Detection Method on Data Accuracy Incorporating Materials Domain Knowledge

doi:10.15541/jim20220149

Abstract

Abstract:

Due to the characteristics of small samples, high dimensions, and much noise, materials data often produce inconsistent results with those obtained from domain experts when used for machine learning modeling. For the whole process of machine learning, developing machine learning models embedding materials domain knowledge is a solution to this problem. The accuracy of materials data directly affects the reliability of data-driven materials performance prediction. Here, a data accuracy detection method incorporating materials domain knowledge is proposed by focusing on the data preprocessing stage in the machine learning application process. Firstly, a materials domain knowledge database is constructed based on the knowledge from materials experts. Secondly, it is coordinated with the data-driven data accuracy detection method to perform single-dimensional data accuracy detection based on the rule for value of descriptors, multi-dimensional data correlation detection based on the rule for correlation of descriptors, and full-dimensional data reliable detection based on multi-dimensional similar sample identification strategy from both data and domain knowledge perspectives. For the anomalous data identified at each stage, they are corrected by incorporating the materials domain knowledge. Furthermore, domain knowledge is incorporated into the whole process of the data accuracy detection method to ensure high accuracy of the dataset from the initial stage. Finally, experiments on the NASICON-type solid electrolyte activation energy prediction dataset demonstrate that this method can effectively identify anomalous data and make reasonable corrections. Compared with the original dataset, the prediction accuracy of all six machine learning models based on the revised dataset is improved to different degrees, among which R² achieves a 33% improvement on the optimal model.

Key words: machine learning, materials science, data quality, domain knowledge

CLC Number:

SHI Siqi, SUN Shiyu, MA Shuchang, ZOU Xinxin, QIAN Quan, LIU Yue. Detection Method on Data Accuracy Incorporating Materials Domain Knowledge[J]. Journal of Inorganic Materials, 2022, 37(12): 1311-1320.

Figures/Tables 14

Fig. 1 Framework of DADMmdk

Fig. 2 Full-dimensional reliability detection n: Number of learning samples; d: Number of features

Table 1 Result comparison of data-driven data accuracy detection methods with DADMmdk

		Data-driven data accuracy detection					DADM_mdk
Stage	N	Number of anomalous		Number of removed		N1	Number of anomalous		Number of removed		Number of corrected		N1
Stage	N	D	S	D	S	N1	D	S	D	S	D	S	N1
1	90	18	0	0	5	85	18	2	0	5	0	0	85
2	85	0	0	0	0	85	0	0	0	0	0	0	85
3	85	0	9	0	0	85	0	9	0	0	0	3	85

Table 2 Anomalous points in single-dimensional data correctness detection

No.	ICSD	Formula	Valence_M1
17	182793	Na_16.74Cr₁₂P₁₈O₇₂	3.105
72	71326	Na₃Nb₁₂P₁₈O₇₂	4.25

Fig. 3 Anomalous points detection results (a) All anomalous points from the box plot; Anomalous points in (b) Radius_X1, (c) Occu_X1, (d) Occu_X2, (e) EaColorful figures are available on website

Fig. 4 Result of PCC The color bands represents the mapping of values to colors; The darker the color (red or cyan), the higher the correlation, and vice versa.

Fig. 5 Clustering results of feature and activation energy (a-h) Clustering overlaps of features and activation energy for each of 8 clusters; Horizontal and vertical coordinates represent two dimensions after dimension reduction by t-SNE (t-distributed Stochastic Neighbor Embedding)Colorful figures are available on website

Table 3 Anomalous data detection and correction

No.	ICSD	Formula	a	c	V_cell	Revised a	Revised c	Revised V_cell
5	15545	Na₂₄Zr₁₂Si₁₈O₇₂	9.186	22.181	1621.04	9.198	22.210	1627.29
6	15546	Na₂₄Zr₁₂Si₁₈O₇₂	9.186	22.181	1621.04	9.199	22.470	1646.70
7	15547	Na₂₄Zr₁₂Si₁₈O₇₂	9.186	22.181	1621.04	9.199	22.706	1663.99

Table 4 Experimental results of ML models

Model	Origin data			Revised data
Model	RMSE	MAPE	R²	RMSE	MAPE	R²
LASSO	0.621	0.218	0.118	0.058	0.035	0.943
GPR	0.637	0.231	0.073	0.051	0.032	0.957
Ridge	0.548	0.244	0.313	0.051	0.033	0.956
SVR	0.638	0.102	0.072	0.071	0.057	0.916
KNN	0.624	0.226	0.108	0.079	0.051	0.894
RF	0.400	0.088	0.629	0.051	0.035	0.956

