Coot-Sine cosine algorithm enabled neural network model for financial distress prediction in federated learning

Abstract

Because of Covid-19 effect economic stability has been shaken and unemployment rates have increased in recent years, predicting financial conditions of consumers and providing a credit rating has become more important. So, to overcome these problems, Coot-Sine Cosine Algorithm (Coot-SCA_NN) is aimed to predict financial distress in federated learning (FL). Proposed method involves different entities, i.e., nodes and server. Process included in the proposed framework includes local training based on local data at each node, updates to server, model aggregation at server, and download of global model at the nodes, update training based on the downloaded global model and local model at every epoch of iteration. Here, in training model, input data is taken from dataset and then data augmentation model is carried out based on the mutual information. Finally, financial distress is predicted utilizing a neural network (NN) that is trained by the proposed optimization algorithm named Coot-SCA. At each node the information is processed and the details are recorded on the server for further processing. Proposed Coot-SCA_NN is derived by combining the Coot algorithm with Sine Cosine Algorithm (SCA). A major contribution is made through local renewal and consolidation of the service performed by replacing CAViaR. The performance of the proposed method is analyzed using Financial Distress Prediction dataset and the proposed method has the accuracy of 0.924, MSE of 0.083, RMSE of 0.289, Loss of 0.079, and MAP of 0.910.

Keywords

Sine cosine algorithm coot algorithm global loss function financial distress mutual information

Introduction

Studies show, because of bad financial structures, financial distress occurs. A firm's financial leverage increases its agency costs and makes top managers more likely to make high-risk decisions,¹ and poor financial structures are generally inversely related to corporate performance.^2,3 Financial distress occurs when a company suffers from a threat from the outward economic environment or a failure of inward financial decisions, causing it to struggle with insufficient cash flow, or worse, it may lose profits or go bankrupt. Many companies suffered heavy losses and went bankrupt during the global financial crisis that exploded in 2008. A company without a financial risk early warning mechanism cannot properly handle financial difficulties and shocks when the external economic environment deteriorates. To some extent, a well-developed internal control mechanism of a company should include a scientific financial distress prediction (FDP) system, which can indicate financial collapse before a financial crisis occurs.⁴ Bankruptcy prediction, is commonly referred to as business failure prediction, financial distress prediction plays a vital role for decision makers like investors, lenders and company managers. Contrarily, managers must determine company's risk while developing a development plan for company. Alternately, lenders or investors need to evaluate the company's financial position, liquidity, solvency and profitability before making a decision on credit rating or investment.⁵

As the core of corporate operations, efficient financial management can predict potential financial crisis.⁶ Because potential financial vulnerabilities or risks revealed by financial distress forecasting, investors’ decision-making can be improved, help financial institutions in their lending decisions, and assist regulatory authorities formulate regulations. If competent authorities, corporate governance bodies, CPAs, auditors and senior management can identify risk warnings or problems as soon as possible, relevant actions can be taken to prevent suffering or deterioration; Therefore, effective financial crisis prediction is very important.^3,7–10 FL enables target model building without assigning local information by device model training on edge resources and also referred by a newly created privacy-preserving distributed ML scheme. By building a global learning model based on local models of distributed agents, FL-based application to predict customers’ financial problems is solved. By network agents utilizing their device data and local resources, Local models are created. FL concept is used because the learning strategy does not need to share any data with the server or any other agent that ensures the protection of clients’ sensitive data.¹¹

To address data privacy¹² issues in machine learning (ML),^13,14 Google introduced a privacy-preserving machine learning framework called FL,^15,16 which allows multiple parties to jointly train a model without sharing data. The model is trained using their local dataset and a copy of model is maintained by each party and only gradients are sent to other parties at every training epoch. So, from these parameters parties cannot derive raw data and for parties with similar data this method is useful i.e., data with the similar feature space. In different parties, data stored with feature space is not always similar. The emergence of this technology solves the conflict between data privacy and data sharing for distributed devices. FL is suitable for use when data is privacy sensitive due to the nature of data not being exposed to a third central server. Developing an efficient FL method for heterogeneous data remains challenging.¹⁷ Investigating powerful financial distress forecasting (FDP) models has always been a necessary research topic attracting academics and practitioners. In the twentieth century, some classical statistical FDP models such as the Z-score model,¹⁸ the zeta-score model, the logistic regression analysis (logit) model, and the probit model were developed, which laid the foundation for further research on FDP modeling. With the development of artificial intelligence, a large number of researchers have devoted themselves to developing more effective FDP models based on artificial intelligence technologies, such as decision trees (DTs), neural networks (NNs),¹⁹ and support vector machines (SVMs), case-based reasoning (CBR), and genetic algorithms (GAs).²⁰

Fundamental aim of this paper is to propose Coot-SCA_NN for predicting financial distress. The proposed method includes various entities such as node and server. The process included in the proposed framework is local training based on each node's local data, server updates, model aggregation at the server, global model download at the nodes, update training based on the downloaded global model and local model, and at every epoch of iteration. In this training model, input data is taken from dataset and a data augmentation model is implemented based on mutual information. Finally, financial distress is predicted using a NN trained by the proposed Coot-SCA optimization algorithm. Data is processed at each node and the data is stored on the server for further processing. Proposed Coot-SCA_NN is obtained by unifying Coot algorithm with SCA. A major contribution is made through local renewal and consolidation of the service performed by replacing CAViaR.

A important role in this paper is given as follows,

Proposed Coot-SCA_NN for financial distress prediction: Financial distress prediction is done by Coot-SCA_NN in FL. Also, Coot-SCA_NN is devised by incorporating Coot algorithm with SCA.

Remaining segment of this paper is structured as: reviewed research papers are given in Section 2, the proposed financial crisis prediction techniques are mentioned in Section 3, and obtained outcome for Coot-SCA_NN is given in Section 4 and conclusion is explained in section 5.

