1 Introduction

Presently, big data gained more advancements and also commonly used in several applications to verify the correlation among specific things [1]. The big data-based techniques execute various data validations to explain data trends and also their association [2]. The big data holds enormous information details as well as valuable information about environmental factors and then renders better decisions to the government organizations [3]. Furthermore, the big data analysis models provide better medical decision support by analyzing enormous information regarding the patients and then offering timely decisions to the medical experts about their health conditions [4]. The data processing speed of the big data models is high that helps to speed up the decision-making efficiency in the complex environment. Moreover, these techniques improve the values of data and also data scalability by enhancing the value of data that aids in providing more accurate outcomes [5].

In the modern era, individuals are facing more issues due to massive data [6]. Moreover, these kinds of data did not get more accurate decisions for the decision providers. Due to the availability of metadata as well as the sequence information, the validation time of the data is getting affected [7]. In a classical environment, collecting comprehensive data is a complicated task due to low data transparency [8]. The decision-making techniques are commonly required for all departments to gather the required resources from various channels [9]. In some cases, these techniques did not have the efficiency to verify the reliability as well as the authenticity of data as it takes more time for the validation [10]. As the operation procedures are higher while collecting these kinds of data and also lose its coordination in other categories [11]. Managing the unrelated set of data in the network is a complicated task while executing the conversion procedures. Classical techniques did not have the efficiency to process and offer more precise insights into the processed data [12]. Classical data analysis techniques are considered as unstable to execute the processing procedure in complicated and large-scale data, which helps to detect the most significant information from it and then attains precise and timely decision support to the decision-makers [13].

The deep learning techniques are widely used in big data validation as it has high processing efficiency than the classical frameworks [14]. Deep learning techniques are employed for the analysis of big data as it provides better ideas for the users. Classical decision-making techniques include the pre-processing and feature extraction procedures that helped to acquire the most efficient features from the original data [15]. Further, prediction procedures are done through machine learning or deep learning techniques along with optimization. Later, the deep learning techniques are integrated with reinforcement learning techniques for implementing a novel framework that has the efficiency to study and optimize the decision-making procedures [16]. Convolutional Neural Network (CNN) is the commonly used deep learning technique for processing data like voice signals and images through similar grid architecture [17]. Recurrent Neural Networks (RNN) are employed to process the sequential data to tackle several limitations presented in the classical neural network techniques. The RNN technique processed the sequential information by including the memory units. Moreover, the deep learning techniques are combined with different criteria to provide better decision-making with cluster techniques for identifying multiple features to improve product availability. Normal deep learning techniques did not have the ability to accomplish better recognition efficiency to offer more precise decisions to the user.

1.1 Research Gaps of Existing Models

In most of the organizations, the big data analytics enables valuable insights with enormous amounts of data. Thus, it can lead to enhance customer satisfaction and loyalty. Various techniques are leveraged in big data analytics to identify the potential risk and enhance profitability. Yet, the conventional deep learning model has potential vulnerabilities in terms of decision-making and privacy concerns, and affects the data quality [18]. Collecting and analyzing an enormous amount of data raise privacy concerns [19] in the conventional techniques. Considering the RNN model [20] introduces data bias that provides the inaccurate decision-making outcomes. For complex datasets, capturing the long-term dependency is complicated in the RNN model that affects data quality and has the possibilities to enhance the risk of unauthorized access. Training and testing the larger data sample shows computationally expensive in the Bi-LSTM model [21]. Maintaining the big data analytics in larger and smaller organizations becomes challenging and increase the privacy concern for securing the data in real time. Inconsistencies in data lead to inaccurate analysis and makes poor decision-making performance. For complex network structures, focusing the essential and fine-tuning parameters becomes complex in the optimization algorithm provides inaccurate outcomes. Hence, it is effective for designing the new decision-making framework for detecting the required patterns and trends effectively than other techniques.

Multiple contributions are related to the developed decision-making framework as given as follows:

  • To propose an effective deep learning-aided decision-making framework with big data analytics and feature extraction procedure, which helps to obtain more accurate decision-making outcomes for the users and also effectively enhances the decision-making efficiency by eliminating the bias while making the decisions in the organizations. Here, the developed decision-making techniques accomplished more precise decision-making outcomes by observing the current and existing information and providing suitable decision-making results that help the organization to maintain adaptability in all conditions.

  • To implement a new decision-making technique named AM-BiRNN by considering the strengths of BiRNN as the basic network with parameter tuning and multiplicative operation. The developed AM-BiRNN uses limited parameters and minimizes the training procedures of the network that helps to reduce the implementation expense. Moreover, complicated patterns presented in the big data sequences are studied quickly through multiplicative layers to eliminate interpretability problems in the network. The developed AM-BiRNN technique provides decision-making outcomes in minimal time without any errors and misclassification issues.

  • To construct a novel tuning framework named IRF-SOA that helps to tune significant parameters in AM-BiRNN for enhancing the decision-making efficiency without any delay and errors. Here, the parameters of AM-BiRNN like epoch count, learning rate, and hidden neuron counts are tuned to enhance the decision-making efficiency by improving the Critical Success Index (CSI) along with less False Discovery Rate (FDR) and False Negative Rate (FNR). In the developed decision-making framework, overfitting issues are tackled by adjusting certain parameters by IRF-SOA and making the developed system suitable for all conditions.

Upcoming sub-sections of developed decision-making frameworks with big data analytics are detailed here. Various research works are considered with the classical technique which are detailed in Sect. 2. Implementation procedures involved in the developed decision-making framework with big data are given in Sect. 3. Map–reduce environment-based feature extraction procedures are described in Sect. 4. Newly designed optimization and recognition techniques for decision-making techniques are presented in Sect. 5. Experimental observations on developed techniques are provided in Sect. 6. The summary of the research and future enhancements are discussed in Sect. 7.

2 Literature Survey

2.1 Related Works

Optimization Algorithm-Based Big Data Analytics: In 2023, Fua et al. [22] have implemented a novel artificial intelligence framework with big data for performing environmental protection monitoring. Here, essential data was required for validating from big data sources. Here, the recognition procedures were designed by considering novel extreme learning procedures, and also, the Whale Optimization Algorithm (WOA) technique was employed to tune the parameters. Later, multiple validations were examined to analyze the model’s effectiveness.

Research Work Based on Decision-Making Models in Big Data Analytics: In 2024, Mukred et al. [23] have designed a novel framework to provide better decision-making outcomes. Here, the required data were collected from standard resources. Then, these data were provided to Partial Least Square-Structural Equation Modeling (PLS-SEM) and attained better decision-making efficiency. Analysis executed in the suggested network has gained superior outcomes than the state-of-the-art framework. In 2022, Zhang et al. [8] have suggested a novel framework named Big Data-assisted Social Media Analytics for Business (BD-SMAB) to provide more improvement in management. The developed framework was highly suitable for various organizations to attain better decision-making outcomes. Analysis displayed that the developed BD-SMAB technique offered better customer satisfaction outcomes. In 2021, Lakshmi et al. [24] have implemented Multi-Criteria Decision-Making (MC-DM) framework to acquire better solutions for big data analysis. The developed framework was highly suitable for different scenarios as it effectively enhanced the network efficacy. In the experimental validation, the MC-DM technique gained superior decision-making outcomes than the classical techniques.