Table S1 The meanings, types, ranges, and sources of all descriptors in NASICON

No.	Descriptors	Description	Type	Range	Source
1	Occu_6b	Occupancy of Na in 6b site	float	[0,1]	CIF
2	Occu_18e	Occupancy of Na in 18e site	float	[0,1]	CIF
3	Occu_36f	Occupancy of Na in 36f site	float	[0,1]	CIF
4	C_Na	Na⁺ concentration	float	(0,+∞)	Formula
5	Occu_M1	Occupancy of element M1	float	[0,1]	CIF
6	Occu_M2	Occupancy of element M2	float	[0,1]	CIF
7	EN_M1	Electronegativity of element M1	float	(0,+∞)	Pauling electronegativity meter
8	EN_M2	Electronegativity of element M2	float	[0,+∞)	Pauling electronegativity meter
9	EN_avg_M	Average effective electronegativity of M site	float	(0,+∞)	Formula
10	Radius_M1	Ionic radius of element M1	float	(0,+∞)	Shannon radius table
11	Radius_M2	Ionic radius of element M2	float	[0,+∞)	Shannon radius table
12	Radius_avg_M	Average effective ionic radius of M site	float	(0,+∞)	Formula
13	Valence_M1	Valence of element M1	int	(0,+∞)	CIF
14	Valence_M2	Valence of element M2	int	[0,+∞)	CIF
15	Valence_avg_M	Average effective ionic valence of M site	float	(0,+∞)	Formula
16	Occu_X1	Occupancy of element X1	float	[0,1]	CIF
17	Occu_X2	Occupancy of element X2	float	[0,1]	CIF
18	EN_X1	Electronegativity of element X1	float	(0,+∞)	CIF
19	EN_X2	Electronegativity of element X2	float	[0,+∞)	CIF
20	EN_avg_X	Average effective electronegativity of X site	float	(0,+∞)	Formula
21	Radius_X1	Ionic radius of element X1	float	(0,+∞)	Shannon radius table
22	Radius_X2	Ionic radius of element X2	float	[0,+∞)	Shannon radius table
23	Radius_avg_X	Average effective ionic radius of X site	float	(0,+∞)	Formula
24	Valence_X1	Valence of element X1	int	(0,+∞)	CIF file
25	Valence_X2	Valence of element X2	int	[0,+∞)	CIF file
26	Valence_avg_X	Average effective ionic valence of X site	float	(0,+∞)	Formula
27	a	Lattice parameter	float	(0,+∞)	CIF file
28	c	Lattice parameter	float	(0,+∞)	CIF file
29	V_cell	Lattice parameter	float	(0,+∞)	Formula
30	V_MO₆	Volume of MO₆ polyhedron	float	(0,+∞)	VESTA file
31	V_XO₄	Volume of XO₄ polyhedron	float	(0,+∞)	VESTA file
32	V_Na₁O₆	Volume of Na₁O₆ polyhedron	float	(0,+∞)	VESTA file
33	V_Na₂O₈	Volume of Na₂O₈ polyhedron	float	(0,+∞)	VESTA file
34	V_Na₃O₅	Volume of Na₃O₅ polyhedron	float	(0,+∞)	VESTA file
35	BT1	Bottleneck	float	(0,+∞)	Formula
36	BT2	Bottleneck	float	(0,+∞)	Formula
37	min_BT	The minimum of BT2 and BT1	float	(0,+∞)	VESTA file
38	RT	Radius of largest sphere probe that can freely pass through the void space packed by framework ions	float	(0,+∞)	Geometry-based Ion-transport Analysis Library CAVD
39	EP_6b	Configurational entropy of Na in 6b site	float	[0,+∞)	Formula
40	EP_18e	Configurational entropy of Na in 18e site	float	[0,+∞)	Formula
41	EP_36f	Configurational entropy of Na in 36f site	float	[0,+∞)	Formula
42	EP_Na	Configurational entropy of Na	float	[0,+∞)	Formula
43	EP_M	Configurational entropy of cationic in M site	float	[0,+∞)	Formula
44	EP_X	Configurational entropy of cationic in X site	float	[0,+∞)	Formula
45	T′	Temperature	float	(0,+∞)	Reference