2. Motivation

In a company, bad decisions regarding pricing or marketing can lead to financial distress. Expensive advertising campaign or ineffectual modifications to a product or pricing structure are other possible causes of a financial crisis that can lead to a loss in sales. Therefore, the prediction of financial crisis is important and it is a challenging process. Hence a useful model is proposed in this paper.

2.1. Literature survey

To predict financial problems of customer, Imteaj, A. and Amini, M.H. et al.¹¹ introduced FL to predict customers financial distress. This method achieved rapid convergence. However, it failed to identify that an agent is malicious or not. Liu, J. et al.⁵ designed a GA-based gradient boosting method to parameter selection in gradient boosting decision tree and integrated network-based variables for financial distress prediction. The developed model was robustness. However, network-based variables can improve the classifier prediction performance relating to accuracy was not explored. Sun, J. et al.²⁰ introduced Support Vector Machine (SVM). SVM-based multiclass financial distress prediction (FDP) merged with decomposition and fusion methods. This method greatly improved multiclass performance. However, it was extremely hard to predict by human expertise. Sun, J. et al.⁴ designed Adaboost-SVM ensemble learning for dynamic FTP. This method greatly improved the recognition ability of minority financial crisis models. But it failed to solve class asymmetric transient classification problems. Jan, C.L.³ introduced deep learning (DL) to develop high accuracy and effective financial crisis forecasting models. This method produced more accurate and useful results. Outcome of this study failed to apply in all situations because of different economic and financial environments and financial regulations of diverse countries, regions or economies. Du, X. et al.²¹ designed clustering-based under-sampling (CUS) with Gradient Boosting Decision Tree (GBDT) to improve the scope and depth of clustering to achieve better predictive performance. With regard to both overall performance and recognition efficiency, this method outperformed benchmark models. Due to class-imbalanced financial datasets, there is further need to explore a better ensemble method. El-Bannany, M. et al.²² introduced MLP + LSTM + CNN for financial Distress prediction. This method was very strong. However, it encountered problems when increasing the number of input attributes. El Bannany, M. et al.²³ introduced a multi-layer perceptron with parameter optimization for financial distress forecasting. Due to standard ML methods, like SVM and DT, this method outperformed. However, it failed to include macroeconomic and other industrial factors.

2.2. Challenges

The challenges faced during financial distress are labeled as follows,

In,¹¹ a mechanism for detecting malicious agents was integrated and fairness is implemented considering the agent's contribution to the global model convergence. This method outperformed the centralized model and the state-of-the-art FL model, mostly in non-IID settings. It failed to incorporate a mechanism to identify malicious agents and execute fairness by examining the agent's contributions regarding global model convergence.

The method developed in¹¹ cannot detect whether an agent is malicious or not, and did not guarantee fairness when assigning computational tasks during training.

Different feature selection procedures may be intended for diverse decomposition and fusion approaches. In addition, the decomposition and fusion methods can also be integrated with other classification algorithms to propose more effective multiclass FDP models.²⁰

The method developed in⁴ failed to address other issues such as default detection, customer classification, and spam filtering. Also, it failed to explore a dynamic model weighting mechanism for integration with ensemble learning algorithms, e.g., Random space and Bagging.

Tough, extended financial distress can eventually cause bankruptcy. When a financial crisis occurs, it should be considered to right away so that the situation does not worsen. Financial problems can cause more financial problems if they are not fixed immediately

3. Proposed coot-SCA for financial distress prediction

Fundamental reason of this research is to devise a method for financial crisis prediction using proposed Coot-Sine Cosine Algorithm based neural network (Coot-SCA_NN). The proposed method involves different entities, i.e., nodes and server. Process included in the proposed framework includes local training based on local data at each node, updates to server, model aggregation at server, downloads of global model at the nodes, update training based on downloaded global model and local model, and executes each time. Here, in the training model, the input data is taken from the dataset and then the data augmentation model is carried out based on the mutual information.²⁴ Finally, financial distress is predicted using NN,²⁵ which is trained by the proposed optimization algorithm named Coot-SCA_NN. At each node the information is processed and the details are recorded on the server for further processing. The proposed Coot-SCA_NN is obtained by integrating the Coot algorithm²⁶ with the SCA.²⁷ A major contribution is made through local renewal and consolidation of the service performed by replacing CAViaR.²⁸ Block diagram of Coot-SCA_NN method is demonstrated in Figure 1.

Figure 1.

Block diagram of coot-SCA_NN method.

3.1. Local training based on local data

Local training data based on local data at every node, training models, training architecture are discussed in the below section.

3.1.1. Training at every node

Data is trained in every device node for every $t_{1}$ time on the basis of the local data and training model includes steps, such as data acquisition and financial stress prediction.

3.1.2. Training models

In training model, tuning Ride NN for financial distress prediction and tuned Ride NN is trained utilizing the proposed Coot-SCA algorithm are discussed in below section,

a)
Data acquisition

Consider dataset as S, which encloses p quantity of input data and exhibited as
$S = S_{1}, S_{2}, \dots \dots S_{q}, \dots . . S_{p}$
(1)

Herein, p denotes total number of data and $q^{t h}$ number of data from dataset is $S_{q}$ . b)
Financial distress prediction

Financial distress prediction is always significant for financial institutions to evaluate the financial health of companies and individuals. Bankruptcy prediction and credit scoring are two significant problems in financial distress prediction, where various statistical and ML methods have been utilized to develop financial prediction models. For decision makers like investors, lenders and company managers, financial distress prediction plays a crucial role. Contrastingly, even if developing a development plan for the company, company's risk must be accessed by the managers. Alternatively, company's financial position like liquidity, solvency and profitability are needed to be evaluated by the lenders or investors before taking credit rating or investment decisions. The Ride NN architecture and the prediction of financial distress applied by the proposed hybrid Coot-SCA algorithm are discussed below. Here, the input fed to of NN for financial distress prediction is $S_{q}$ . i)
Ride NN architecture

