The paper studies the peculiarities of processing big data in industrial systems. Existing methods of optimizing user information and the effectiveness of recommender systems have been considered. The Funk SVD algorithm was analyzed, and the practicality of its application to large sparse data was determined. A modification of the Funk SVD algorithm was proposed, which employs a smaller amount of user data to form recommendations. It was also suggested to use additional parameters that better characterize the services for more accurate work of recommender systems. Simulations were carried out, and a decrease in the duration and an increase in the accuracy of calculations using the proposed methods were determined. 

Model of Large Sparse Datasets Processing Efficiency in IIOT

The paper studies the peculiarities of processing big data in industrial systems. Existing methods of optimizing user information and the effectiveness of recommender systems have been considered. The Funk SVD algorithm was analyzed, and the practicality of its application to large sparse data was determined. A modification of the Funk SVD algorithm was proposed, which employs a smaller amount of user data to form recommendations. It was also suggested to use additional parameters that better characterize the services for more accurate work of recommender systems. Simulations were carried out, and a decrease in the duration and an increase in the accuracy of calculations using the proposed methods were determined.

Continuous improvement of digital technologies allows for the introduction of new and improvement of existing areas of human life. Medicine, education, industry and many other areas have now, due to the pandemic situation, changed the usual way of functioning. The involvement of modern methods of data processing and management of large-scale systems allows for performing work tasks with less human intervention. The Industrial Internet of Things (IIoT) has become an important stage in the development of industrial systems. The organization of IIoT allows us to flexibly manage the production system, rationally use resources and provide users with a wide range of services. It is necessary to involve a large number of intelligent devices that process data from the environment and transmit it for further processing to control devices. For efficiently and quickly analyzing the information coming from different sensors we should use the methods of working with Big Data. Optimization of information that is not important for further analysis and decision-making can significantly reduce computational time while maintaining high accuracy. Machine learning methods simplify the process of Big Data analysis and create an industrial system based on the information obtained. Because IIoT systems are distributed and consist of many components, federated machine learning is used. The peculiarities of the use of distributed machine learning for Big Data analysis are investigated. Preliminary optimization of data arrays using the Singular Value Decomposition (SVD) method was proposed. The research results proved the proposed SVD method's effectiveness for Big Data pre-optimization in the IIoT systems. Also in the paper, we offered the modified method of SVD, which is adapted to work in the distributed IIoT systems. The research results showed high accuracy and reasonableness of calculations. To improve the efficiency of sparse data analysis in IIoT, it is also suggested to use the Funk-SVD algorithm. 

A Modified Federated Singular Value Decomposition Method for Big Data and ML Optimization in IIoT Systems

Driven by Industry 4.0 and intelligent manufacturing, computer vision has emerged as a core technology in industrial automation due to its non-contact sensing capabilities and real-time processing advantages. However, challenges such as environmental interference and real-time performance limitations persist. A bibliometric analysis of $\mathbf{1, 0 0 0}$ publications (2014-2025) using VOSviewer reveals several key findings: author productivity is characterized by a stratified distribution, with a limited number of high-impact scholars; high-output research institutions are scarce, and collaborative networks remain underdeveloped; globally, research is led by China and the United States within a multi-polar framework, with increasing international collaboration; and there is a clear transition from traditional image analysis to deep learning, with artificial intelligence serving as a pivotal driver for future innovation. Despite progress, environmental adaptability and real-time efficiency remain critical unresolved issues. Future research should prioritize the enhancement of algorithm robustness, interdisciplinary collaboration, standardization efforts, and greater involvement of the industrial sector.

Research Status and Trends of Industrial Automation Based on Computer Vision Technology

