New acceleration technique for the backpropagation algorithm

Artificial neural networks have been studied for many years in the hope of achieving human like performance in the area of pattern recognition, speech synthesis and higher level of cognitive process. In the connectionist model there are several interconnected processing elements called the neurons that have limited processing capability. Even though the rate of information transmitted between these elements is limited, the complex interconnection and the cooperative interaction between these elements results in a vastly increased computing power; The neural network models are specified by an organized network topology of interconnected neurons. These networks have to be trained in order them to be used for a specific purpose. Backpropagation is one of the popular methods of training the neural networks. There has been a lot of improvement over the speed of convergence of standard backpropagation algorithm in the recent past. Herein we have presented a new technique for accelerating the existing backpropagation without modifying it. We have used the fourth order interpolation method for the dominant eigen values, by using these we change the slope of the activation function. And by doing so we increase the speed of convergence of the backpropagation algorithm; Our experiments have shown significant improvement in the convergence time for problems widely used in benchmarKing Three to ten fold decrease in convergence time is achieved. Convergence time decreases as the complexity of the problem increases. The technique adjusts the energy state of the system so as to escape from local minima

A novel modification to backpropagation sample selection strategy

Random sample selection method in backpropagation results in convergence on the error (root of mean squared error, RMSE) surface. These problems, which are caused by the extreme (worst-case) errors, can be solved by a different sample selection strategy. A sample selection strategy has been proposed, which provides lower maximal errors and a higher confidence level on the expense of slightly increased RMSE. Applications are presented in the field of spectroscopic ellipsometry (SE), a sensitive, non-destructive but indirect analytical technique. Demonstrative example shows feature common to simulated annealing in the sense of escaping local minima

Chemical and biological reactions of solidification of peat using ordinary portland cement (OPC) and coal ashes

Construction over peat area have often posed a challenge to geotechnical engineers. After decades of study on peat stabilisation techniques, there are still no absolute formulation or guideline that have been established to handle this issue. Some researchers have proposed solidification of peat but a few researchers have also discovered that solidified peat seemed to decrease its strength after a certain period of time. Therefore, understanding the chemical and biological reaction behind the peat solidification is vital to understand the limitation of this treatment technique. In this study, all three types of peat; fabric, hemic and sapric were mixed using Mixing 1 and Mixing 2 formulation which consisted of ordinary Portland cement, fly ash and bottom ash at various ratio. The mixtures of peat-binder-filler were subjected to the unconfined compressive strength (UCS) test, bacterial count test and chemical elemental analysis by using XRF, XRD, FTIR and EDS. Two pattern of strength over curing period were observed. Mixing 1 samples showed a steadily increase in strength over curing period until Day 56 while Mixing 2 showed a decrease in strength pattern at Day 28 and Day 56. Samples which increase in strength steadily have less bacterial count and enzymatic activity with increase quantity of crystallites. Samples with lower strength recorded increase in bacterial count and enzymatic activity with less crystallites. Analysis using XRD showed that pargasite (NaCa2[Mg4Al](Si6Al2)O22(OH)2) was formed in the higher strength samples while in the lower strength samples, pargasite was predicted to be converted into monosodium phosphate and Mg(OH)2 as bacterial consortium was re-activated. The Michaelis�Menten coefficient, Km of the bio-chemical reaction in solidified peat was calculated as 303.60. This showed that reaction which happened during solidification work was inefficient. The kinetics for crystallite formation with enzymatic effect is modelled as 135.42 (1/[S] + 0.44605) which means, when pargasite formed is lower, the amount of enzyme secretes is higher

The Early Restart Algorithm

Consider an algorithm whose time to convergence is unknown (because of some random element in the algorithm, such as a random initial weight choice for neural network training). Consider the following strategy. Run the algorithm for a specific time T. If it has not converged by time T, cut the run short and rerun it from the start (repeat the same strategy for every run). This so-called restart mechanism has been proposed by Fahlman (1988) in the context of backpropagation training. It is advantageous in problems that are prone to local minima or when there is a large variability in convergence time from run to run, and may lead to a speed-up in such cases. In this article, we analyze theoretically the restart mechanism, and obtain conditions on the probability density of the convergence time for which restart will improve the expected convergence time. We also derive the optimal restart time. We apply the derived formulas to several cases, including steepest-descent algorithms

A novel approach to error function minimization for feedforward neural networks

Feedforward neural networks with error backpropagation (FFBP) are widely applied to pattern recognition. One general problem encountered with this type of neural networks is the uncertainty, whether the minimization procedure has converged to a global minimum of the cost function. To overcome this problem a novel approach to minimize the error function is presented. It allows to monitor the approach to the global minimum and as an outcome several ambiguities related to the choice of free parameters of the minimization procedure are removed.Comment: 11 pages, latex, 3 figures appended as uuencoded fil

Comparative performance of some popular ANN algorithms on benchmark and function approximation problems

We report an inter-comparison of some popular algorithms within the artificial neural network domain (viz., Local search algorithms, global search algorithms, higher order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and Two Spiral. Apart from giving a brief description of these algorithms, the results obtained for the above benchmark problems are presented in the paper. The results suggest that while Levenberg-Marquardt algorithm yields the lowest RMS error for the N-bit Parity and the Two Spiral problems, Higher Order Neurons algorithm gives the best results for the IRIS data problem. The best results for the XOR problem are obtained with the Neuro Fuzzy algorithm. The above algorithms were also applied for solving several regression problems such as cos(x) and a few special functions like the Gamma function, the complimentary Error function and the upper tail cumulative $\chi^2$-distribution function. The results of these regression problems indicate that, among all the ANN algorithms used in the present study, Levenberg-Marquardt algorithm yields the best results. Keeping in view the highly non-linear behaviour and the wide dynamic range of these functions, it is suggested that these functions can be also considered as standard benchmark problems for function approximation using artificial neural networks.Comment: 18 pages 5 figures. Accepted in Pramana- Journal of Physic

3D freeform surfaces from planar sketches using neural networks

A novel intelligent approach into 3D freeform surface reconstruction from planar sketches is proposed. A multilayer perceptron (MLP) neural network is employed to induce 3D freeform surfaces from planar freehand curves. Planar curves were used to represent the boundaries of a freeform surface patch. The curves were varied iteratively and sampled to produce training data to train and test the neural network. The obtained results demonstrate that the network successfully learned the inverse-projection map and correctly inferred the respective surfaces from fresh curves