Dimensionality reduction, and function approximation of poly(lactic-co-glycolic acid) micro- and nanoparticle dissolution rate

Figures & data

Table 1 The PLGA dataset description

Sl No	Group name	No of features	Importance
1	Protein descriptors	85	Describes the type of molecules and proteins used
2	Formulation characteristics	17	Describe the molecular properties such as molecular weight, particle size, etc
3	Plasticizer	98	Describe the properties such as fluidity of the material used
4	Emulsifier	99	Describe the properties of stabilizing/increase the pharmaceutical product life
5	Time in days	1	Time taken to dissolve
6	% of molecules dissolved	1	Output

Abbreviations: PLGA, poly(lactic-co-glycolic acid); SI, serial; No, number.

Figure 1 Evolutionary weighted ensemble algorithm.

Table 2 Parameters setting of the respective regression models used for the feature selection and feature extraction experiments

Predictor	Parameters
GPReg	RBF kernel, gamma value = 1.0
LReg	–
MLP	Three-layer MLP, hidden layer nodes - 50, learning rate -0.3, momentum rate - 0.2
SMOReg	Polynomial kernel, epsilon value - 0.001, tolerance level - 0.001
REP tree	Max depth – no restriction

Abbreviations: GPReg, Gaussian process regression; RBF, radial basis function; LReg, linear regression; MLP, multilayer perception; SMOReg, sequential minimal optimization regression; REP, reduced error pruning; –, no such parameter.

Table 3 Experimental results for 10-CV datasets prepared with distinct random partitions of the complete dataset using feature selection technique (Identification of regression model)

Selection method	Selected features	GPReg	LReg	MLP	REP	SMOReg
No selection	300	16.81	17.07	18.57	13.05	17.95
BFE	1	27.47	26.61	28.33	24.37	26.97
BFE	5	17.11	23.45	23.11	14.23	23.38
CFS	5	20.80	25.08	22.41	18.31	25.42
Class-MLP-greedy	7	17.96	25.03	22.26	14.96	25.35
BFE	10	15.93	19.98	21.00	13.19	19.53
Class-MLP-BFS	15	15.88	22.90	16.83	13.91	24.23
Wrapper-GPReg-greedy	15	14.88	20.22	15.20	13.34	20.86
Class-GPReg-BFS	16	18.46	23.07	19.71	14.19	23.69
Class-GPReg-greedy	19	15.06	19.05	15.61	14.03	19.68
Wrapper-MLP-greedy	19	16.44	24.01	20.42	14.26	24.85
Wrapper-LReg-greedy	24	15.91	17.46	17.03	13.54	18.02
BFE	Optimal*	15.71	17.85	17.82	13.90	17.88
Class-LReg-BFS	31	15.95	16.92	15.63	14.00	17.58
Class-LReg-greedy	37	16.31	17.14	16.27	14.02	17.69

Notes: Values are the average of ten RMSE.

* Optimal set of attributes for the GPReg, LReg, MLP, REP and SMOReg regression models are 18, 32, 31, 31, and 30, respectively.

Abbreviations: 10-CV, ten-fold cross-validation; GPReg, gaussian process regression; LReg, linear regression; MLP, multilayer perception; REP, reduced error pruning; SMOReg, sequential minimal optimization; No, number; BFE, backward feature elimination; CFS, correlation-based feature selection; BFS, best fit search; wrapper, wrapper feature selection; greedy, greedy search; class, classifier-based feature selection.

Table 4 Experimental results for 10-CV datasets prepared with distinct random partitions of the complete dataset using feature extraction techniques

Feature extraction method		Regression model	Dimension reduction
			5		10		20		30		50
			Mean	VAR	Mean	VAR	Mean	VAR	Mean	VAR	Mean	VAR
Linear method	PCA	GPReg	28.88	1.62	27.22	3.00	24.80	3.85	19.82	2.49	16.08	3.16
		LReg	29.55	1.74	29.22	1.70	27.73	2.21	23.93	1.63	17.17	2.79
		MLP	30.36	3.36	29.77	6.37	26.58	3.98	19.89	2.27	13.59	1.56
		SMOReg	30.14	3.17	29.78	3.62	27.95	2.67	24.31	1.89	17.66	3.09
	FA	GPReg	29.23	1.77	28.56	2.67	28.31	3.34	28.30	3.42	28.26	3.31
		LReg	29.97	1.77	29.97	1.77	29.97	1.77	29.97	1.77	29.98	1.82
		MLP	30.64	2.02	30.50	1.91	31.01	1.83	30.93	2.30	30.91	0.77
		SMOReg	30.28	3.45	30.28	3.45	30.26	3.37	30.29	3.44	30.28	3.46
Non-linear method	Kernel	GPReg	28.60	1.68	27.08	2.12	24.96	1.96	24.32	2.17	22.81	4.43
	PCA	LReg	29.31	1.52	28.05	1.78	25.35	2.05	25.17	2.23	22.98	4.27
		MLP	29.81	3.57	29.65	7.94	27.07	4.09	25.97	5.52	25.27	8.49
		SMOReg	29.43	1.41	28.68	1.65	25.90	1.70	25.79	2.00	23.24	4.76
	MDS	GPReg	28.91	2.17	28.73	2.47	28.41	3.16	28.24	3.17	28.16	3.27
		LReg	29.56	1.86	29.21	2.08	29.19	2.08	29.11	1.92	29.14	2.04
		MLP	30.42	3.71	29.38	4.11	29.93	3.10	30.01	4.53	29.98	4.42
		SMOReg	29.98	2.62	29.64	2.55	29.64	2.76	29.66	2.85	29.65	2.89

Note: Mean and variance (VAR) is computed on ten RMSE obtained.

Abbreviations: 10-CV, ten-fold cross-validation; RMSE, root mean square error; PCA, principal component analysis; FA, factor analysis; MDS, multidimensional scaling; GPReg, Gaussian process regression; LReg, linear regression; MLP, multilayer perception; SMOReg, sequential minimal optimization regression.

Figure 2 Results of the feature extraction experiment for the reduced dimension set of 30 features: a comparison between the regression models. a comparison using average RMSE (A); a comparison using variances (B).

Abbreviations: RMSE, root mean square error; ICA, independent component analysis; PCA, principle component analysis; FA, factor analysis; kPCA, kernel PCA; MDS, multidimensional scaling; GPReg, Gaussian process regression; LReg, linear regression; MLP, multilayer perception; SMOReg, sequential minimal optimization regression.

Table 5 A comprehensive conclusion of the results obtained from each regression model, including the ensemble techniques used