In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems.

Ex Output:
Flexible Multi-layer Sparse Approximations of Matrices and Applications


Ex Input:
This paper presents capabilities of using genetic algorithms to find approximations of function extrema, which cannot be found using analytic ways. To enhance effectiveness of calculations, algorithm has been parallelized using OpenMP library. We gained much increase in speed on platforms using multithreaded processors with shared memory free access. During analysis we used different modifications of genetic operator, using them we obtained varied evolution process of potential solutions. Results allow to choose best methods among many applied in genetic algorithms and observation of acceleration on Yorkfield, Bloomfield, Westmere-EX and most recent Sandy Bridge cores.

Ex Output:
GENERATING EXTREMA APPROXIMATION OF ANALYTICALLY INCOMPUTABLE FUNCTIONS THROUGH USAGE OF PARALLEL COMPUTER AIDED GENETIC ALGORITHMS


Ex Input:
The Bacterial Foraging Optimization (BFO) is one of the metaheuristics algorithms that most widely used to solve optimization problems. The BFO is imitated from the behavior of the foraging bacteria group such as Ecoli. The main aim of algorithm is to eliminate those bacteria that have weak foraging methods and maintaining those bacteria that have strong foraging methods. In this extent, each bacterium communicates with other bacteria by sending signals such that bacterium change the position in the next step if prior factors have been satisfied. In fact, the process of algorithm allows bacteria to follow up nutrients toward the optimal. In this paper, the BFO is used for the solutions of Quadratic Assignment Problem (QAP), and multiobjective QAP (mQAP) by using updating mechanisms including mutation, crossover, and a local search.

Ex Output:

Bacteria Foraging Algorithm with Genetic Operators for the Solution of QAP and mQAP