Deep Learning-Based Works: In 2024, Mary et al. [25] have designed a new decision-making framework using feature selection procedures. Here, the feature extraction process was executed through Fuzzy Entropy Mutual Information (FEMI) and an optimization mechanism to attain the significant features. The Auxiliary Classifier Generative Adversarial Network (ACGAN) was employed to perform the data augmentation that aids in better decision-making outcomes. Analysis reports displayed superior performance was recorded in the developed techniques over the existing frameworks. In 2024, Hang et al. [26] have implemented a new Artificial Neural Network (ANN)-based decision-making framework with big data. The work required the samples from various big data resources. The ANN technique was used to execute the decision-making process. Further, multiple analysis was done in the recommended framework to display its effectiveness over the traditional frameworks. In 2022, Li et al. [27] have investigated a novel decision-making framework using CNN and big data procedures. Moreover, the digital twin technology was introduced in the developed framework to perform decision-making tasks in the developed framework by validating enormous data. Analysis displayed that the suggested model gained comparatively higher performance in providing better decisions.

Clustering-Based Works for Big Data Analytics: In 2024, Yan and Yang [28] have designed a new decision-making framework using big data and deep learning models. In the initial stage, significant features from the original data were extracted and pre-processed. The developed framework utilized the Fuzzy C Clustering (FCM) technique to execute the decision-making process. Then, significant analysis was performed with the suggested technique to verify its performance.

2.2 Problem Statement

Big data is said to be the phase of gathering, securing, handling, and detecting huge-scale data to analyze valuable knowledge and information. The big data-based application helps in business decision-making systems, which is becoming a high involvement in multiple sectors. It also provides challenges for enterprises and extraordinary opportunities. Hence, it helps to find out the competition and application of big data-based business models in decision-making. Big data is utilized in providing efficient and accurate timely decision support for the decision-makers by extracting valuable information from the large data immediately. However, the conventional models issue various challenges while making decisions that are explained as below:

  • The conventional models decrease the dimensionality of data, which shows information loss. While the majority of the information is obtained, it is highly significant to note whether the loss is bearable for the application.

  • While making decisions, the traditional models suffered from a lack of interpretability, data security concerns, potential biases found in the data, computational problems, and the requirement for human oversight to verify the validity of insights created by the networks. These problems cause poor decision-making if not accurately processed.

  • While extracting the features, a loss of data interpretability occurs, and the transformation process is too expensive to be processed.

  • The existing model resulted that the network can only utilize information from the beginning steps when making decisions at later time steps. Hence this results; the network may not obtain significant contextual details that are suitable for the decision-making output.

To overcome the above-mentioned problems, several techniques have been developed that are stated in Table 1. The techniques adopted in the literature works have been adopted to analyze the strengths and weakness of diverse techniques. This exploration helps the researchers to gain more knowledgeable information in big data analytics to implement a new deep learning framework to ensure accurate decision-making performance.

Table 1 Features and challenges of big data analytics in decision-making using deep learning methods
Full size table

2.2.1 Critical Analysis of Cited Literature Works and Advances of the Proposed Model

The literature survey demonstrated with various deep learning and machine learning models for providing better decision-making performance. Moreover, introducing the techniques in the existing literature works often faces challenges that impact the model’s performance. The metaheuristic optimization algorithm [22] was inspired by the hunting behavior of humpback whales. The primary advantage of the WOA algorithm gets easily trapped into the local optima issues. Also, it is time-consuming process while tuning the more complicated network parameters and, thus, affects the convergence rate. Most of the existing works focus on deep learning models for getting significant outcomes. In accordance, the ACGAN model [25] has limited performance in data accessibility, quality, and handling the enormous of data with diverse classes. However, big data often contains data inconsistencies, noise, and missing values that merely impact the model performance in the ACGAN model. For handling sequential data in big data analytics, the LSTM model [24] is a powerful mechanism to enhance the model’s performance. However, capturing the long-term dependencies in the LSTM model becomes complex in larger data. Inappropriate hyperparameter tuning in the ANN model [26] is computationally expensive and degrades the model performance. Also, training too well data gradually increases the overfitting issues leads to poor generalization performance of the unseen data. Although the CNN model [27] shows significant outcomes, it is difficult to interpret the complex data and understanding the features is complex that hinders the performance in decision-making.

For speedup the convergence, the research work adopts SOA algorithm by updating with improved random function. It strategically improves convergence by adopting the exploration and exploitation phase to enable faster response for getting the optimal solutions. Focusing the minute details of sculptors helps the model to explore in the local search capabilities and converges more quickly to get the desired optimal solutions. In this research work, the presence of noise and data inconsistencies in the big data can be mitigated by extracting the relevant features using the SI-PCA model. This model adopts the map and reduces the framework by focusing the data streams and spatial relationships in the complicated data. This process helps to handles large and intrinsic datasets to enhance the model performance. To capture long-term dependencies, the adaptive multiplicative is incorporated in the BiRNN model by processing the input data into the forward as well as backward directions to access the meaningful information. It helps to understand the complex features at each time step to enable better predictions and enhance decision-making performance using the developed model.

3 A Novel Big Data Analytics for Decision-Making Model

3.1 Challenges on Decision-Making in Big Data Analytics

In recent days, big data plays a major role in industrial up-gradation. It acts as an important element to improve the business and also the information technologies using cloud-based storage to provide big data analytics. Rapid growth in data is accomplished due to the advancement of cloud computing and the Internet of Things (IoT) makes the data storing and data managing procedure simple. Big data analytics are performed by considering dual major ideas like data analysis as well as data storage. The major complications faced by the big data analysis models are privacy and poor security in the respective big data repositories. Accessing big data information from outside the cloud may be prone to data breaches and sensitive information leakage. Big data is widely used to acquire significant information and then used to perform prediction and decision-making through different techniques and procedures. Performing decision-making through big data is termed as an action executed to resolve certain issues in the organization. The decision-making process needs proper factor selection procedures to generate an alternate key according to the values obtained by decision-makers. The Analytic Network Process (ANP) tool is commonly used to execute the analyzing procedures and also it helps to resolve complicated multiple-criteria-based decision-making issues to achieve the desired outcomes. The ANP model effectively tackles several issues presented in the network; also, it is designed by considering the clusters for all the elements. However, these techniques need to consider privacy, accuracy, and security measures.

