Clustering techniques have received attention in many fields of study such as engineering, medicine, biology and data mining. The aim of clustering is to collect data points. The K-means algorithm is one of the most common techniques used for clustering. However, the results of K-means depend on the initial state and converge to local optima. In order to overcome local optima obstacles, a lot o...

Data clustering considers the problem of grouping data into clusters based on its similarity measure. It is one of the central problems for data analysis, with a wide applications to a variety of areas such as marketing research, data mining and social behavior analysis.Real world objects can be modeled as points in a high dimensional metric. So clustering these real world data is corresponded ...

Traditional odd lot trades (i.e., involving fewer than 100 shares) now comprise over half of all equity on U.S. exchanges. Under Regulation National Market System, however, these are excluded from a market center’s trade execution statistics. In addition, while brokers required to consider quotes as part their duty best execution, formally the calculation national bid and offer. This Article, w...