ABSTRACT
Many practical problems in operations research can be modeled or approximated as Semidefined programming (SDP) problems. Studies show that SDP has great potential to effectively solve various Data Analysis problems. Advances in technology have led to the development of effective data analysis techniques to extract meaningful information that can be further used to expand knowledge from ever-growing data sets. Principal Component Analysis (PCA) and Clustering, widely used to reduce the dimensionality of attribute space and identify some patterns hidden between objects, underlie many data analysis methodologies. However, it appears that the use of SDP models in these two techniques is not common, which may be due to the unfamiliarity of the data analysts community with such developments. In this chapter, we review and explore existing research studies on the application of SDP-based approaches to efficient solving problems related with PCA and Clustering. We show that SDP is an important tool for reliable and robust estimates for a wide range of statistical methodologies. We expect this survey chapter to highlight the most important capabilities of SDP for effective data analysis, making it a useful tool for data analysts.