Input layer, hidden layer and outcome layers are the three layers in the RideNN classifier and each layer contains neurons. In different layers, by linking outcome of one neuron to input of another neuron, a network is constructed. Given input to RideNN classifier is listed below,
$g_{1}^{c_{1}} = [g_{1}^{c_{1}}, g_{2}^{c_{2}}, \dots . ., g_{w_{1}}^{c_{1}}, \dots \dots . . g_{W_{1}}^{c_{1}}]; 1 \leq w_{1} \leq W_{1}$
(2)
where entire quantity of features and input neurons is $W_{1}$ . Based on weights, classification is done and designated to neurons in layers of the network. In hidden layers, weight assignment of neurons is expressed as,
$E = E_{1}, E_{2}, \dots \dots \dots E_{W_{1}}$
(3)

To have a bias and generate a potential is assumed by hidden layer neurons. $E_{W_{1}} + 2$ denote neuron in output layer also have weights and output layer bias referred to as $E_{W_{1}} + 3$ . Utilizing a transfer function output of the classifier is calculated.
$l^{c_{1}} = E_{W_{1}} + 2 * [\log s i g (\sum_{w_{1} = 1}^{W_{1}} g_{w_{1}}^{c_{1}} * E_{w_{1}} + E_{W_{1}} + 1)] + E_{W_{1}} + 3$
(4)

$\log s i g$ computes output from a given net input and also known as log-sigmoid transfer function. Input of $w_{1}^{t h}$ neuron is $g_{w_{1}}^{c_{1}}$ . In hidden layer $w_{1}^{t h}$ neuron, weight is represented as $E_{w_{1}}$ . Output weight $E_{W_{1}} + 2$ and dependencies are $E_{W_{1}} + 1$ , and $E_{W_{1}} + 3$ .

Here, using mutual information loss function is computed and it is fundamental measure of relationship among random variables. Mutually informative two random variables $Q_{4}$ and $Z_{4}$ . It is expressed as,
$J_{3} (Q_{4}; Z_{4}) = \int_{Q_{4} \times Z_{4}} \log \frac{d N_{Q_{4} Z_{4}}}{d N_{Q_{4}} \otimes N_{Z_{4}}}$
(5)
where, $N_{Q_{4} Z_{4}}$ and are the edges of the joint probability distribution, and marginals are $N_{Q_{4}} = \int_{Z_{4}} d N_{Q_{4} Z_{4}}$ and $N_{Z_{4}} = \int_{Q_{4}} d N_{Q_{4} Z_{4}}$ . Between variables mutual information captures non-linear statistical dependences and can serve as a measure of true dependence in contrast with correlation. Output obtained by Ride NN is $N_{q}$ . Figure 2 shows the architecture diagram for Ride NN. ii)
Tuning Ride NN using Coot-SCA

Figure 2.
Architecture of rideNN.

In this section the tuned neural network is trained by the intended optimization algorithm known as Coot-SCA. This is derived by incorporating Coot algorithm with SCA. The principle of the

The COOT optimization algorithm is on the basis of diverse movement behaviors of coot flocks on water surface. Coots are tiny waterfowl that exhibit several distinct group behaviors at water surface, with the final aim of the behavior being to move near food or a precise location. On water surface, coot group mostly has four diverse movement behaviors: random movement, chain movement, position adjustment according to the leader, and leader movement. The Sine Cosine Algorithm (SCA) is a population-based optimization algorithm for solving multiple optimization problems. SCA produce diverse initial random solutions and moves near the best solution utilizing a mathematical model on the basis of sine and cosine functions. Diverse stochastic and adaptive variables are incorporated into this algorithm to preserve exploration and exploitation of the search space at diverse milestones of the optimization.

The main two approaches of SCA (Population Search Strategy and Local Search Strategy) are provided to expand an intelligent algorithm suitable for efficient search through two main search strategies (Global Search and Local Exploration). The optimization process include two phases: exploration and exploitation phase.

Solution encoding

Solution encoding is employed to find simplest solution in a $U_{1}$ dimensional space. It is expressed as $[1 \times μ_{1}]$ .
$U_{1} = [1 \times μ_{1}]$
(6)

Wherein, $μ_{1}$ is the learning parameter of Ride NN.

Fitness function

It is used for computation of best solution. It is the difference between the target value and the output of ride NN. From the previous iteration the optimal solution is determined as each solution to achieve a best location.
$F_{5} = \frac{1}{p} \sum_{q = 1}^{p} {[T A_{q} - N_{q}]}^{2}$
(7)
where, $N_{q}$ is the output of Ride NN and $T A_{q}$ denotes the target value.

Step 1: initialization

Consider input data Y in $U_{1}$ spatial dimensional grid,
$Y = Y_{1}, Y_{2}, \dots \dots . Y_{i}, \dots \dots . Y_{j}$
(8)
wherein, $i^{t h}$ input data given to $M_{i}$ and $M_{j}$ is the total number of input.

Step 2: exploration phase

There are gradual modifications in the stochastic solutions, and the stochastic variations are significantly lower than in the exploration phase.

In exploration phase, random variations are significantly lower.
$Y_{i} (t + 1) = Y_{i} (t) + f_{1} \times \sin (f_{2}) * | f_{3} R_{i} (t) - Y_{i} (t) | f_{3} < 0.5$
(9)
wherein, current solution position at $i^{t h}$ iteration is denoted as $Y_{i} (t)$ ,

Assume,
$\begin{aligned} f_{3} R_{i} (t) > Y_{i} (t) \end{aligned}$
(10)

$\begin{aligned} Y_{i} (t + 1) = Y_{i} (t) + f_{1} \sin (f_{2}) * f_{3} R_{i} (t) - f_{1} \sin (f_{2}) Y_{i} (t) \end{aligned}$
(11)

$\begin{aligned} Y_{i} (t + 1) = Y_{i} (t) [1 - f_{1} \sin (f_{2})] + f_{1} \sin (f_{2}) * f_{3} R_{i} (t) \end{aligned}$
(12)

herein, $f_{1}, f_{2}$ and $f_{3}$ implies the random numbers and $R_{i} (t)$ is the destination point position.