The processing of big data is an exceedingly urgent challenge in the functioning of modern information systems. The latest information technologies must be employed to collect, store, and analyze vast amounts of information. Intelligent data processing systems were implemented in numerous fields, particularly in the industry. Smart industrial systems also utilize data from various devices, enabling automated management processes and network component analysis. A prime example of an intelligent industrial system is the smart grid, which efficiently distributes electricity to users by considering demand, network parameters, load, etc. Processing large amounts of information necessitates the use of machine learning methods and mathematical data analysis. Matrix factorization serves as an exemplary technique for transforming information into a more convenient form for further processing, establishing relationships between elements, and optimizing outcomes. In particular, the SVD (Singular Value Decomposition) and Funk-SVD algorithms are employed to address big data processing challenges, and they were discussed in this work. The key features of processing large data volumes in industrial smart grid systems were analyzed in the paper. The advantages of distributed computing for more efficient information analysis were identified. The recommendation algorithms that enable faster and more accurate processing of extensive data were explored in the study. Specifically, the SVD and Funk-SVD algorithms, used in recommendation systems for large data processing, were examined. A method of distributed matrix factorization to provide recommendations to smart grid system users was proposed in the paper. This approach involves the exchange of public data between devices and the local processing of private data. The advantages of this distributed model include flexibility in adjusting parameters, improved calculation accuracy through result exchange between nodes, high data processing speed, and scalability were identified. The conclusion that the proposed method can be effectively used in recommendation systems within the smart grid context, enhancing automated management processes and resource distribution was exclaimed. 

pdf/investigation-of-distributed-matrix-factorisation-efficiency-50xbq8wp0y.pdf

Investigation of distributed matrix factorisation efficiency in the industrial systems

The problem of effective Big Data processing in the Industrial Internet of Things was investigated in the work. The method of Federated Machine Learning as a tool for the analysis of large volumes of information in IIoT was described. The algorithm of Singular Value Decomposition was analyzed, which effectively analyzes the user data and the possibility of its modification. The increase of computational reliability using the FedSVD algorithm was investigated. The software modeling which confirms the efficiency of the proposed method has been carried out.

Big Data Analysis in IIoT Systems Using the Federated Machine Learning Method

The creation of new technologies and their implementation in various fields necessitated Big Data processing and storage. In industrial systems, modernization means the use of a large number of smart devices that perform specialized functions. Data from such devices are used to control the system and automate production processes. A change in the parameters of individual components of the manufacturing system may indicate the need to adjust the global management strategy. The intelligent industrial systems main characteristics were defined in the paper. The Industrial Internet of Things concept and the relevance of the modernization problem for manufacturing were analyzed. The problems of processing Big Data in Industrial Internet of Things systems were examined in the paper. The use of recommendation systems for quickly finding relationships between users and production services was considered. The advantages of Big Data analysis by recommendation systems, which have a favourable effect on industrial enterprise efficiency were given. The use of SVD and FunkSVD matrix factorization algorithms for processing sparse data matrices was analyzed. The possibility of optimizing arrays of information, choosing the most important, and rejecting redundancy with the help of the above algorithms was determined. The proposed algorithms were simulated. The advantages of FunkSVD for working with sparse data were assigned. It was found that the FunkSVD algorithm processes the data in a shorter time than SVD, but this does not affect the accuracy of the result. The SVD is also more difficult to implement and it requires more computing resources was established. It has been shown that FunkSVD uses a lot of data to determine the relationships between it and make recommendations about the products most likely to be of interest to users. To increase the efficiency of processing large sets of information the FunkSVD algorithm was improved in such a way that it uses fewer data to generate recommendations. Based on the results of the research, the modified method works faster than the non-modified one but retains high calculation accuracy, which is important for work in recommender systems. The possibility of providing recommendations to users of industrial systems in a shorter period, thus improving their relevance, was revealed. It was proposed to continue research for finding the optimal parameters of the FunkSVD algorithm for Big Data processing.

Matrix factorization of big data in the industrial systems

The problems of automating production processes using the intelligent analysis of big data were discussed in the paper. Existing methods of processing information from various devices, and determining data patterns or regularities were studied. The effectiveness of the SVD and Funk SVD algorithms for processing big data was determined. A modified Funk SVD data analysis algorithm was proposed, which provides distributed calculations, and exchanges the results between local nodes in a safe way. The research results of the proposed algorithm demonstrate its high speed and accuracy. The recommender model for improving the Industrial Automation Systems' efficiency based on the modified method was proposed.

Research on the Automated Decision-Making Effectiveness in Industrial Automation System

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Big Data Analysis in IIoT Systems Using the Federated Machine Learning Method

Matrix factorization of big data in the industrial systems

Research on the Automated Decision-Making Effectiveness in Industrial Automation System