Hybrid random projection technique for enhanced representation in high-dimensional data

This paper introduces a novel hybrid random projection method (HRP) that effectively combines the strengths of normal random projection (NRP) and plus-minus one random projection (PMRP). By incorporating a blending parameter, HRP optimises the contributions of the NRP and PMRP, reducing the dimensions of the data while ensuring that the structure of the data is preserved. Conventional methods, such as NRP and PMRP, are recognised for their benefits; however, they also have limitations. NRP is generally accurate but can encounter difficulties with certain data types or noise. The PMRP is simple, but occasionally fails to capture complex relationships within the data. The performance of HRP is investigated through comprehensive evaluations, including simulations and real-world data analyses from key machine learning datasets, such as period change, toxicity, MNIST, and human activity recognition (HAR). We examine various factors such as sample size, dimensions of the original and reduced data, and sparsity. Distance distortion is the primary metric utilised to measure performance, and indicates how well the dataset structure is maintained after dimension reduction. In every test, HRP consistently demonstrates the least distance distortion, performing superiorly to the NRP and PMRP. This is true for a range of scenarios and datasets. HRP represents a significant advancement in dimension reduction techniques. Its ability to minimise information loss during the reduction process demonstrates its potential as a powerful tool for managing complex high-dimensional data in practical applications. This renders HRP an important development in the fields of machine learning, intelligent systems, and artificial intelligence, offering improved efficiency and precision in data analyses.