From Coot,
$C o o t P o s (i + 1) = C o o t P o s (i) + A_{3} \times T_{2} \times (P - C o o t P o s (i))$
(13)
position of coot is denoted as $C o o t P o s (i)$ ,In the interval $[0, 1]$ , random number is indicated as $T_{2}$ .
$\begin{aligned} C o o t P o s (i + 1) & = Y_{i} (t + 1) \end{aligned}$
(14)

$\begin{aligned} C o o t P o s (i) & = Y_{i} (t) \end{aligned}$
(15)

$\begin{aligned} Y_{i} (t + 1) & = Y_{i} (t) + A_{3} \times T_{2} \times (P - Y_{i} (t)) \end{aligned}$
(16)

$\begin{aligned} Y_{i} (t + 1) & = Y_{i} (t) [1 - A_{3} \times T_{2}] + A_{3} \times T_{2} \times P \end{aligned}$
(17)

$\begin{aligned} Y_{i} (t) & = \frac{Y_{i} (t + 1) - A_{3} \times T_{2} \times P}{[1 - A_{3} \times T_{2}]} \end{aligned}$
(18)

Substituting the Equation (18) in Equation (12),
$\begin{aligned} Y_{i} (t + 1) & = (\frac{Y_{i} (t + 1) - A_{3} \times T_{2} \times P}{[1 - A_{3} \times T_{2}]}) [1 - f_{1} \sin (f_{2})] + f_{1} \sin (f_{2}) * f_{3} R_{i} (t) \end{aligned}$
(19)

$\begin{aligned} Y_{i} (t + 1) [1 - A_{3} \times T_{2}] & = Y_{i} (t + 1) [1 - f_{1} \sin f_{2}] \\ - A_{3} \times T_{2} \times P [1 - f_{1} \sin f_{2}] + (1 - A_{3} \times T_{2}) [f_{1} f_{3} R_{i} (t) \sin f_{2}] \end{aligned}$
(20)

$\begin{aligned} [1 - A_{3} \times T_{2}] Y_{i} (t + 1) - Y_{i} (t + 1) [1 - f_{1} \sin (f_{2})] = - (A_{3} \times T_{2} \times P) \\ [1 - f_{1} \sin (f_{2})] + (1 - A_{3} \times T_{2}) [f_{1} f_{3} R_{i} (t) \sin f_{2}] \end{aligned}$
(21)

$\begin{aligned} Y_{i} (t + 1) [f_{1} \sin f_{2} - A_{3} T_{2}] & = (A_{3} \times T_{2} \times P) [f_{1} \sin (f_{2}) - 1] \\ + (1 - A_{3} T_{2}) [f_{1} f_{3} R_{i} (t) \sin (f_{2})] \end{aligned}$
(22)

Updated solution is expressed as follows,
$\begin{aligned} Y_{i} (t + 1) & = \frac{(A_{3} \times T_{2} \times P) [f_{1} \sin (f_{2}) - 1] + (1 - A_{3} \times T_{2}) [f_{1} f_{3} R_{i} (t) \sin (f_{2})]}{[f_{1} \sin f_{2} - A_{3} T_{2}]} \end{aligned}$
(23)

$\begin{aligned} P & = r a n (1 - d) * (u b - l b) + l b \end{aligned}$
(24)
wherein, $u b$ and $l b$ is the higher bound and lesser bound, $T_{2}$ is the random number (0,1).
$L e t, A_{3} = 1 - L_{4} \times (\frac{1}{I t e r})$
(25)
wherein, current iteration is $L_{4}$ , Iteration of maximum is $I t e r$ .

Step 3: exploitation phase

In random solution there are some gradual changes in exploitation phase.
$Y_{i} (t + 1) = Y_{i} (t) + f_{1} \times \cos (f_{2}) \times | f_{3} R_{i} (t) - Y_{i} (t) |$
(26)

Equation (9) and equation (26) are combined as follows,
$Y_{i} (t + 1) = {\begin{aligned} Y_{i} (t) + f_{1} \times \sin (f_{2}) \times | f_{3} R_{i} (t) - Y_{i} (t) | f_{4} < 0.5 \\ Y_{i} (t) + f_{1} \times \cos (f_{2}) \times | f_{3} R_{i} (t) - Y_{i} (t) | f_{4} \geq 0.5 \end{aligned}$
(27)

In the interval $[0, 1]$ , random number indicated as $f_{4}$ . $f_{1}, f_{2}, f_{3}$ and $f_{4}$ are four parameters in SCA. Next position is indicated as $f_{1}$ , it could be in the space among destination or outside and the solution. The parameter $f_{2}$ denotes far movement near or outer the end. Parameter $f_{3}$ displays weights for end. Parameter, it switches equally among sine and cosine mechanism in equation (21). Because of using sine and cosine in the expression, SCA algorithm is defined. Exploitation of space between two solutions can guarantee that, by cyclic pattern of sine and cosine function, a solution is allowed to realign around another solution.

Search the solutions outside the space among their correlated destination and also for exploring the search space. In interval $[0, 2 π]$ , by defining a random number randomness is achieved. Exploration of search space is known for this mechanism. An algorithm must be balanced in exploration and exploitation to find trustable regions of search space and global optimum coverage. In order to achieve balance exploration and exploitation, equation (9) sine and cosine range to equation (26) is varied by resulting expression,
$f_{1} = a_{4} - t \frac{a_{4}}{T}$
(28)
wherein, t is the current iteration, highest value of iteration is T and $a_{4}$ constant.

When ranges of sine and cosine functions are in $(1, 2]$ and $[- 2, - 1)$ SCA algorithm explores search space and it exploits search space when ranges are in $[- 1, 1]$ .

