The support vector machine （SVM） is a novel machine learning tool in data mining. In this paper, the geometric approach based on the compressed convex hull （CCH） with a mathematical framework is introduced to solve SVM classification problems. Compared with the reduced convex hull （RCH）, CCH preserves the shape of geometric solids for data sets; meanwhile, it is easy to give the necessary and sufficient condition for determining its extreme points. As practical applications of CCH, spare and probabilistic speed-up geometric algorithms are developed. Results of numerical experiments show that the proposed algorithms can reduce kernel calculations and display nice performances.
Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.
In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.
Protein-protein interactions play a crucial role in the cellular processsuch as metabolic pathways and immunological recognition. This paper presents a new domain score-based support vector machine （SVM） to infer protein interactions, which can be used not only to explore all possible domain interactions by the kernel method, but also to reflect the evolutionary conservation of domains in proteins by using the domain scores of proteins. The experimental result on the Saccharomyces cerevisiae dataset demonstrates that this approach can predict protein-protein interactions with higher performances compared to the existing approaches.