3.2 Developed Decision-Making Model in Big Data Analytics

Presently, decision-making approaches with big data are widely used in different fields like social network analysis, data mining, statistics, and visualization techniques. Big data is a complicated data structure, which faces more complications while collecting and managing the data and then offering better decisions to the users. A novel decision-making framework is implemented in this research work through big data analytics and deep learning models, which helped to obtain significant information and offer better decisions to the organization according to their trends and patterns. Here, required social media data are collected from the benchmark resources. Next, these data are forwarded to the feature extraction phase. Here, the SI-PCA technique is leveraged to acquire the significant features for providing better decision-making outcomes in the map–reduce environment. In the map phase, feature mapping is performed and in the reduce phase, feature extraction is done with the help of SI-PCA technique. Then, the SI-PCA-based extracted features are fed to the AM-BiRNN-based decision-making phase. In the developed AM-BiRNN, various parameters of BiRNN like learning rate, epoch count, and hidden neuron counts are tuned by IRF-SOA. The research aims to minimize the FNR and FDR and also to maximize the CSI that helps for enhancing decision-making efficiency of the developed framework AM-BiRNN. At last, the decision-making outcomes are obtained from developed AM-BiRNN. Finally, extensive validation are executed in the suggested model to validate the efficiency over a conventional framework for different performance measures. A pictorial illustration of the suggested decision-making framework using big data is provided in Fig. 1.

Fig. 1
Fig. 1
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Structural presentation of developed big data-based decision-making framework

4 Feature Analysis Using Spatial Incremental Principal Component Analysis

4.1 Principles of Map Reduce Framework

The map–reduce framework is a programming model that uses parallel processing procedures to process the enormous data in the network. The map–reduce mode uses the split–apply–combine procedure for analyzing the data. This framework includes two major functions like map and reduce, which are executed in the sequence data.

  • Map: The input data are progressed to create the intermediate key-value pairs.

  • Reduce: Here, the output data are processed from the map function to generate the final group of key-value pairs.

In the developed decision-making framework, map–reduce procedures are executed by SI-PCA technique to acquire the extracted features. The map–reduce model has four different phases that are mapping, reducing, combining, shuffling, and sorting.

Working Procedure of Map Reduce Model: Several procedures included in the Map Reduce model are listed as follows.

  • Dividing Inputs: This is the initial step where the input data are divided into small blocks.

  • Blocks Allocation to Mappers: Every block is allocated to the corresponding mappers to execute the processing.

  • Data Redistribution: In this step, the worker nodes re-distribute the specific data according to the output keys presented in the map function.

  • Executing Reduce Function: Here, the reduce function is executed in the outcomes obtained from the map function.

  • Communication Management: In this phase, entire communications as well as data transfer are performed among different parts of the system.

An architectural illustration of the map–reduce framework is provided in Fig. 2.

Fig. 2
Fig. 2
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Pictorial view of map reduce framework

From the above figure, the map and reduce framework performed in parallel processing, for effectively handling the complexities of the large-scale datasets. Moreover, the collected big data \(Da_{j}^{Ip}\) is given into the map and reduce framework. However, the collected data splits into smaller chunks that can limit the processing time. Moreover, each chunk facilitates to progress independently with the help of map function. Thus, it generates and converts the data into several key-value pairs. Also, output generates the intermediate key-value pairs. For each block, the intermediate outcomes then pass through the reduce phase. In the map phase, the generated intermediate key-value pairs are sorted with the help of keys. For each keys, the aggregation operation has performed to enable the data aggregation process. The output attained from the reduce phase is inputted in the SI-PCA block. The operation of SI-PCA block is discussed below.

  • Maps the input data

  • Convert into matrix

  • Validate the mean

  • Validate the deviation from mean

  • Validate the covariance matrix

  • Validate Eigen values and vectors.

In the end, the extracted features get attained for enhancing the performance of the model. Also, the extracted features are termed as \(Fe_{r}^{map}\).

4.2 Feature Mapping Based on SI-PCA: Map Phase

In the developed AM-BiRNN-based decision-making technique, feature analysis procedures are executed in a map–reduce environment using the SI-PCA [29] technique. In the map phase, feature mapping procedures are executed by collected big data \(Da_{j}^{Ip}\). The input data are presented in the form of files and stored in the Hadoop file system. Next, the input files are forwarded to the map function in a line-by-line format. Then, the data are processed and generated as tiny chunks of data. In the map phase, features are mapped to the respective input data according to the key-value pairs and SI-PCA technique. The key-value pairs are given as the inputs to execute the mapping. Here, the key is termed as the specific address, and the values are known as the actual values needed to be stored in it. Next, a mapping function is employed for the execution in the memory space with a particular input key-value pairs and then produces intermediate key-value pairs that act as an input to the reduce phase.

Map Function: It includes a sequence of key pair values and processes every value and then generates zero or more outcome key pairs. Here, the input is divided into pairs and generated key pair values of all the samples.

The developed framework utilized the SI-PCA to execute the feature procedure in the map phase. Performing feature mapping procedures helps to recognize the user needs quickly and also eliminates distraction, while communication is performed between the users. The developed SI-PCA technique helps to accomplish superior outcomes by providing more precise data representation. Moreover, dimensionality issues presented in the data are eliminated that help to offer clear visualization and then execute the remaining process. The SI-PCA-based feature mapping outcomes attained in the map phase are represented as \(Fe_{r}^{map}\) that fed into the feature extraction phase.

4.3 Feature Extraction Based on SI-PCA: Reduce Phase

The feature-mapped outcomes \(Fe_{r}^{map}\) are used to execute the further process. In the reduction phase, features are extracted using the SI-PCA technique. Here, intermediate key-value pairs are taken as inputs. It is a combination of shuffle and reduced procedure. Here, the reducer processed the data attained from the mapper. Next, sorting and shuffling procedures are performed in the intermediate key values and forward to the reduced function. Reducer helps to group the particular data according to the key-value pairs.

Reduce Function: It aids to perform sorting in entire unique keys. The reduced functions are integrated by their specific values related to their keys.

PCA [30] is a statistical technique employed to summarize a huge dataset by minimizing the dimension counts in the data. It generates a small group of variables by transforming the correlated variables. In the initial stages of PCA, input data are organized in matrix format. Here, the samples are specified as \(M\), and also, the descriptor variables are denoted as \(Q\). The PCA model decomposes the input samples \(Y\) to detect the principal components, where \(B = Mn\left( {M,Q} \right)\). Further, a linear combination of matrix \(Y\) columns with maximum variance is provided in Eq. (1)

$$\begin{gathered} Y = UQ + F \hfill \\ \,\,\,\, = u_{1} Q_{1} + u_{2} Q_{2} + ... + u_{b} Q_{b} + F. \hfill \\ \end{gathered}$$
(1)

