This study investigates use of echocardiography to assess the related issues about whether the heart function of a subject examined is normal or not. Two-dimensional echocardiography can make the heart inspection, and provide very detailed informations for each part of the cardiovascular structures with a high degree of accuracy. Many studies indicated that the systolic and diastolic function with left ventricle of heart disease in patients was poorer than those of normal patients. Therefore it is of interest to study the systolic and diastolic function for examining whether there are heart problems. In this work, the data is the gray-scale values of left ventricular static ultrasound images. The gray-scale differences between systolic and diastolic period, are used to assess whether the patient suffers from the heart diseases or not. Here, we use factor analysis to simplify and select the crucial factors, namely the function in different area of the left ventricle. Finally, linear and quadratic discriminant analyses are used to distinguish the normal and the abnormal subjects.

Due to the association of heart diseases and the patterns of the diastoles and systoles of heart in left ventricle, we analyze and classify the data gathered form Kaohsiung Veterans General Hospital by using the cardiology ultrasound images. We make use of the differences between the gray-scale values of diastoles and systoles in left ventricle to evaluate the function of heart. Following Chen (2011) and Kao (2011), we modified the way about the reduction and alignment of the image data. We also add some more subjects into the study. We treat images in two manners, saving the parts of concern. Since the ultrasound image after transformation to data form is expressed as a high-dimensional matrix, the principal component analysis is adapted to retain the important factors and reduce the dimensions. In this work, we compare the loadings calculated by the usual principal and sparse principal component analysis, then the factor scores are used to carry out the discriminant analysis and discuss the accuracy of classification. By the statistical methods in this work, the accuracy, sensitivity and specificity of the original classifications are over 80% and the cross validations are over 60%.

Most of the cardiac structural abnormalities will be examined by echocardiography. With more understanding of heart diseases, it is commonly recognized that heart failures are closely related to left ventricular systolic and diastolic functions. This work discusses the association between gray-scale differences and the risk of heart disease from the changes in left ventricular systole and diastole of ultrasound image. Owing to the large dimension of data matrix, following Chen (2011), we also simplify the influence factors by factor analysis and calculate factor scores to present the characteristics of subjects. Two kinds of classification criteria are used in this work, namely logistic model with distance indicator and discriminant function. According to Guo et al. (2001), we calculate the Mahalanobis distance from each subject to the center of normal and abnormal group, then use logistic model to fit the distances for classification later. This is called logistic model with distance indicator. For the discriminant analysis, the regularized method by Friedman (1989) for estimation of covariance matrix is used, which is more flexible and can improve the covariance matrix estimates when the sample size is small. As far as the cut-point of ROC curve, following the approach as in Hanley et al. (1982), we find the most appropriate cut-point which has good performances for both sensitivity and specificity under the same classification criteria. Then the regularized method and the cut-point of ROC curve are combined to be a new classification criterion. The results under the new classification criterion are presented to classify normal and abnormal groups.