Step 4: termination

Termination process is repeated until the best solution arises. By default, when the iteration counter is higher than greater number of iterations, the optimization process terminated. Pseudo code for Coot-SCA is mentioned in algorithm 1.

3.2. Aggregation at the server

Trained data are sent to the global model and nodes are aggregated at the server. Aggregate weight from different local training data and using CAViar model weights are averaged in aggregation at the server. Figure 3 represents aggregation at the server.

Figure 3.

Aggregation at the server.

$w_{1}, w_{2}$ implies various local nodes weight.

Apply caviar,

W_{g l o b a l} = β + β W_{l o c 1} (t - 1) + β_{r} W_{l o c 2} (t - 2) + β f_{y} (W_{l o c 1} (t - 1)) + β_{x} f_{y} (W_{l o c 2} (t - 2))

(29)

wherein,

W_{l o c 1} (t - 1)

and

W_{l o c 2} (t - 2)

represents local node weight 1,2 at

(t - 1)^{t h} (t - 2)^{t h}

iteration.

β

implies P vector of unknown parameter.

f_{y} (W_{l o c 1} (t - 1))

and

f_{y} (W_{l o c 2} (t - 2))

indicates fitness of value weight at

(t - 1)^{t h} (t - 2)^{t h}

iteration.

3.3. Apply global trained model on every local node

Applying global trained model at every local node and at last, averaged weights are upgraded to server and every local node (devices).

4. Results and discussion

Experimental outcome of Coot-SCA_NN method for financial distress prediction is examined in this part.

4.1. Experimental setup

Using python tool, Coot-SCA_NN method for financial distress prediction is successfully executed.

4.2. Dataset description

Financial Distress Prediction dataset:²⁹ This dataset focuses on predicting financial distress for a sample of companies. The first column, ‘Company,’ represents the sample companies. The second column, ‘Time,’ indicates the different time periods to which the data corresponds. The time series length varies from 1 to 14 for each company. The third column contains the target variable, ‘Financial Distress.’ If the value is greater than −0.50, the company is considered healthy (0); otherwise, it is classified as financially distressed (1). Columns four through the last column represent the features, labeled x1 to x83, which include both financial and non-financial characteristics of the companies. These features are from the previous time period and are used to predict whether a company will experience financial distress. Feature x80 is a categorical variable.

Taiwanese Bankruptcy Prediction Dataset:³⁰ The data were obtained from the Taiwan Economic Journal for the years 1999 to 2009. Company bankruptcy was defined based on the business regulations of the Taiwan Stock Exchange. The dataset is multivariate in nature and falls within the business domain, specifically designed for classification tasks. It comprises 6819 instances, each characterized by 95 integer-valued features that capture various financial and operational attributes of the companies.

4.3. Data visualization

SHAP (SHapley Additive Explanations) is an explainability framework for machine learning models that helps interpret how individual features contribute to a model's predictions. It is based on Shapley values, a concept from cooperative game theory, which assigns a fair contribution score to each feature in a model's decision-making process. Figure 4 presents the SHAP visualization to show the impact of each input feature on the model's predictions. Figure 4(a) shows the SHAP heatmap that visualizes the impact of different features on a machine learning model's prediction across multiple instances. Figure 4(b) is a SHAP feature importance plot, which visualizes the impact of individual features on the model's predictions. Figure 4(c) is a SHAP summary plot that illustrates the mean absolute SHAP values for different features, showing their average impact on model predictions. Figure 4(d) is a SHAP summary dependence plot, which shows how different features contribute to the model's output, highlighting their impact and interactions. Figure 4(e) explains how individual features contribute to a specific prediction. It shows how the base value (expected model output) is adjusted by each feature's SHAP value to arrive at the final prediction.

Figure 4.

SHAP visualization.

4.4. Performance metrics

Coot-SCA_NN method for financial distress prediction has five performance measures like accuracy, Loss Function, MSE, RMSE, and MAP are listed below.

4.4.1. Accuracy

Accuracy is utilized to estimate the ability of a categorical decision and referred to as performance measure.

a c c u r a c y = \frac{t_{p} + t_{n}}{t_{p} + t_{n} + s_{p} + s_{n}}

(30)

$t_{p}, t_{n}$ true positive and negative, $s_{p}, s_{n}$ is false positive and negative.

4.4.2. MSE

MSE computes error by squaring differences among predicted and actual value and on the dataset averaging it. Expression for MSE is explained in equation (7).

4.4.3. RMSE

RMSE is utilized in ML and to calculate accuracy of a predictive model. It is a popular metric and computes the differences among the predicted and actual values, squaring errors, takes mean, and then finds square root.

R M S E = \sqrt{\frac{1}{p} {\sum_{q = 1}^{p} [T A_{q} - N_{q}]}^{2}}

(31)

4.4.4. Loss function

Loss function is a function, which computes loss for one data point.

L o s s f u n c t i o n = (T A_{q} - N_{q})^{2}

(32)

4.4.5. MAP

It calculates by finding (AP) average precision for each class and average over a number of classes.

M A P = \frac{1}{E_{1}} \sum_{i = 1}^{E_{1}} C_{i}

(33)

