A Study of the Ink Drop Spread Method using Heuristic Rules

Abstract

The ink drop spread (IDS) method is a modeling technique based on the idea of soft computing. This method divides a multi-input-single-output (MISO) modeling target system into multiple single-input-single-output (SISO) systems, which correspond to each input-output pair and are divided into small SISO systems. In order to make multiple images for each SISO system, the IDS method plots the input-output data of the target system on the two-dimensional planes like the wave pattern generated when the ink is dropped into the water. For each data point, an ink drop is dropped onto the two-dimensional plane so that the density of the ink is lower at the point more distant from the data point. By plotting all the data points in this way, the cumulative density of ink is higher at the point where more ink drops overlap, and as a result, a characteristic ink pattern appears on the plane. The IDS method extracts the features of the target system from these ink patterns, and integrates them into fuzzy inference to model the target system. It is important for the IDS method to decide an appropriate partitions of each input for accurately modeling the target system. Therefore, some methods have been proposed to decide partitions. However, there are some problems with these methods. For examle, they cannot decide both the positions and number of partitions simultaneously and require a long processing time to decide partitions. In this article, we propose a new partition method for the IDS method using the information exploited from images. The proposed method extracts the information useful for deciding appropriate partitions from the images generated on the two-dimensional plane, decides partitions using that information, and adjusts the generated partitions. In this article, we compare our method with the existing partition methods such as equal divide method and Genetic IDS and show that our method can generate better partitions with less search steps. Furthermore, through comparing our method with other modeling methods such as Feedforward Neural Network and Support Vector Machine, we demonstrate that our IDS method is more effective in approximating complex functions and solving binary classification problems.