In the above equation, \(Y\) is a \(\left( {M \times Q} \right)\) matrix with mean-centered patterns, \(u_{b}\) is a score vector, \(Q_{b}\) is a loading vector, and residual matrix is specified as \(F\) for \(\left( {M \times Q} \right)\). Here, the noises are mainly presented in the residual matrix. Moreover, \(U\) is the \(M \times B\) matrix for \(M\) scores in the principle component \(B\). The term \(Q\) is the matrix of \(Q \times B\) with \(Q\) loadings and \(B\) principal components. At the principal components, latent variables are presented in linear combination for every raw descriptor to describe the entire sum of squares of \(Y\). Sum of variance in all \(B\) principal components of the entire variance of data is given in Eq. (2)

$$\sum\limits_{b = 1}^{{Mn\left( {M,Q} \right)}} {\lambda_{b} } = Var\left( Y \right).$$
(2)

The first principal components describe the major variations; rest of the PC details the fraction of variation, which is not detailed in the initial principal components. The second principal component attains the orthogonal constraints for the first principal components. The PCA outcome vectors are in the form of an uncorrelated orthogonal set, which represents the orthogonal data as \(u_{b}\) and ortho-normal data as \(Q_{a}\) signified in the below equations

$$Q^{\prime}_{w} Q_{s} = 0\left( {w \ne s} \right)$$
(3)
$$U^{\prime}_{w} U_{s} = 0\left( {w \ne s} \right)$$
(4)
$$Q^{\prime}_{w} Q_{s} = 1.$$
(5)

The most commonly used PCA techniques are Nonlinear Iterative Partial Least Squares (NIPALS) and Single Value Decompositions (SVD). These techniques are widely employed to identify the Eigen values and eigenvectors of the covariance matrix \(Y\) in the form of \(Y^{\prime}Y\). Moreover, correlation is executed in the matrix, if the data matrix \(Y\) is standardized through an auto-scaling procedure. Respective Eigenvector is determined with a loading vector and it is represented as \(Q_{b}\). Later, the loading matrix \(Q\) is used to validate the score matrix \(U\) and attain the scores of test samples using Eqs. (6) and (7)

$$U = YQ$$
(6)
$$U_{Nw} = Y_{Nw} Q.$$
(7)

The incremental function in PCA is used to execute the coefficient updating incrementally by generating a data chunk toward the incremental fit function. Here, the spatial functions are employed to validate the spatial coordination of all data points while computing the principal components. The spatial function has the efficiency to detect the most accurate patterns presented in the data whether they are presented in the correlated or clustered format.

4.4 Spatial Incremental PCA Chosen over Standard PCA

Standard PCA Model: PCA is a powerful technique for dimensionality reduction, especially applied in big data analytics. Moreover, the standard PCA model has the ability to convert high-to-low dimensional data to preserve more information. Thus, it helps to provide better visualization analysis to enable decision-making performance. In essence, the standard PCA technique facilitates to filter the noise and irrelevant information, which effectively identifies the true patterns in the data. Although the PCA model shows effective performance, yet it is difficult to interpret the results in the principle components and potentially leads to information loss. Also, the PCA model is sensitive to outliers, whereas it disproportionately influences the direction of the principle components leading to inaccurate and misleading outcomes. While minimizing the dimensionality of the data, some of the information is lost and failed to generate accurate outcomes. To solve the aforementioned issues, the spatial incremental is combined in the PCA model and termed as SI-PCA model.

Developed SI-PCA Model: In feature extraction process, the spatial incremental combines the strength of PCA model. Thus, it is well suited in the big data analytics. Here, the spatial incremental in PCA facilitates addressing the issues of the standard PCA model to enhance the incremental processing and allows the data streams for further analysis. Thus, it incorporates the spatial information by determining the relationship among the data points based on their position. Moreover, the developed SI-PCA model effectively identifies the principle components, in which it captures the most variance in the data by determining the data points and spatial values. Henceforth, the selected principle components help to diminish the dimensionality reduction to capture the relevant information to enhance the model’s efficiency. The extracted features in the SI-PCA model could effectively train the model to understand the patterns and enables informed decision-making performance. Incorporating the spatial incremental in the PCA model has the capabilities to extract valuable information in complex and large datasets. The developed SI-PCA is employed to handle the spatial data as it has the inherent relationship to validate the principal components by considering the spatial context of all data points as original data. The developed SI-PCA is widely suited for extracting significant features from enormous data and also it offers comparatively higher efficiency for real-world applications. Moreover, these techniques effectively eliminate the dimension issues and create the loading vector, which helps to eliminate the noise. The developed SI-PCA eliminates the noise presented in the inputted data and also effectively eliminates the redundant data that help to enhance accuracy in decision-making and resolves the overfitting. The SI-PCA-based extracted features in the reduce phase are termed as \(Fe_{b}^{Si - pca}\), which is used as the input in the decision-making phase.

Handling Big Data Using Spatial Incremental-PCA Model: Unlike traditional PCA model, it minimizes the number of features in the datasets to effectively preserve the meaningful information and it is easily manageable and process the data. Moreover, reducing the dimensionality in the data can easily update the model incrementally to further enhance the computational efficiency in big data analytics for maximizing the decision-making and models efficiency. Based on the dimensionality reduction in the SI-PCA model could effectively handles the big data sequentially to enhance the model performance. Handling the big data serves various advantageous performances by understanding the underlying patterns and relationships among the data points to enable faster response time.

5 Adaptive Multiplicative Bidirectional Recurrent Neural Network for Decision-Making

5.1 Bidirectional Recurrent Neural Network

BiRNN [31] is a kind of RNN used to process the sequential data in the backward and forward directions. The BiRNN uses two different recurrent hidden layers to process the input sequences in both directions. The BiRNN technique helped to validate prior and upcoming information available in the network. Outputs of the BiRNN model by adding the hidden layers are provided in the below equation

$$W\left( {L_{m} \left| {\left[ {V_{n} } \right]_{n \ne m} } \right.} \right) = \sigma \left( {Z_{r}^{t} f_{r}^{t} + Z_{r}^{q} f_{r}^{a} + h_{r} } \right)$$
(8)
$$f_{r}^{t} = \tan f\left( {Z_{c}^{t} f_{r - 1}^{t} + Z_{s}^{t} V_{r} + h_{r}^{t} } \right)$$
(9)
$$f_{r}^{a} = \tan f\left( {Z_{c}^{a} f_{r - 1}^{a} + Z_{s}^{a} V_{r} + h_{r}^{a} } \right).$$
(10)

Here, the bias of output layers is specified as \(h_{r}\), weights of hidden to output are given as \(Z_{r}^{t}\), hidden-to-hidden layer weights is represented as \(Z_{c}^{t}\), and input to hidden layer weight is provided as \(Z_{s}^{a}\). The backward pass procedure executed in BiRNN helps to reduce the mean square errors. A structural representation of BiRNN is provided in Fig. 3.