wherein,

C_{i}

implies average precision

4.5. Analysis using financial distress prediction dataset

4.5.1. Performance analysis

Performance analysis of devised methodology using time step is discussed in Figure 5. Analysis of Coot-SCA_NN regarding accuracy is displayed in Figure 5(a). When time step = 20, accuracy achieved by the proposed method is 0.848, 0.852, 0.856, 0.860 and 0.865 for epochs 20, 40, 60, 80, and 100, respectively. For time step = 80, the proposed method has the accuracy of 0.894, 0.905, 0.910, 0.913, and 0.921 for epochs 20, 40, 60, 80, and 100, respectively. The estimation of new methodology in relation to MSE is discussed in Figure 5(b). When time step = 20, 0.392, 0.358, 0.312, 0.288 and 0.249 are the MSE values obtained by the proposed method for epochs 20, 40, 60, 80, and 100, respectively. For time step = 80, intended method obtained MSE of 0.235, 0.186, 0.170, 0.130, and 0.093 for epochs 20, 40, 60, 80, and 100, respectively. Assessment of intended method with respect to RMSE is demonstrated in Figure 5(c). The RMSE values attained by proposed method for epochs 20, 40, 60, 80, and 100 is 0.626, 0.598, 0.559, 0.537, and 0.499, respectively. Performance analysis with respect to loss function is displayed in Figure 5(d). For time step = 20, loss values of the proposed method with epoch 20 is 0.152, epoch 40 is 0.148, epoch 60 is 0.144, epoch 80 is 0.140, and epoch 1000 is 0.135. The loss value decreases when the time step increases. Figure 5(e) shows the analysis based on MAP. When time step = 20, the MAP values attained by the proposed method is 0.822, 0.770, 0.786, 0.792, and 0.813 for epochs 20, 40, 60, 80, and 100, respectively.

Figure 5.

Performance analysis with time step, a) accuracy b) MSE c) RMSE d) Loss e) MAP.

4.5.2. Comparative analysis

This section presents the comparative analysis based on time step and cross validation. The comparative methods used for analysis are FL,¹¹ GA-based gradient boosting,⁵ OVO-SVM,²⁰ DNN + CNN,³ Decision Tree (DT),³¹ Logistic Regression (LR),³¹ and Random Forest (RF).³²

(a)
Comparative Analysis based on time step

Figure 6 shows comparative analysis of Coot-SCA_NN. In Figure 6(a), the evaluation of proposed method referring to accuracy is presented. Accuracy values achieved by FL is 0.785, GA-based gradient boosting is 0.804, OVO-SVM is 0.821, DT is 0.837, DNN + CNN is 0.843, LR is 0.850, RF is 0.854, and the proposed methodology is 0.865, when time step =20. While time step = 80, intended method achieved accuracy of 0.921 and traditional methods achieved an accuracy of 0.849, 0.864, 0.879, 0.898, 0.901, 0.905, and 0.913. The analysis of new methodology regarding MSE is displayed in Figure 6(b). Existing methods and proposed method reached MSE values of 0.648, 0.522, 0.463, 0.410, 0.365, 0.348, 0.299, and 0.249, when time step = 20. The MSE values attained by devised methodology about 0.093 and classic methods about 0.440, 0.361, 0.270, 0.218, 0.160, 0.138, and 0.110 for time step = 80. Evaluation of Coot-SCA_NN in relation to RMSE is mentioned in Figure 6(c). Traditional method and proposed method achieved RMSE of 0.805, 0.722, 0.681, 0.640, 0.604, 0.590, 0.547, and 0.499 for time step = 20. RMSE values attained by FL is 0.663, GA-based gradient boosting is 0.601, OVO-SVM is 0.519, DT is 0.467, DNN + CNN is 0.400, LR is 0.371, RF is 0.331, and Coot-SCA_NN is 0.306, while time step = 80. Figure 6(d) displays the estimation of intended method regarding loss function. When time step = 20, traditional methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, RF, and the proposed Coot-SCA_NN have the loss values of 0.215, 0.196, 0.179, 0.163, 0.157, 0.150, 0.146, and 0.135, respectively. For time step = 80, devised methodology reached loss value of 0.079 and traditional methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF reached loss value of 0.151, 0.136, 0.121, 0.102, 0.099, 0.095, and 0.087, respectively. Assessment of Coot-SCA_NN relative to MAP is shown in Figure 6(e). For time step = 20, the MAP obtained by intended method is 0.822 and traditional methods is 0.749, 0.763, 0.789, 0.798, 0.800, 0.815, and 0.819. Similarly, for time step = 80, the MAP values attained by proposed method is 0.897 and FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF is 0.759, 0.794, 0.821, 0.854, 0.861, 0.869, and 0.877, respectively. (b)
Comparative Analysis based on cross validation

Figure 6.
Comparative analysis with time step, a) accuracy b) MSE c) RMSE d) Loss e) MAP.

Figure 7 shows the comparative analysis based on cross validation. Figure 7(a) shows the analysis based on accuracy. For K-value = 5, the accuracy obtained by the proposed method is 0.890, on the other hand, the accuracy obtained by the existing methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF is 0.802, 0.810, 0.850, 0.860, 0.863, 0.877, and 0.884, respectively. The accuracy increases with the increase in the K-value. The analysis based on MSE is given in Figure 7(b). The MSE of the Coot-SCA_NN, FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF is 0.126, 0.352, 0.308, 0.199, 0.189, 0.157, 0.147, and 0.133, respectively, when K-value is 6. Similarly, the performance of the comparative methods considering RMSE is shown in Figure 7(c). When K-value is 8, the RMSE of the comparative methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, Coot-SCA_NN, LR, and RF is 0.554, 0.502, 0.387, 0.371, 0.341, 0.330, 0.324, and 0.289, respectively. The comparative analysis based on loss is given in Figure 7(d). For K-value = 7, the loss of FL is 0.187, GA-based gradient boosting is 0.154, OVO-SVM is 0.127, DT is 0.120, DNN + CNN is 0.114, LR is 0.106, RF is 0.101, and Coot-SCA_NN is 0.092. Figure 7(e) shows the MAP values of the proposed method and existing methods for different K-values. When K-value is 6, the MAP of the proposed Coot-SCA_NN is 0.868, while the MAP of FL is 0.732, GA-based gradient boosting is 0.766, OVO-SVM is 0.826, DT is 0.837, and DNN + CNN is 0.846, LR is 0.854, RF is 0.859.

