Owsinski’s book provides an interesting “bi-partial” strategy for analyzing data; it is not only uniquely general, but also successful in building several useful methods to tackle issues related to data analysis, including algorithms and models. It focuses essentially on the fundamental clustering problem, that is, grouping the similar and distinguishing the dissimilar. This approach introduces readers to a general objective function and thereby to a bigger class of concrete implementation through which a sub-optimizing procedure can be developed together with a variety of applications.

Chapter 1 familiarizes readers with the notation and main assumptions through a situation and its features. Chapter 2 describes the problem of cluster analysis; subtopics include the general formulation, the nature of partition, similarity and dissimilarity, cluster definition, the use of metaheuristics, the number and shapes of clusters, and so on. Chapter 3, “The General Formulation of the Objective Function,” presents the well-illustrated logic behind the construction of the objective function. The subtopics in chapter 4, “Formulations and Rationales for Other Problems in Data Analysis,” include categorization, optimum histogram, block-diagonalization, rule extraction, and so on. The subtopics in chapter 5, “Formulations in Cluster Analysis,” include the bi-partial version of the k-means algorithm and other implementations, comparing and assessing cluster quality, and so on. Chapter 6, “The General Suboptimization Algorithm and Its Implementation,” includes some comments on the procedure, concrete realizations and properties of the algorithm, algorithms for the objective functions, both additive and nonadditive with respect to clusters, and a note on how to design an algorithm. Chapter 7, “Applications to Preference Aggregation,” includes the linear programming formulation, the parameterization, and the alternative algorithmic approach. Chapter 8 concludes the book.

I enjoyed reading this book and recommend it as a helpful reference material to undergraduate students of computing and data science.