Fig. 3
Fig. 3
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Presentation of basic BiRNN

The BiRNN model is initiated by focusing the past and future context and process sequentially. BiRNN model processing with backward (right to left) and forward (left to right) directions. Moreover, it considers the sequence of data points to represent a vector. In the forward function, the hidden state is calculated by considering the input data points and previous hidden states. On the other hand, backwards can process in the reverse direction by considering the current input data and the next hidden state. For each time step, the outputs from the forward and backward directions combined for getting an accurate solution. Thus, it represents the final model outcomes effectively reduces the error rate and maximize the overall performance. Utilizing the both directions in BiRNN model facilitates to effectively capture sequential patterns and dependencies to improve the accuracy of the model.

5.2 Decision-Making-Based Adaptive Multiplicative BiRNN

An efficient AM-BiRNN-based decision-making framework for big data analysis is designed by deep learning techniques to provide more accurate decision-making outcomes to the users. The developed AM-BiRNN technique is designed by considering the BiRNN as the basic network along with multiplicative operations. Using developed AM-BiRNN helps to improve the decision-making efficiency over enormous data and also helps to enhance the user experiences. The BiRNN has the efficiency to collect the contextual dependencies from past and feature data in the input data sequences. BiRNN can easily handle the variable length sequential information with higher accuracy. Moreover, it eliminates the redundant and noisy data presented in the input sequences. Yet, the BiRNN needs more time to process the sample data in both directions that tends to cause overfitting issues in the network. The BiRNN also requires enormous memory space to store the processing data, and also, it faces some complications while handling the noisy data. Thus, it is essential to tackle several limitations associated with the BiRNN technique. Thus, a multiplicative layer is employed and parameter tuning is also suggested for the BiRNN technique and the newly developed technique is termed AM-BiRNN. Including a multiplicative layer analyze the complicated patterns and also to verify the non-linear relationship among the features multiplied together. Moreover, the multiplicative layers offer higher interpretability efficiency that helps to accomplish better decision-making outcomes. Using developed AM-BiRNN in the decision-making procedures helps to minimize the bias issues while providing the decisions, and also, it effectively eliminates the errors. Here, better outcomes are accomplished when enormous information is used. Hence, the developed AM-BiRNN technique aids in estimating quick decision-making by observing the prior information and also using a bidirectional network helps to gather and process enormous information and validate the risk factors for every option.

Architectural Description of the Developed Model: In the developed AM-BiRNN-based decision-making framework, extracted features \(Fe_{b}^{Si - pca}\) from SI-PCA are offered as the input to the multiplicative layer that is used to fuse the significant information collected from various sequences of information. Here, the adaptive multiplicative mechanism allows the network to receive meaningful information from backward and forward directions. At each time step, it facilitates to focus on relevant information makes the model more effective. The outcome from the multiplicative layer then passes through the BiRNN model, in which it considers input state, hidden state, and output state. This allows the model to capture the long-term dependency patterns and minimize the overfitting issues. Here, the decision-making outcomes are attained from developed AM-BiRNN. Moreover, parameter tuning is executed in the developed AM-BiRNN that helps to enhance decision-making by minimizing the FDR and FNR and also by maximizing the CSI. In developed AM-BiRNN, different parameters of BiRNN like epoch count, learning rate, and hidden neuron counts are tuned by developed IRF-SOA. The main objective of the developed AM-BiRNN-based decision-making model is derived in Eq. (11)

$$ft = \mathop {\arg \min }\limits_{{\left\{ {hn_{g}^{birnn} ,ps_{d}^{birnn} ,lt_{k}^{birnn} } \right\}}} \left( {\frac{1}{{Bu_{f} }}} \right) + Xt_{f} + Hr_{d} .$$
(11)

Here, the hidden neurons \(hn_{g}^{birnn}\) of BiRNN are selected in the bound \(\left[ {5,255} \right]\), the learning rate \(lt_{k}^{birnn}\) of BiRNN is chosen in the limit of \(\left[ {0.01,0.09} \right]\), and epochs \(ps_{d}^{birnn}\) are selected in the range \(\left[ {5,50} \right]\) in BiRNN.

5.3 Selection of Hyperparameters

Selecting the appropriate hyperparameters plays a significant role to get the precise outcome for maximizing accuracy and provide better generalization of the unseen data. Deriving Eq. (11), the developed IRF-SOA algorithm optimizes the parameters of hidden neurons, learning rate and epoch of BiRNN model. Focusing the right parameters can automatically boost the decision-making performance in data analytics. Tuning the effective hyperparameters can lead to speed up the convergence rate in the process of training and capture the underlying patterns to eliminate the overfitting and underfitting issues. Also, this selected hyperparameters provides better computational complexity to generate accurate outcomes. Moreover, analyzing the large number of hidden neuron can understand the complicated patterns and enable better decision-making outcomes. During the process, training too well data can potentially enhance overfitting issues and training small amount of hidden neuron emphasizes the underfitting issues. Here, the research work adopts a significant number of hidden neurons as [5, 255] without degrading the performance. In this research, the learning rate within the range of \(\left[ {0.01,0.09} \right]\). Focusing the sufficient learning rate allows the model to get the optimal solution and leads to maximize accuracy rate. The epoch of BiRNN model contains \(\left[ {5,50} \right]\) also optimize using the developed IRF-SOA algorithm. It determines how many times the model can iterate toward the training data. For each epoch count, it monitors continuously to evaluate the model’s performance in training and testing the model to learn intrinsic patterns to rectify from avoiding the overfitting problems. In summary, selecting the accurate hyperparameters provides better generalization outcomes of the unseen data shows better decision-making performance in data analytics.

Different objectives associated with the developed model are explained as follows.

FDR is specified in Eq. (12)

$$Xt_{f} = \frac{{Q_{a} }}{{Q_{a} + X_{a} }}.$$
(12)

CSI is provided in Eq. (13)

$$Bu_{f} = \frac{{X_{a} }}{{\left( {X_{a} + E_{a} + Q_{a} } \right)}}.$$
(13)

FNR is offered in Eq. (14)

$$Hr_{d} = \frac{{E_{a} }}{{X_{a} + E_{a} }}.$$
(14)

False negative is specified as \(E_{a}\), truly positive values are given as \(X_{a}\), false-positive values are denoted as \(Q_{a}\), and truly negative is given as \(W_{a}\). An architectural presentation of the developed AM-BiRNN-based decision-making model is visualized in Fig. 4.

Fig. 4
Fig. 4
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Representation of AM-BiRNN-based decision-making framework

The step-by-step process of the designed AM-BiRNN model for decision-making in big data analytics is listed in Table 2.

