A Study on Noise Tolerance of the IDS Method in Regression

Abstract

The ink drop spread (IDS) method is a modeling technique that provides several advantages with regard to real- time capabilities, tractability, and interpretability of models; thus, it has a good potential to be a useful soft computing tool. Robustness is one of the criteria that determine the effectiveness of a soft computing approach. This paper deals with the noise tolerance of the IDS method in regression. In the experiments, the generalization performance of the IDS models is compared with that of feedforward neural networks in a noisy environment. The experimental results demonstrated that the IDS method provides sufficient model accuracy and stable noise sensitivity. IDS modeling is based on the processing of pattern information using two-dimensional data planes. Thus, reducing the resolution of the data planes significantly increases the learning speed. This paper also reveals that low resolutions of the data planes are applicable to real-time modeling regardless of the presence of noise. I. INTRODUCTION Soft computing is a discipline that involves low-cost, tractable, and robust computing in the presence of uncer- tainty (1). Humans possess a remarkable ability to process intricate information with ease; it is difficult to model such in- formation by using classical mathematical approaches. There- fore, some soft computing methodologies focus on human thought processes and physical characteristics. For example, fuzzy logic is modeled on the linguistic and logical aspects of the human thought processes, and neural networks are physically modeled on the human brain. Shouraki et al. (2)- (4) have proposed the active learning method (ALM) as a soft computing methodology. The ALM is analogous to fuzzy logic since it is algorithmically modeled on the intelligent information-handling processes of the human brain. While fuzzy logic uses linguistic and logical processing, the ALM is characterized by intuitive pattern-based processing. This concept is based on the hypothesis that humans interpret information in the form of pattern-like images rather than as numerical or logical forms. The ink drop spread (IDS) method is a modeling technique used within the framework of ALM. IDS modeling is based on simple processing that uses pattern information instead of complex formulas and is capable of stable and fast con- vergences. We have examined the performance of the IDS method by using several benchmarks in terms of the model accuracy and real-time capabilities; we have demonstrated that this method can deal with various modeling targets, ranging from logic operations to complex nonlinear systems (5)(6). Robustness is one of the criteria that determine the effec- tiveness of a soft computing approach. In this paper, the noise tolerance of the IDS method is presented. In the experiments, we employed Hwang's five-function set (7) for regression modeling. This benchmark has often been utilized by many researchers to measure the generalization performance of feedforward neural networks (FNNs). The generalization of the IDS models was compared with that of the FNNs using noisy training data. The experimental results revealed that the IDS models exhibited sufficient accuracy and stable noise sensitivity in comparison with the average performance of the FNNs. One of the considerations in selecting the modeling method is that either high-accuracy modeling or fast rough modeling is prioritized. Real-time and dynamic learning applications may prioritize fast rough modeling. In the modeling process of the IDS method, information from a modeling target is described as pattern images on multiple two-dimensional data planes, and these images are processed to generate learning data. This implies that the selection of the resolution of the data planes affects the learning speed and model accuracy. In (6) and (8), the effect of the resolution of the data planes was examined by comparing the 256£256 and 1024£1024 resolutions. The use of the 256£256 resolution resulted in very fast convergence and had almost negligible effect on the model accuracy. Thus, we considered that the resolution of the data planes was the major factor that determined the real-time performance of the IDS method. In (9), it is concluded that a rough resolution such as 128£128 or 256£256 is useful in real-time modeling in terms of both the learning speed and accuracy. For example, the learning speed when using the 128£128 resolution is approximately 64 times faster than that when using the 1024£1024 resolution. In this paper, the noise tolerance of the IDS method when using the 128£128 resolution was compared with that when using the 1024£1024 resolution. The experimental results showed that the difference in the resolution of the data planes does not affect the noise tolerance of the IDS modeling. Thus, we ensured that the use of low resolutions is effective for real-time modeling.