Logical analysis of data—An overview: From combinatorial optimization to medical applications

Abstract

The paper presents a review of the basic concepts of the Logical Analysis of Data (LAD), along with a series of discrete optimization models associated to the implementation of various components of its general methodology, as well as an outline of applications of LAD to medical problems. The combinatorial optimization models described in the paper represent variations on the general theme of set covering, including some with nonlinear objective functions. The medical applications described include the development of diagnostic and prognostic systems in cancer research and pulmonology, risk assessment among cardiac patients, and the design of biomaterials.

Application of Support Vector Machine Classifiers to Preoperative Risk Stratification With Myocardial Perfusion Scintigraphy

“…There seems to be only 1 report using the SVM for cardiac risk stratification, 26 in which the SVM classifiers offered more favorable results compared with others. The SVM affords a complex hyperplane by using support vectors and maximization of the margin, even when a linear separation is difficult or impossible.…”

“…Among supervised learning methods, SVM is thought to be one of the most accurate techniques. However, as far as we investigated, there seems to be only 1 report using SVM for the risk assessment of patients with cardiac diseases, 26 and no data is available using SVM for stratifying perioperative cardiac risk.…”

Logical analysis of multi-class data

“…Below we briefly outline the basic components of the LAD algorithm. A more detailed overview can be found in [4,29].…”

Bichromatic separability with two boxes: A general approach

“…In some cases, as in Medical Data Analysis [8], methods can produce slanted classifications due to the fact that some data may be defective or contain values out of reasonable ranges. In other cases, we may obtain data hard to classify due to relatively small similarities between different classes.…”