Table 2 Step-by-step process of the recommended AM-BiRNN model
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5.4 Parameter Optimizer as Proposed IRF-SOA

A new optimization approach named IRF-SOA is implemented in the developed decision-making model for tuning essential parameters in AM-BiRNN that helps in increasing the decision-making efficiency in the complex environment. The developed IRF-SOA is the modified version of SOA [32], in which random numbers are modified. The developed AM-BiRNN-based decision-making model accomplished high CSI by minimizing FNR and FDR by tuning various parameters (learning rate, hidden neuron, and epoch) of BiRNN through developed IRF-SOA. In the developed decision-making model, the SOA technique is employed as it has simple implementation procedures and also enhanced the performance of the developed framework. Moreover, it helps to attain superior outcomes to accomplish more accurate decision-making outcomes. As it has simple implementation process, it enhances reliability, productivity, and network efficiency. It has the efficiency to adapt to various changes obtained in the network and also provides higher compatibility over different platforms. Yet, the SOA techniques always need updated values, and also, it is non-optimal in several cases. This technique falls easily into the local optimal issues and faces more complications in finding the truly optimal solutions. Thus, it is essential to address multiple problems in the traditional SOA technique; hence, the random parameters presented in the SOA technique are modified and the novel model as IRF-SOA. The suggested IRV-SOA model has the efficiency to resolve the local optimal problems in the network and also makes the processing easier. In the developed AM-BiRNN technique, the proposed IRF-SOA helps to accomplish superior decision-making outcomes by enhancing the overall decision-making efficiency than other techniques. Random parameters \(Ry\) in classical SOA are optimized using a novel concept by considering different parameters like worst fitness \(Yv\), best fitness \(Jv\), mean fitness \(Hv\), and current fitness is signified as \(Sv\), and it is provided in the Eq. (15)

$$Ry = \left( {\frac{Sv}{{\left( {Yv + \left( {Hv * Jv} \right) + Sv} \right)}}} \right).$$
(15)

5.5 Mathematical Derivations of SOA Algorithm

By focusing the search power of the SOA member, the complex optimization problem is solved by getting accurate solutions. Moreover, the members in the SOA represents the candidate solution whereas, it generates more valuable information to provide better decision variables. The algorithmic initialization of SOA member in problem solving space is generated randomly and shown in Eq. (16)

$$Y = \left[ \begin{gathered} Y_{1} \,\,\,\,\,\,\,\,\, \hfill \\ \,\, \vdots \hfill \\ Y_{j} \hfill \\ \,\,\, \vdots \hfill \\ Y_{M} \hfill \\ \end{gathered} \right] = \left[ \begin{gathered} Y_{1,1} \cdots Y_{1,d} \cdots \,\,\,\,\,\,\,Y_{\begin{subarray}{l} 1,n \vdots \\ \end{subarray} } \hfill \\ \vdots \,\,\,\,\, \ddots \,\,\,\,\,\,\,\,\,\, \vdots \,\,\,\,\, {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} \,\,\,\,\,\,\,\,\, \vdots \hfill \\ Y_{j,1} \cdots Y_{j,d} \cdots \,\,\,\,\,\,\,Y_{\begin{subarray}{l} j,n \vdots \\ \end{subarray} } \hfill \\ \vdots \,\,\,\,\,\,\, {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} \,\,\,\,\,\,\,\, \vdots \,\,\,\,\, \ddots \,\,\,\,\,\,\,\,\, \vdots \hfill \\ Y_{M,1} \cdots Y_{M,d} \cdots \,\,\,\,Y_{\begin{subarray}{l} M,n \vdots \\ \end{subarray} } \hfill \\ \end{gathered} \right]_{M \times n}$$
(16)
$$y_{j,d} = l_{d} + rd.(u_{d} - l_{d} ).$$
(17)

The variable \(Y_{j}\) denotes the member of candidate solution, whereas the search space dimension denotes the \(Y_{j,d}\). Here, the number of population is termed as \(M\)(population size). The decision variable \(m\) and the radon variable \(rd\) are expressed in above equations. For \(d^{th}\) decision variables, the lower and upper bound is executed as \(l_{d}\) and \(u_{d}\). In essence, the candidate solution of each SOA member is derived based on its objective function, which is formulated in the vector and given in Eq. (18)

$$OF = \left[ \begin{gathered} OF_{1} \,\,\,\,\,\,\,\,\, \hfill \\ \,\, \vdots \hfill \\ OF_{j} \hfill \\ \,\,\, \vdots \hfill \\ OF_{M} \hfill \\ \end{gathered} \right]_{M \times 1} = \left[ \begin{gathered} OF(Y_{1} ) \hfill \\ \,\,\,\,\,\,\, \vdots \hfill \\ OF(Y_{j} ) \hfill \\ \,\,\,\,\,\,\,\, \vdots \hfill \\ OF(Y_{N} ) \hfill \\ \end{gathered} \right]_{M \times 1} .$$
(18)

The vector objective function is denoted as \(OF\), whereas the attained objective function \(OF_{j}\) is determined based on the \(j^{th}\) member of SOA. Additionally, the SOA is initiated by considering the exploration and exploitation phase.

  1. (a)

    Exploration: The best population member position has been initiated in the sculpting pattern. The position of the corresponding member in the exploration is expressed in Eq. (19)

    $$y_{j,i}^{p1} = y_{j,i} + rd.(bt_{j} - I*y_{j,i} ).$$
    (19)

    In SOA population, the best member position is denoted as \(bt_{j}\) with its \(j^{th}\) dimension. Moreover, the attained new position of the \(j^{th}\) member represents the \(y_{j,i}^{p1}\) in SOA algorithm. The random value lies in the interval of [0, 1], whereas the randomly selected member as \(I\) with the range of 1 or 2.

  2. (b)

    Exploitation: With the help of sculpting strategy, the new position of the member gets updated in SOA and it is expressed in Eq. (20)

    $$y_{j,i}^{p2} = \frac{S - s}{S}.y_{j,i} + \frac{s}{S}.bt_{j}^{{}} .$$
    (20)

The new calculated position of SOA member is termed as \(y_{j,i}^{p2}\). Moreover, the terms \(S\) and \(s\) denotes the maximum iteration and iteration counter. Based on this process, the member position is updated in the SOA to find the desired and effective outcomes. In Algorithm 1, the pseudocode for designed IRF-SOA is provided.

figure a

Algorithm 1: Proposed IRF-SOA

6 Experimental Analysis

6.1 Experimental Setting

An efficient decision-making framework with big data was developed using deep learning model and executed through Python. The developed mechanism considered the iteration counts as 50, population counts as 10, and chromosome length as 10 to offer more accurate decision-making outcomes. Traditional decision-making techniques employed for the validations were LSTM [24], ACGAN [25], CNN [27], and AM-BiRNN. Optimization mechanisms employed in the validation were Cray Fish Optimization (CFO) [33], Gold Rush Optimizer (GRO) [34], Dark Forest Algorithm (DFA) [35], and SOA [32].

6.2 Social Media Dataset: Experimental Data

The developed decision-making framework utilized the social media data for the analysis and it is provided in Table 3. The data collected for the validation are specified as \(Da_{j}^{Ip}\) and it is used as the input in the upcoming phase. Twitter US airline sentiment dataset is used in this research work to get accurate decisions by classifying customer suggestions into positive, negative, and neutral comments. This dataset also helps to enhance the target improvements in a particular area and tackle the negatives with quick decision-making and enhance customer satisfaction.

