Bankruptcy Prediction Using Stacked Auto-Encoders

Figures & data

Figure 1. The structure of an auto-encoder.

Figure 2. The structure of the used stacked auto-encoders with softmax layer.

Table 1. Financial ratios of darden dataset.

ID	Description	ID	Description
R1	Cash/Current debt	R13	Income/Sales
R2	Cash/Sales	R14	Income/Total assets
R3	Cash/Total assets	R15	Income/Total debt
R4	Cash/Total debt	R16	Income plus depreciation/Sales
R5	Cash flow from operations/Sales	R17	Income plus depreciation/Total assets
R6	Cash flow from operations/Total	R18	Income plus depreciation/Total assets debt
R7	Cash flow from operations/Total	R19	Sales/Receivables debt
R8	Cost of goods sold/Inventory	R20	Sales/Total assets
R9	Current assets/Current debt	R21	Total assets/Total debt
R10	Current assets/Sales	R22	Working capital from operations/Sales
R11	Current assets/Total assets	R23	Working capital from operations/Total assets
R12	Current Debt/Total debt	R24	Working capital from operations/Total debt

Table 2. Financial ratios of polish dataset.

ID	Description	ID	Description
R1	net profit/total assets liabilities	R33	operating expenses/short- term
R2	total liabilities/total assets	R34	operating expenses/total liabilities
R3	working capital/total assets	R35	profit on sales/total assets
R4	current assets/short-term liabilities	R36	total sales/total assets
R5	[(cash+short-term securities +	R37	(current assets- inventories)/long-receivables – short-term liabilities)/term liabilities (operating expenses-depreciations)] *365
R6	retained earnings/total assets	R38	constant capital/total assets
R7	EBIT/total assets	R39	profit on sales/sales
R8	book value of equity/total liabilities	R40	(current assets – inventory receivables)/short-term liabilities
R9	sales/total assets	R41	total liabilties/((profit on operating activities+depreciation)*(12/365))
R10	equity/total assets	R42	profit on operating activities/sales
R11	(gross profit + extraordinary items +	R43	rotation receivables + inventory financial expenses)/total assets turnover in days
R12	gross profit/short-term liabilities	R44	(receivables*365)/sales
R13	(gross profit + depreciation)/sales	R45	net profit/inventory
R14	(gross profit + interest)/total assets	R46	(current assets – inventory)/short- term liabilities
R15	(total liabilities * 365)/(gross profit +	R47	(inventory * 365)/cost of depreciation) products sold
R16	(gross profit + depreciation)/total	R48	EBITDA (profit on operating activities – depreciation)/total liabilities assets
R17	total assets/total liabilities	R49	EBITDA (profit on operatingactivities – depreciation)/sales
R18	gross profit/total assets	R50	current assets/total liabilities
R19	gross profit/sales	R51	short-term liabilities/total assets
R20	(inventory * 365)/sales	R52 (short-term liabilities * 365)/cost of products sold)
R21	sales (n)/sales (n-1)	R53	equity/fixed assets
R22	profit on operating activities/total assets	R54	constant capital/fixed assets
R23	net profit/sales	R55	working capital
R24	gross profit (in 3 years)/total assets	R56	(sales – cost of products sold)/sales
R25	(equity – share capital)/total assets	R57	(current assets – inventory – short-term liabilities)/(sales – gross profit – depreciation)
R26	(net profit + depreciation)/total liabilities	R58	total costs/total sales
R27	profit on operating activities/financial expenses	R59	long-term liabilities/equity
R28	working capital/fixed assets	R60	sales/inventory
R29	logarithm of total assets	R61	sales/receivables
R30	(total liabilities – cash)/sales	R62	(short-term liabilities *365)/sales
R31	(gross profit + interest)/sales	R63	sales/short-term liabilities
R32	(current liabilities * 365)/cost of products sold	R64	sales/fixed assets

Table 3. A confusion matrix.

	Actual class (%)
Predicted class (%)	Non-bankrupt	Bankrupt
Non-Bankrupt	TP	FN
Bankrupt	FP	TN

Figure 3. The impact of the number of SAE hidden layers and the number of hidden units on classification accuracy for Darden dataset.

Figure 4. The impact of the number of SAE hidden layers and the number of hidden units on classification accuracy for Polish dataset.

Table 4. Comparison of our approach with similar works for Darden dataset.

	Methods	Accuracy	AUC
Our model	SAE+softmax	87.9	87.7
(Wang, Ma, and Yang 2014)	LRA	73.90	–
	NB*	77.78	–
	DT	75.99	–
	ANN	75.69	–
	SVM	79.99	–
	Bagging	81.22	–
	Boosting	79.40	–
	FS-Boosting	86.79	–
(Zhang et al. 2017)	RBF	74.2	82.1
	MLP	68.9	79.1
	Bayesnet	72	76.6
	J48	62.9	63
	Logistic	77.8	80.3
	FV-SMO	74.3	82.6

NB: Naive Bayes

Table 5. Comparison of our approach with similar works for Polish dataset.

	Methods	Accuracy	AUC
Our model	SAE+softmax	0.98	0.961
(Zieba, Tomczak, and Tomczak 2016)	LDA	–	0.639
	MLP	–	0.543
	LR	–	0.620
	AB*	–	0.916
	SVM	–	0.502
	RF	–	0.851
	XGB*	–	0.945
	XGBE*	–	0.953
	EXGB*	–	0.959
(Zhang et al. 2017)	Isolation Forest	–	0.93
	One-Class SVM	–	0.92
	Multivariate Gaussian	–	0.89
	NN	–	0.84
	GBDT*	–	0.85

AB: AdaBoost.

XGB: Boosted trees trained with Extreme Gradient Boosting.

XGBE: only the last tree of the ensemble of boosted trees, i.e., fk, trained with the

ensemble of boosted trees with synthetic features.

EXGB: Ensemble of boosted trees trained with the Ensemble of boosted trees with

synthetic features.

GBDT: Gradient boosted decision tree.

Wang, G., J. Ma, and S. Yang. 2014. An improved boosting based on feature selection for corporate bankruptcy prediction. Expert Systems With Applications 41:2353–61. doi:10.1016/j.eswa.2013.09.033.

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Zhang, Q., J. Wang, A. Lu, S. Wang, and J. Ma. 2017. An improved SMO algorithm for financial credit risk assessment–evidence from China’s banking. Neurocomputing. doi:10.1016/j.neucom.2017.07.002.

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Zieba, M., S. K. Tomczak, and J. K. Tomczak. 2016. Ensemble boosted trees with synthetic features generation in application to bankruptcy prediction. Expert Systems With Applications 58:93–101. doi:10.1016/j.eswa.2016.04.001.

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