Logical analysis of data --- the vision of Peter L. Hammer

Logical analysis of data (LAD) is a special data analysis methodology which combines ideas and concepts from optimization, combinatorics, and Boolean functions. The central concept in LAD is that of patterns, or rules, which were found to play a critical role in classification, ranked regression, clustering, detection of subclasses, feature selection and other problems. The research area of LAD was defined and initiated by Peter L. Hammer, who was the catalyst of the LAD oriented research for decades, and whose consistent vision and efforts helped the methodology to move from theory to data analysis applications, to achieve maturity and to be successful in many medical, industrial and economics case studies. This overview presents some of the basic aspects of LAD, from the definition of the main concepts to the efficient algorithms for pattern generation, and from the complexity analysis of the difficult problems embedded in LAD to its biomedical applications. We focus in this paper only on some recent developments in LAD which were of particular interest to Peter L. Hammer, who played a key role in obtaining all the results described here. The presentation in this overview is based on the original publications of Peter L. Hammer and his co-authors. We dedicate this paper to the memory of Peter L. Hammer.