Figure 7.
Comparative analysis based on cross validation, a) accuracy b) MSE c) RMSE d) Loss e) MAP.
4.5.3. Comparative discussion

(a)
Discussion based on time step = 80 and K-value = 8

Comparative discussion is displayed in Table 1. Here, the discussion is provided based on the best performance (time step = 80 and K-value = 8) attained by the comparative methods. On seeing Table 1, it is noted that the proposed method offers the high performance than the existing methods with the accuracy of 0.924, MSE of 0.083, RMSE of 0.289, Loss of 0.086, and MAP of 0.910 for K-value = 8.

Table 1.
Comparative discussion.

Metrics/ FL GA-based OVO-SVM DT DNN + LR RF Proposed

Methods gradient CNN Coot-SCA_

boosting NN

When time step = 80 accuracy 0.849 0.864 0.879 0.898 0.901 0.905 0.913 0.921

MSE 0.440 0.361 0.270 0.218 0.160 0.138 0.110 0.093

RMSE 0.663 0.601 0.519 0.467 0.400 0.371 0.331 0.306

Loss 0.151 0.136 0.121 0.102 0.099 0.095 0.087 0.079

MAP 0.759 0.794 0.821 0.854 0.861 0.869 0.877 0.897

K-value = 8 accuracy 0.823 0.852 0.878 0.889 0.893 0.904 0.910 0.924

MSE 0.307 0.252 0.150 0.138 0.116 0.109 0.105 0.083

RMSE 0.554 0.502 0.387 0.371 0.341 0.330 0.324 0.289

Loss 0.177 0.148 0.122 0.111 0.107 0.096 0.090 0.086

MAP 0.767 0.816 0.843 0.865 0.874 0.884 0.895 0.910

(b)
Statistical Analysis

Statistical analysis is a tool for analyzing raw, unstructured data to extract meaningful insights and draw reliable conclusions. The Analysis of Variance (ANOVA) test is a statistical method used to assess whether significant differences exist between the means of two or more groups. It assumes two hypotheses, (1) The means of all groups are equal. (2) At least one group's mean is different. The ANOVA test is performed using the following steps: Define Hypothesis, Calculate the Sum of Squares, Determine degrees of freedom, Determine F-value, and Accept or Reject the Null Hypothesis. Table 2 shows the results of ANOVA test. The ANOVA test result showed statistically significant results of the proposed Coot-SCA_NN with accuracy: F = 40.48827, and P = 2.29E-14. So, the Null Hypothesis is rejected.

Table 2.
ANOVA test.

Degree of freedom Sum of squares Mean squares F P value

C(methods) 4 0.138592 0.034648 40.48827 2.29E-14

Residual 45 0.038509 0.000856

(c)
Training Time

Training time refers to the duration required for a machine learning model to learn from a dataset and build its structure. During this process, the model examines the data, identifies patterns, and constructs the final model. Table 3 shows the training time of the proposed method and the exiting methods. Here, the training time of the proposed method is minimum than the training time of the existing methods.

Table 3.
Training time.

Methods FL GA-based OVO-SVM DT DNN + CNN LR RF Proposed Coot-

gradient boosting SCA_NN

Training Time (Sec.) 35.486 32.1048 28.04246 27.562 26.4488 25.746 25.068 23.524

4.6. Analysis using Taiwanese bankruptcy prediction dataset

	Metrics/	FL	GA-based	OVO-SVM	DT	DNN +	LR	RF	Proposed
When time step = 80	accuracy	0.849	0.864	0.879	0.898	0.901	0.905	0.913	0.921
MSE	0.440	0.361	0.270	0.218	0.160	0.138	0.110	0.093
RMSE	0.663	0.601	0.519	0.467	0.400	0.371	0.331	0.306
Loss	0.151	0.136	0.121	0.102	0.099	0.095	0.087	0.079
MAP	0.759	0.794	0.821	0.854	0.861	0.869	0.877	0.897
K-value = 8	accuracy	0.823	0.852	0.878	0.889	0.893	0.904	0.910	0.924
MSE	0.307	0.252	0.150	0.138	0.116	0.109	0.105	0.083
RMSE	0.554	0.502	0.387	0.371	0.341	0.330	0.324	0.289
Loss	0.177	0.148	0.122	0.111	0.107	0.096	0.090	0.086
MAP	0.767	0.816	0.843	0.865	0.874	0.884	0.895	0.910

	Degree of freedom	Sum of squares	Mean squares	F	P value
C(methods)	4	0.138592	0.034648	40.48827	2.29E-14
Residual	45	0.038509	0.000856

Methods	FL	GA-based	OVO-SVM	DT	DNN + CNN	LR	RF	Proposed Coot-
Training Time (Sec.)	35.486	32.1048	28.04246	27.562	26.4488	25.746	25.068	23.524

(a)
Comparative Analysis based on time step

Figure 8 depicts the comparative analysis of Coot-SCA_NN using Taiwanese Bankruptcy Prediction Dataset by varying the time step. The analysis of the proposed method based on accuracy is presented in Figure 8(a). When time step =20, accuracy values obtained by FL is 0.788, GA-based gradient boosting is 0.799, OVO-SVM is 0.817, DT is 0.827, DNN + CNN is 0.837, LR is 0.858, RF is 0.865, and the proposed methodology is 0.877. While time step is increased to 80, the proposed method obtained an accuracy of 0.918 and traditional methods achieved an accuracy of 0.827, 0.847, 0.866, 0.877, 0.889, 0.898, and 0.909. The analysis using MSE is provided in Figure 8(b). The existing methods and proposed method have MSE values of 0.688, 0.648, 0.588, 0.558, 0.510, 0.477, 0.328, and 0.225, when time step = 20. Similarly, for time step = 80, the MSE value obtained by the proposed method is 0.158 and the existing methods is 0.638, 0.566, 0.499, 0.477, 0.457, 0.409, and 0.266. The analysis using RMSE is shown in Figure 8(c). The existing methods and the proposed method have RMSE of 0.829, 0.805, 0.767, 0.747, 0.714, 0.690, 0.573, and 0.474 for time step = 20. RMSE values of FL is 0.799, GA-based gradient boosting is 0.752, OVO-SVM is 0.706, DT is 0.690, DNN + CNN is 0.676, LR is 0.639, RF is 0.515, and Coot-SCA_NN is 0.397, while time step = 80. Figure 8(d) shows the analysis based on loss function. When time step = 20, the existing methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, RF, and the proposed Coot-SCA_NN have the loss values of 0.212, 0.201, 0.183, 0.173, 0.163, 0.142, 0.135, and 0.123, respectively. For time step = 80, the proposed method has the loss value of 0.082 and traditional methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF have the loss value of 0.173, 0.153, 0.134, 0.123, 0.111, 0.102, and 0.091, respectively. The analysis of Coot-SCA_NN based on MAP is shown in Figure 8(e). For time step = 20, the MAP obtained by intended method is 0.847 and traditional methods is 0.727, 0.747, 0.759, 0.777, 0.798, 0.810, and 0.827. Similarly, for time step = 80, the MAP values attained by proposed method is 0.891 and FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF is 0.767, 0.788, 0.799, 0.826, 0.838, 0.847, and 0.877, respectively.