Table 3 Dataset details of decision-making framework with big data
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6.3 Performance Measures

The proposed decision-making framework using big data is computed by considering different performance measures.

Precision is given in Eq. (21)

$$Ug_{b} = \frac{{X_{a} }}{{X_{a} + Q_{a} }}.$$
(21)

Specificity is represented in Eq. (22)

$$Yj_{g} = \frac{{W_{a} }}{{W_{a} + Q_{a} }}.$$
(22)

Sensitivity is provided in Eq. (23)

$$Qg_{b} = \frac{{X_{a} }}{{X_{a} + E_{a} }}.$$
(23)

MCC is given in Eq. (24)

$$Mb = \frac{{X_{a} \times W_{a} - Q_{a} \times E_{a} }}{{\sqrt {(X_{a} + Q_{a} )\left( {X_{a} + E_{a} } \right)(W_{a} + Q_{a} )\left( {W_{a} + E_{a} } \right)} }}.$$
(24)

F1-Score is specified in Eq. (25)

$$Sf_{b} = 2 \times \frac{{2X_{a} }}{{2X_{a} + Q_{a} + E_{a} }}.$$
(25)

NPV is signified in Eq. (26)

$$DR_{g} = \frac{{W_{a} }}{{W_{a} + E_{a} }}.$$
(26)

Accuracy is offered in Eq. (27)

$$Yc_{a} = \frac{{\left( {X_{a} + W_{a} } \right)}}{{\left( {X_{a} + W_{a} + Q_{a} + E_{a} } \right)}}.$$
(27)

6.4 Confusion Matrix Validation on Developed IRF-SOA-AM-BiRNN

In this phase, the analysis of confusion matrix in the developed IRF-SOA-AM-BiRNN-based decision-making model is validated and it is specified in Fig. 5. Confusion matrix analyses are performed over the predicted and actual values. In the developed IRF-SOA-AM-BiRNN-based decision-making technique, analyses are executed over Like positive, negative, and neutral. This analysis included the overall performance of test data by displaying the accurate and inaccurate outcomes. Here, the developed IRF-SOA-AM-BiRNN recognized 2577 negative samples, 473 neutral classes, and 310 positive classes from the entire dataset. Performing confusion matrix analysis in the developed IRF-SOA-AM-BiRNN-based decision-making model helped to verify the errors and also to detect the imbalanced dataset presented in the network. Moreover, it helps to execute several modifications to enhance the decision-making efficiency in a particular class. Analysis displayed that the developed technique IRF-SOA-AM-BiRNN gained superior outcomes.

Fig. 5
Fig. 5
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Confusion matrix validation on developed IRF-SOA-AM-BiRNN-based decision-making framework

6.5 Convergence and ROC Analysis of Suggested IRF-SOA-AM-BiRNN

Convergence and ROC computation analysis in the designed IRF-SOA-AM-BiRNN-based decision-making framework using big data are provided in Fig. 6. Convergence analysis is performed to analyze efficiency of the recommended model over the iteration. Executing convergence validation helps to identify the errors that arise, while training is executed. Convergence analysis helps to identify the desired solutions. In convergence validation, the developed IRF-SOA-AM-BiRNN gained superior convergence than the classical techniques like GRO-AM-BiRNN, DFA-AM-BiRNN, CFO-AM-BiRNN, and SOA-AM-BiRNN, correspondingly. Attaining improved convergence in the recommended framework facilitates to tackle the local optima issues raised in the network. Performing convergence validation in the recommended technique improved the decision-making efficiency and also increased the stability and flexibility of the developed system. The ROC computations are performed over the false-positive and true-positive values. The ROC curve validation helps to verify the trade-off between specificity and sensitivity. Here, the true-positive values are identified correctly by reducing the false-positive values over different threshold values. The ROC validations are commonly performed in different applications and also it is highly suitable for all types of observations. Accomplishing higher ROC in the developed IRF-SOA-AM-BiRNN-based decision-making framework assists to provide more precise decision-making outcomes to the user.

Fig. 6
Fig. 6
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Performance analysis on developed IRF-SOA-AM-BiRNN-based decision-making framework over a cost function and b ROC curve

6.6 State-of-the-Art Analysis on Suggested IRF-SOA-AM-BiRNN

Various performance analyses have executed in the suggested IRF-SOA-AM-BiRNN-based decision-making framework over existing heuristic models and decision-making models shown in Figs. 7 and 8. In this phase, entire validations are done with several batch size up to 64. Executing the analysis by changing the batch size helps to assure the consistency as well as the quality of a framework under different conditions. Performance validation using batch size helps to protect the developed decision-making model IRF-SOA-AM-BiRNN from overfitting and data variation issues. Moreover, this validation offers higher generalizability outcomes. Here, the accuracy validation is executed in the suggested IRF-SOA-AM-BiRNN to analyze the performance over several batch sizes. In the initial stage, the developed technique IRF-SOA-AM-BiRNN gained higher accuracy. Accomplishing comparatively maximize accuracy than the classical technique displayed that the recommended IRF-SOA-AM-BiRNN is more efficient than the traditional techniques. Improving the accuracy in the developed IRF-SOA-AM-BiRNN helps to eliminate the biasing issues and also offers higher risk management outcomes with transparency. Moreover, in the FDR validation, the suggested IRF-SOA-AM-BiRNN-based decision-making technique reduces the false alarm rate and errors in the network. Eliminating the error is essential in the model’s training speed and also reduces the validation time. Thus, it is revealed that the developed IRF-SOA-AM-BiRNN is widely used to enable better decisions to the user by analyzing enormous information in minimal time.

Fig. 7
Fig. 7
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Analysis of suggested IRF-SOA-AM-BiRNN-based decision-making framework over classical heuristic technique with a accuracy, b F1-Score, c FDR, d MCC, e NPV, f precision, g sensitivity, and h specificity

Fig. 8
Fig. 8
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Analysis of suggested IRF-SOA-AM-BiRNN-based decision-making framework over existing decision-making schemes with a accuracy, b F1-Score, c FDR, d MCC, e NPV, f precision, g sensitivity, and h specificity

6.7 Performance Analysis on Suggested IRF-SOA-AM-BiRNN

Representation of overall performance on suggested IRF-SOA-AM-BiRNN-based decision-making model over traditional heuristic technique and decision-making schemes in Tables 4 and 5. In this phase, performance analyses are done by varying the activation Functions. Here, the activation Functions are employed to execute the validation by processing the complicated data. Moreover, the activation function helps to study the non-linear relationship among the distant features. The ReLU activation function has a quick convergence rate; also, it processes the respective samples in a minimal time and also tackles the vanishing gradient issues. The sigmoid activation function is recommended to execute the binary classification and it generates higher output probably representation for all classes. In the accuracy computation, the developed IRF-SOA-AM-BiRNN-based decision-making technique accomplished higher performance as 3.57%, 9.35%, 7.18%, and 2.12% higher accuracy of decision-making than the classical techniques Like GRO-AM-BiRNN, DFA-AM-BiRNN, CFO-AM-BiRNN, and SOA-AM-BiRNN, respectively, at ReLU activation. The softmax activation gained a superior decision-making outcome as 93.92% than other activation functions like Leaky ReLU, sigmoid, Tanh, and ReLU. In other validations, the suggested IRF-SOA-AM-BiRNN provided a better decision-making performance than other techniques.