Table S1 The meanings, types, ranges, and sources of all descriptors in NASICON

No.	Descriptors	Description	Type	Range	Source
1	Occu_6b	Occupancy of Na in 6b site	float	[0,1]	CIF
2	Occu_18e	Occupancy of Na in 18e site	float	[0,1]	CIF
3	Occu_36f	Occupancy of Na in 36f site	float	[0,1]	CIF
4	C_Na	Na⁺ concentration	float	(0,+∞)	Formula
5	Occu_M1	Occupancy of element M1	float	[0,1]	CIF
6	Occu_M2	Occupancy of element M2	float	[0,1]	CIF
7	EN_M1	Electronegativity of element M1	float	(0,+∞)	Pauling electronegativity meter
8	EN_M2	Electronegativity of element M2	float	[0,+∞)	Pauling electronegativity meter
9	EN_avg_M	Average effective electronegativity of M site	float	(0,+∞)	Formula
10	Radius_M1	Ionic radius of element M1	float	(0,+∞)	Shannon radius table
11	Radius_M2	Ionic radius of element M2	float	[0,+∞)	Shannon radius table
12	Radius_avg_M	Average effective ionic radius of M site	float	(0,+∞)	Formula
13	Valence_M1	Valence of element M1	int	(0,+∞)	CIF
14	Valence_M2	Valence of element M2	int	[0,+∞)	CIF
15	Valence_avg_M	Average effective ionic valence of M site	float	(0,+∞)	Formula
16	Occu_X1	Occupancy of element X1	float	[0,1]	CIF
17	Occu_X2	Occupancy of element X2	float	[0,1]	CIF
18	EN_X1	Electronegativity of element X1	float	(0,+∞)	CIF
19	EN_X2	Electronegativity of element X2	float	[0,+∞)	CIF
20	EN_avg_X	Average effective electronegativity of X site	float	(0,+∞)	Formula
21	Radius_X1	Ionic radius of element X1	float	(0,+∞)	Shannon radius table
22	Radius_X2	Ionic radius of element X2	float	[0,+∞)	Shannon radius table
23	Radius_avg_X	Average effective ionic radius of X site	float	(0,+∞)	Formula
24	Valence_X1	Valence of element X1	int	(0,+∞)	CIF file
25	Valence_X2	Valence of element X2	int	[0,+∞)	CIF file
26	Valence_avg_X	Average effective ionic valence of X site	float	(0,+∞)	Formula
27	a	Lattice parameter	float	(0,+∞)	CIF file
28	c	Lattice parameter	float	(0,+∞)	CIF file
29	V_cell	Lattice parameter	float	(0,+∞)	Formula
30	V_MO₆	Volume of MO₆ polyhedron	float	(0,+∞)	VESTA file
31	V_XO₄	Volume of XO₄ polyhedron	float	(0,+∞)	VESTA file
32	V_Na₁O₆	Volume of Na₁O₆ polyhedron	float	(0,+∞)	VESTA file
33	V_Na₂O₈	Volume of Na₂O₈ polyhedron	float	(0,+∞)	VESTA file
34	V_Na₃O₅	Volume of Na₃O₅ polyhedron	float	(0,+∞)	VESTA file
35	BT1	Bottleneck	float	(0,+∞)	Formula
36	BT2	Bottleneck	float	(0,+∞)	Formula
37	min_BT	The minimum of BT2 and BT1	float	(0,+∞)	VESTA file
38	RT	Radius of largest sphere probe that can freely pass through the void space packed by framework ions	float	(0,+∞)	Geometry-based Ion-transport Analysis Library CAVD
39	EP_6b	Configurational entropy of Na in 6b site	float	[0,+∞)	Formula
40	EP_18e	Configurational entropy of Na in 18e site	float	[0,+∞)	Formula
41	EP_36f	Configurational entropy of Na in 36f site	float	[0,+∞)	Formula
42	EP_Na	Configurational entropy of Na	float	[0,+∞)	Formula
43	EP_M	Configurational entropy of cationic in M site	float	[0,+∞)	Formula
44	EP_X	Configurational entropy of cationic in X site	float	[0,+∞)	Formula
45	T′	Temperature	float	(0,+∞)	Reference

Algorithm S1 Data accuracy detection algorithm incorporating descriptor knowledge

Input	Original dataset $D$ ; Anomalous data set $D$ ; Feature set $D$ ; Material property set $D$ ; Statistical analysis driven anomalous detection method $D$ ; Correlation detection method $D$ ; Multi-dimensional data outlier detection method $D$
Output	Revised dataset $D 3$
	# Single-dimensional data correctness detection
1	For $d i$ in $d i$ :
2	For $d i j$ in $d i j$ :
3	If $Ind 1 (d i j) = 1$ Or $Ind 1 (d i j) = 1$ Then
4	$O = O ∪ {d i j}$
5	If $O ≠ ∅$ Then
6	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
7	$O = ∅$
8	For $d i$ in $d i$ :
9	$O = O ∪ F 1 (d i)$
10	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
	# Multi-dimensional data correlation detection
11	For $d i$ , $d i$ in $d i$ :
12	$R (d i, d j) = F 2 (d i, d j)$
13	If $Ind 3 (d i, d j) = 1$ Then
14	$O = O ∪ {d i}$
15	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
	# Full-dimensional data reliability detection
16	$Cluster (F), Cluster (T)$
17	For $S j$ in $S j$ :
18	If $Ind 4 (S j) = 1$ Then
19	$O = O ∪ {S j}$
20	If $O ≠ ∅$ Then
21	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
22	$O = ∅$
23	For $S j$ in $S j$ :
24	$O = O ∪ F 3 (S j)$
25	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained

