	0.122	1	2.305	0.032	2.446	0.764
	FcM	0.096	1	1.607	1.982	2.325	0.997
	MI	0.125	1	2.261	0.043	2.391	0.792
	MICE	0.124	0.999	2.233	0.045	42.495	0.791
	missForest	0.101	1	1.726	0.876	2.901	0.854
	na.approx	0.109	1	1.99	0.475	1.94	0.811
	DTWUMI	0.066	0.465	1.172	0.004	2.079	0.547
5%	FSMUMI	0.063	0.404	1.062	0.062	4.508	0.577
	Amelia	0.122	1	2.273	0.028	4.109	0.798
	FcM	0.092	1	1.619	1.984	2.192	0.998
	MI	0.123	1	2.287	0.024	5.582	0.797
	MICE	0.121	1	2.267	0.044	2.326	0.792
	missForest	0.097	0.999	1.731	0.923	2.473	0.859
	na.approx	0.114	1	1.988	0.567	2.247	0.809
	DTWUMI	0.063	0.454	1.166	0.003	1.594	0.545
7.5%	FSMUMI	0.06	0.408	1.063	0.049	4.843	0.566
	Amelia	0.117	1	2.232	0.034	3.306	0.792
	FcM	0.09	1	1.605	1.981	3.562	0.998
	MI	0.119	0.999	2.259	0.025	1.946	0.793
	MICE	0.118	1	2.238	0.032	9.359	0.794
	missForest	0.094	0.999	1.695	0.907	1.259	0.858
	na.approx	0.108	1	1.958	0.461	3.089	0.816
	DTWUMI	0.065	0.477	1.19	0.004	3.851	0.566
10%	FSMUMI	0.061	0.4226	1.086	0.051	5.558	0.572
	Amelia	0.117	1	2.269	0.021	3.074	0.793
	FcM	0.089	1	1.607	1.981	2.683	0.997
	MI	0.118	0.9996	2.233	0.02	2.05	0.793
	MICE	0.118	0.9998	2.254	0.018	3.424	0.793
	missForest	0.094	0.9999	1.702	0.909	1.87	0.857
	na.approx	0.11	1	1.958	0.541	2.006	0.798
	DTWUMI	0.067	0.5371	1.293	0.012	3.093	0.577