## 1 Introduction
The main objective of this paper is to develop a reliable CAD system to distinguish between hepatocellular carcinoma (HCC), i.e., the most common type of primary liver malignancy and a leading cause of death in people with cirrhosis worldwide, and liver abscess based on the support vector machine (SVM) method [37; 38; 39; 40; 41] and ultrasound images of textural features. To date, there is no algorithm that is best in machine learning. A good classifier depends on the data. Some algorithms work with certain data or applications better than others. The major advantage of SVM is the need for fewer parameters to make it operational with high accuracy rates, and various features can be extracted. However, the textural feature applied the most is the gray-level co-occurrence matrix (GLCM) (e.g., see [42; 43; 44; 45; 46]). GLCM feature extraction, proposed by [PERSON] [42] in 1973 to analyze an image as a texture, belongs to the second-order statistics. GLCM means a tabulation of the frequencies or how often a combination of pixel brightness values in an image occurs. In this paper, the other method we used to analyze the ROIs is the gray-level run-length matrix (GLRLM) (e.g., see [47; 48; 49; 50; 51]). It was first proposed by [PERSON] in 1975 with five features [47]. GLRLM is a matrix including the texture features that can be extracted for texture analysis. In 1990, [PERSON] et al. [48] suggested two new features to extract gray-level information in the matrix before [PERSON] and [PERSON] [49] offered another four features following the idea of a joint statistical measure of gray level and run length. [PERSON] [50] provided a good summary of some features achieved by the GLRLM. In this paper, we compared the results from the popular features of the GLCM and the gray-level run-length matrix (GLRLM). In this paper, three feature selection models--(i) sequential forward selection (SFS) [52; 53], (ii) sequential backward selection (SBS) [53; 54], and (iii) F-score [55]--are adopted to distinguish the two liver diseases. [PERSON] and [PERSON] introduced a feature selection technique using the divergence distance as the criterion function and the SBS method as the search algorithm [52; 53]. [PERSON] discussed its 'bottom-up' counterpart, known as SFS [53; 54]. In this research, a large number of features are included, comprising 96 features from each sample. If all of them are used to train a classifier, it not only takes too much time but also cannot easily achieve high accuracy. To reduce the processing time and improve the accuracy, it is necessary to search for the important features from the feature set. Then, the crucial features of the samples are used to train and test by SVM. We took several steps to achieve this goal. First, in the ultrasound images, the liver lesions are marked by experienced physicians and the regions of interest (ROIs) are circled inside a red boundary, as illustrated in Figure 1, meaning that part of the liver lesion is located inside the red boundary of the whole-liver image. Second, all features are extracted from the collected ROIs. Third, several feature selection processes are carried out to optimize the feature set. Finally, the optimal feature sets are used to train and test by SVM.