Figure 8.
Comparative analysis with time step, a) accuracy b) MSE c) RMSE d) Loss e) MAP.
4.7. Analysis based on perturbation radius

This section the analysis based on the perturbation radius, which plays a key role in enhancing privacy protection. When handling sensitive financial data, selecting an appropriate perturbation radius is crucial for maintaining a balance between privacy and model accuracy, ensuring data protection against reconstruction attacks while preserving its analytical value. Figure 9 provides the performance of the proposed method by varying the perturbation radius.

Figure 9.

Analysis by varying the perturbation radius, a) accuracy b) MSE c) RMSE d) Loss e) MAP.

Figure 9(a) shows the performance based on accuracy. When the perturbation radius is set to 0, the accuracy of the proposed method is 0.858, while the accuracy of the existing methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, and RF is 0.735, 0.759, 0.778, 0.799, 0.809, 0.826, and 0.848, respectively. When the perturbation radius is set to 0.4, the accuracy of the methods increases. The analysis based on MSE is shown in Figure 9(b). The MSE of the methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, RF, and the proposed method is 0.665, 0.637, 0.558, 0.488, 0.448, 0.377, 0.317, and 0.258, respectively, when the perturbation radius is set to 0.4. Similarly, the analysis based on RMSE, loss, and MAP is shown in Figure 9(c), Figure 9(d), and Figure 9(e), respectively. When the perturbation radius is 0.4, the RMSE of the comparative methods, such as FL, GA-based gradient boosting, OVO-SVM, DT, DNN + CNN, LR, RF, and Coot-SCA_NN is 0.816, 0.798, 0.747, 0.698, 0.669, 0.614, 0.563, and 0.508, respectively. When the perturbation radius is set to 0.4, the loss and MAP of the proposed method is 0.123 and 0.847, respectively. On seeing Figure 8, it is noted that the proposed method offers the good performance than the existing methods. Moreover, the results demonstrate how different perturbation levels impact the model performance while maintaining privacy. By introducing controlled perturbation, the privacy can be enhanced without significantly compromising the accuracy of financial distress prediction.

5. Conclusion

Shareholders don't know the true financial position of a firm until a financial crisis occurs because of financial information imbalance. Operational sustainability of a company not only affected by financial crisis and also shareholders interest, damages the rights, it harms national economy and society. Therefore, Coot-SCA_NN is proposed for financial distress prediction. The proposed method involves different entities: nodes and servers. The processes in the proposed framework include local training such as local data of each node, updates of server, integration of models in server, and downloading of global model to the nodes. This includes training updates on the basis of downloaded global model and local model and at every epoch of iteration. Here, training model takes input data from the dataset and runs a data augmentation model based on mutual information. Finally, financial distress is predicted using a NN trained with a proposed optimization algorithm called Coot-SCA. The information is processed at each node and the details are logged to the server for further processing. By incorporating Coot algorithm and SCA, proposed Coot-SCA is derived. A major contribution is made through local renewal and consolidation of the service performed by replacing CAViaR. It attained accuracy of 0.924, MSE of 0.083, RMSE of 0.289, Loss of 0.079, and MAP of 0.910. In future work, the predictive outcomes can be further improved by using clustering and feature selection approaches. Also, noise injection techniques (such as Laplace or Gaussian mechanisms), cryptographic methods, and privacy-preserving aggregation techniques, such as Secure Aggregation will be considered to secure and resilient against potential threats.

Footnotes

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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	Metrics/	FL	GA-based	OVO-SVM	DT	DNN +	LR	RF	Proposed
	Methods		gradient			CNN			Coot-SCA_
			boosting						NN
When time step = 80	accuracy	0.849	0.864	0.879	0.898	0.901	0.905	0.913	0.921
	MSE	0.440	0.361	0.270	0.218	0.160	0.138	0.110	0.093
	RMSE	0.663	0.601	0.519	0.467	0.400	0.371	0.331	0.306
	Loss	0.151	0.136	0.121	0.102	0.099	0.095	0.087	0.079
	MAP	0.759	0.794	0.821	0.854	0.861	0.869	0.877	0.897
K-value = 8	accuracy	0.823	0.852	0.878	0.889	0.893	0.904	0.910	0.924
	MSE	0.307	0.252	0.150	0.138	0.116	0.109	0.105	0.083
	RMSE	0.554	0.502	0.387	0.371	0.341	0.330	0.324	0.289
	Loss	0.177	0.148	0.122	0.111	0.107	0.096	0.090	0.086
	MAP	0.767	0.816	0.843	0.865	0.874	0.884	0.895	0.910

Methods	FL	GA-based	OVO-SVM	DT	DNN + CNN	LR	RF	Proposed Coot-
		gradient boosting						SCA_NN
Training Time (Sec.)	35.486	32.1048	28.04246	27.562	26.4488	25.746	25.068	23.524