BACKGROUND: The huge quantity of data produced in Biomedical research needs sophisticated algorithmic methodologies for its storage, analysis, and processing. High Performance Computing (HPC) appears as a magic bullet in this challenge. However, several hard to solve parallelization and load balancing problems arise in this context. Here we discuss the HPC-oriented implementation of a general purpose learning algorithm, originally conceived for DNA analysis and recently extended to treat uncertainty on data (U-BRAIN). The U-BRAIN algorithm is a learning algorithm that finds a Boolean formula in disjunctive normal form (DNF), of approximately minimum complexity, that is consistent with a set of data (instances) which may have missing bits. The conjunctive terms of the formula are computed in an iterative way by identifying, from the given data, a family of sets of conditions that must be satisfied by all the positive instances and violated by all the negative ones; such conditions allow the computation of a set of coefficients (relevances) for each attribute (literal), that form a probability distribution, allowing the selection of the term literals. The great versatility that characterizes it, makes U-BRAIN applicable in many of the fields in which there are data to be analyzed. However the memory and the execution time required by the running are of O(n(3)) and of O(n(5)) order, respectively, and so, the algorithm is unaffordable for huge data sets. RESULTS: We find mathematical and programming solutions able to lead us towards the implementation of the algorithm U-BRAIN on parallel computers. First we give a Dynamic Programming model of the U-BRAIN algorithm, then we minimize the representation of the relevances. When the data are of great size we are forced to use the mass memory, and depending on where the data are actually stored, the access times can be quite different. According to the evaluation of algorithmic efficiency based on the Disk Model, in order to reduce the costs of the communications between different memories (RAM, Cache, Mass, Virtual) and to achieve efficient I/O performance, we design a mass storage structure able to access its data with a high degree of temporal and spatial locality. Then we develop a parallel implementation of the algorithm. We model it as a SPMD system together to a Message-Passing Programming Paradigm. Here, we adopt the high-level message-passing systems MPI (Message Passing Interface) in the version for the Java programming language, MPJ. The parallel processing is organized into four stages: partitioning, communication, agglomeration and mapping. The decomposition of the U-BRAIN algorithm determines the necessity of a communication protocol design among the processors involved. Efficient synchronization design is also discussed. CONCLUSIONS: In the context of a collaboration between public and private institutions, the parallel model of U-BRAIN has been implemented and tested on the INTEL XEON E7xxx and E5xxx family of the CRESCO structure of Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), developed in the framework of the European Grid Infrastructure (EGI), a series of efforts to provide access to high-throughput computing resources across Europe using grid computing techniques. The implementation is able to minimize both the memory space and the execution time. The test data used in this study are IPDATA (Irvine Primate splice- junction DATA set), a subset of HS3D (Homo Sapiens Splice Sites Dataset) and a subset of COSMIC (the Catalogue of Somatic Mutations in Cancer). The execution time and the speed-up on IPDATA reach the best values within about 90 processors. Then the parallelization advantage is balanced by the greater cost of non-local communications between the processors. A similar behaviour is evident on HS3D, but at a greater number of processors, so evidencing the direct relationship between data size and parallelization gain. This behaviour is confirmed on COSMIC. Overall, the results obtained show that the parallel version is up to 30 times faster than the serial one.

We propose an incremental support vector machine (SVM) approach to regularization. Support vectors are added in an iterative manner during the training process. For each new vector added, the kernel parameters are settled according to an extended chained version of the Nadaraja-Watson estimator. We show this approach minimize the expected risk and leads to an efficient learning procedure.