Relationship and connectivity of incomplete data collection

Abstract

A basic problem in data science is to classify a massive data set into different categories. In addition, when more new data samples are collected or come from online sources, we want to know how to put the new data sample into an appropriate category. This problem contains such information as classification, learning, and reconstruction. As we discussed in Chap. 2, the problem is central to several disciplinary areas including artificial intelligence, pattern recognition, and statistics. It is obvious that this is still a main problem in data science but the size of the data set has been changed to "BigData" and the ultimate goal of the process has become online based in many cases. In this chapter, we introduce a comprehensive method for this complex problem. This method provides a unified framework for concurrent data science to solve the related problem. The method begins by considering data relations and connectivity among data points or data groups. These relations and connectivity are mostly incomplete. Then, we build a model to analyze, classify, or reconstruct the data or data sets, which is called the λ-connectedness method. The method is built on general graphs. It also has some relations to persistent analysis that will be discussed in Chap. 6. Persistent analysis tries to find topological structures in cloud data. Combining λ-connectedness with persistent analysis can result in the classification of data sets into geometrically meaningful components, such as desired shapes or having characteristics of tracking and recognition.