A novel multivariate analysis method with noise reduction

In this paper, we develop a novel Partial Regularized Least Squares (PRLS) method which combined regularization algorithm with Partial Least Squares (PLS) analysis for noise reduction application. In general, Least Squares and PLS fall into an overfitting problem with ill-posed condition. It means that some feature selections make the training data to have better adaptability to the model, but the quality of prediction would be poorly compared to the training data for the testing information. We usually expected that the selected model should have consistent predicted result between the training data and testing data. In order to evaluate the performance of PRLS method, we generate two simulation data, i.e. cosine waveform and 8^th polynomial waveform with Gaussian distribution noisy for calculating two values, i.e. Correlation Coefficient value (RR value) and Root Mean Square Error (RMSE) for testing. The results show that the RR value of PRLS is higher than PLS's at increasing noise-to-signal ratio. As well the RMSE of PRLS is lower than PLS's at same S/N ratio. We also show that the PRLS approximates to the desired output at calibration. It can be applied in real-world noise reduction in the future.