Algorithm S1 Data accuracy detection algorithm incorporating descriptor knowledge

Input	Original dataset $D$ ; Anomalous data set $D$ ; Feature set $D$ ; Material property set $D$ ; Statistical analysis driven anomalous detection method $D$ ; Correlation detection method $D$ ; Multi-dimensional data outlier detection method $D$
Output	Revised dataset $D 3$
	# Single-dimensional data correctness detection
1	For $d i$ in $d i$ :
2	For $d i j$ in $d i j$ :
3	If $Ind 1 (d i j) = 1$ Or $Ind 1 (d i j) = 1$ Then
4	$O = O ∪ {d i j}$
5	If $O ≠ ∅$ Then
6	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
7	$O = ∅$
8	For $d i$ in $d i$ :
9	$O = O ∪ F 1 (d i)$
10	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
	# Multi-dimensional data correlation detection
11	For $d i$ , $d i$ in $d i$ :
12	$R (d i, d j) = F 2 (d i, d j)$
13	If $Ind 3 (d i, d j) = 1$ Then
14	$O = O ∪ {d i}$
15	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
	# Full-dimensional data reliability detection
16	$Cluster (F), Cluster (T)$
17	For $S j$ in $S j$ :
18	If $Ind 4 (S j) = 1$ Then
19	$O = O ∪ {S j}$
20	If $O ≠ ∅$ Then
21	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained
22	$O = ∅$
23	For $S j$ in $S j$ :
24	$O = O ∪ F 3 (S j)$
25	According to the material domain knowledge, the anomaly points in $O$ are modified and the modified data set $O$ is obtained

Table S2 Anomalous data detection and correction

No.	Descriptor	Description
1	Occu_6b	Occupancy of Na in 6b site
2	Occu_36f	Occupancy of Na in 36f site
3	Occu_M2	Occupancy of element M2
4	Occu_X1	Occupancy of element X1
5	Occu_X2	Occupancy of element X2
6	EN_M1	Electronegativity of element M1
7	EN_avg_M	Average effective electronegativity of M site
8	EN_avg_X	Average effective electronegativity of X site
9	Radius_X1	Ionic radius of element X1
10	Radius_avg_X	Average effective ionic radius of X site
11	Valence_avg_X	Average effective ionic valence of X site
12	V_XO₄	Volume of XO₄polyhedron
13	V_Na₃O₅	Volume of Na₃O₅ polyhedron
14	min_BT	The minimum of BT2 and BT1
15	EP_36f	Configurational entropy of Na in 36f site
16	EP_X	Configurational entropy of Na in X site
17	T	Temperature
18	E_a	Activation energy

Table S3 Anomalous samples based on OCSVM

No.	ICSD	Formula
6	15546	Na₂₄Zr₁₂Si₁₈O₇₂
29	202713	Na_14.94Zr_10.8Sc_1.2Si_7.74P_10.26O₇₂
30	202860	Na₆Mo₁₂P₁₈O₇₂
47	260210	Na₂₄Fe₁₂P₁₈O₇₂
56	35770	Na_4.0002Co₃Mo_22.332O₇₂
59	421531	Na₆Ti1₂As₁₈O₇₂
75	72218	Na₆Sn₁₂P₁₈O7₂
84	97956	Na₆Zr₁₂As₁₈O₇₂
89	235775	Na₃MnZr(PO₄)₃

Table S4 Comparison of anomaly detection methods for multi-dimensional data

Method	Description	Advantage	Disadvantage	Application scope
KNN^[4]	The nonparametric and distance-based outlier detection method in one-dimensional or multi-dimensional feature space, which depends on the distance measure between data points.	Simple; There is no need to estimate the distribution.	The results are susceptible to the influence of parameters; Not applicable to large data sets.	Small and medium sample data sets.
LOF^[5]	An outlier detection method based on "density", which considers the outlier data points different from the surrounding data points in density.	Provide quantitative measurement of outliers.	It is difficult to select parameters; It is not suitable for detecting outliers in the whole region.	Small-scale dataset
IForest^[6]	A method considering the division of sample data from each dimension, the earlier the data points are divided into separate areas, the more likely they are outliers.	It has linear time scaling.	Only sensitive to sparse global points, not ideal for dealing with locally sparse points.	Low dimensional data with a small proportion of abnormal data in the total sample size.
OCSVM^[7]	A method that the normal samples are divided in the sphere, and the abnormal samples are divided outside the sphere by looking for the hypersphere.	It can be used for high-dimensional data.	The computation cost is higher.	Data distribution has no hypothesis of high dimensional data.
MCD^[8]	A method for detecting outliers by location and distribution estimation algorithm.	Simple implementation and robustness.	With the increase of data dimension, the efficiency decreases.	Large-scale high dimensional data.

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