No abstract

Cluster analysis organizes data into sensible groupings and is one of fundamental modes of understanding and learning. The widely used K-means and hierarchical clustering methods can be dramatically suboptimal due to local minima. Recently introduced convex clustering approach formulates clustering as a convex optimization problem and ensures a globally optimal solution. However, the state-of-the-art convex clustering algorithms, based on the alternating direction method of multipliers (ADMM) or the alternating minimization algorithm (AMA), require large computation and memory space, which limits their applications. In this paper, we develop a very efficient smoothing proximal gradient algorithm (Sproga) for convex clustering. Our Sproga is faster than ADMM-or AMA-based convex clustering algorithms by one to two orders of magnitude. The memory space required by Sproga is less than that required by ADMM and AMA by at least one order of magnitude. Computer simulations and real data analysis show that Sproga outperforms several well known clustering algorithms including K-means and hierarchical clustering. The efficiency and superior performance of our algorithm will help convex clustering to find its wide application.

With the increase of water-inrush accidents from coal mine, water-inrush prediction has become a significant aim for coal mine safety experts. As an intelligent classifying algorithm, the Classification and Regression Tree (CART) is a potential method for predicting the possibility of water inrush from coal seam floor. One of its main advantages is that the Decision Rules (DRs) can be extracted from its structure.Another is that these DRs can be used to analysis safety problems.However, the time of establishing the decision tree is too long because of the existence of the redundant information. This paper presents an effective method named NRS-CART, which is a hybrid method by combining neighborhood rough set (NRS) and classification and regression tree (CART). Moreover, the novel approach was used to detect and classify water-inrush possibilities. The experimental results showed that it only took 0.3455 seconds to predict the water-inrush possibility using the proposed method, whereas the CART spent 1.0411 seconds to predict for the same dataset, and at the same time the prediction accuracy was also improved from 88.78% to 93.90%.