Table 4 Analysis of developed decision-making technique IRF-SOA-AM-BiRNN over classical heuristic techniques
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Table 5 Validation on suggested IRF-SOA-AM-BiRNN-based decision-making technique over existing decision-making models
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Deriving Eq. (11), the objective Function is formulated to maximize CSI and minimize FDR and FNR. Considering the FDR, it evaluates to measure the proportion of false positives among all rejected null hypothesis. On the other hand, the FNR determines the proportion of true positives that are incorrectly determined as negatives. The presence of high FDR and FNR values in the experimental evaluation suggests inaccurate predictions and generates sub-optimal outcomes. During this evaluation, the conventional GRO-AM-BiRNN model and LSTM model shows 29.47% and 25.80% in terms of FNR measure. The higher error rates shows ineffective performance and enables poor decision-making process. However, the proposed method shows that the FNR rate of 11.40% provides accurate outcomes. For enhancing customer satisfaction, CSI measure is a crucial role for maximizing the decision-making outcomes. Moreover, the recommended technique achieves the increased CSI rate of 92.78% than the existing techniques. Thus, the analysis outcomes displayed that the recommended technique is highly suitable for providing more accurate decisions in complex environments.

6.8 Statistical Computation on Developed IRF-SOA-AM-BiRNN

Statistical validation performed in the suggested IRF-SOA-AM-BiRNN-based decision-making technique over existing approaches is tabulated in Table 6. Validation is performed over the iterations to verify the decision-making efficiency of the developed technique. Executing statistical validation in the developed IRF-SOA-AM-BiRNN helped to identify its functionality over different conditions. Better statistical validation outcomes are accomplished according to the fitness functions. Minimal outcomes accomplished over multiple iterations are considered as the best value that helps to determine the performance of the developed framework. Furthermore, better statistical analysis-based outcomes are accomplished by fulfilling objectives Like improving the CSI and also reducing the FNR and FDR. Fulfilling the objective helps to secure more precise decision-making outcomes. In the best validation, suggested IRF-SOA-AM-BiRNN gained superior performance as 15.4%, 12.43%, 12.23%, and 12.09% higher than the classical techniques like GRO-AM-BiRNN, DFA-AM-BiRNN, CFO-AM-BiRNN, and SOA-AM-BiRNN, respectively. Hence, the analysis displayed that the recommended IRF-SOA-AM-BiRNN is highly suitable in all the complex conditions and enormous data are used.

Table 6 Statistical observation on recommended IRF-SOA-AM-BiRNN-based decision-making framework over classical techniques
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6.9 Computational Complexity and Run-Time Comparison of the Designed Model

The run time comparison and computational complexity of the developed big data analytics for the decision-making framework are tabulated in Tables 7 and 8. The decision-making performance in big data analytics has been provided within a Limited time. Thus, it helps to improve the satisfaction level in various organizations and industries by eliminating the risk of security concerns. Here, the developed IRF-SOA-AM-BiRNN model attains 19.509 min to provide accurate and reliable solutions. Thus, the empirical findings of the model show significant outcomes rather than the existing models. Based on the population size \(N_{pop}\) and iteration count \(Maxiter\) of the SOA algorithm, the computational complexity is examined to strengthen the model performance. Based on this analysis, it enables a better convergence rate to boost up the training efficiency. Here, the chromosome length is denoted as \(ch\ln\).

Table 7 Run-time comparison of the developed model
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Table 8 Computational complexity of the developed model
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6.10 Scalability Analysis of the Developed Model

Figure 9 visualizes the scalability analysis of the developed model. Here, the scalability analysis is further examined in terms of data size versus accuracy. Moreover, analyzing the scalability performance has the ability to applicable in a wide range of applications and effectively manages the complicated underlying patterns in the dataset. This can minimize the occurrence of data bias and strengthen the performance of the model.

Fig. 9
Fig. 9
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Scalability analysis of the developed model

7 Conclusion

An efficient big data analytics-based decision-making framework was designed by considering deep learning techniques for providing more accurate decisions to the users. Big data used for the validation were collected from benchmark resources and offered to the feature extraction phase. Here, the feature extraction procedures were performed in the map–reduce environment using the SI-PCA technique to acquire the significant features in the upcoming procedure. In the map–reduce environment, the feature mapping procedure was executed in the map phase, and also, the feature extraction procedure was performed in the reduce phase using SI-PCA. Next, the extracted features were provided as the input to the AM-BiRNN-based decision-making phase. In AM-BiRNN, significant parameters were optimized by developed IRF-SOA that helped to reduce the FDR and FNR and also boost the CSI. Finally, the decision-making outcomes were attained from AM-BiRNN, and then, multiple experiments were executed over the existing technique to verify its effectualness. In the accuracy validation, suggested IRF-SOA-AM-BiRNN gained superior decision-making outcomes as 9.89%, 3.28%, 7.29%, and 1.57% than the traditional decision-making techniques Like LSTM, ACGAN, CNN, and AM-BiRNN, correspondingly, in the sigmoid Function. Also, the outcome of the developed model attains 93.15% and 87.98% of accuracy and sensitivity in terms of ReLU and TanH activation function. Analysis outcomes displayed that the developed framework gained comparatively higher performance than the classical techniques without any errors.

Limitations and Future Work: Although the developed model shows significant outcomes, it needs to enhance the models efficiency. Dealing with a larger number of data arises data quality issues due to the presence of inaccurate and incomplete data. Therefore, the developed model needs to adopt with the pre-processing techniques to enhance the data quality. Additionally, data breaches and unauthorized access is randomly occurred. Therefore, the work needs to adopt with considering advanced encryption and decryption techniques to secure the data from unauthorized access. In the future, the developed big data-based decision-making framework will be extended by considering the security conditions for protecting sensitive information. Moreover, ensemble features will be considered to verify the performance, and also encryption standards will be introduced to provide better security and privacy in forthcoming research works.

Practical Applications: In real-time scenarios, big data analysis is specifically applied in improving the customer experience in various online platforms, financial services, healthcare, and smart city applications. Generally, the hospital utilizes big data analytics for monitoring the patient’s health condition, ensures better treatment planning strategies, and effectively enhances the patient outcomes. Moreover, the public health organizations have the ability to easily track and analyze the patient disease to maximize the decision-making performance by eliminating the risk at critical scenarios. Big data analytics in smart applications could effectively optimize traffic planning management and resource allocation in smart cities. In financial sector, the big data analytics are effectively applied in protecting the details of the customer and minimizing the industries to detect the fraudulent activities.