Reducing parameter space for neural network training

For neural networks(NNs)with rectified linear unit(ReLU)or binary activation functions,we show that their training can be accomplished in a reduced parameter space.Specifically,the weights in each neuron can be trained on the unit sphere,as opposed to the entire space,and the threshold can be trained in a bounded interval,as opposed to the real line.We show that the NNs in the reduced parameter space are mathematically equivalent to the standard NNs with parameters in the whole space.The reduced parameter space shall facilitate the optimization procedure for the network training,as the search space becomes(much)smaller.We demonstrate the improved training performance using numerical examples.

A Comparative Study on Two Techniques of Reducing the Dimension of Text Feature Space

With the development of large scale text processing, the dimension of text feature space has become larger and larger, which has added a lot of difficulties to natural language processing. How to reduce the dimension has become a practical problem in the field. Here we present two clustering methods, i.e. concept association and concept abstract, to achieve the goal. The first refers to the keyword clustering based on the co occurrence of

CT Scan of the Foot in Patients with Chronic Non-Healing Diabetic Foot Ulcer

Background: Diabetes mellitus is a chronic disease where there is an increased blood sugar level in the body which is either caused due to inability of the pancreas to secrete insulin or the body’s inability to utilize it. The prevalence of diabetes mellitus is growing rapidly worldwide. Statistics show that in the year 2014, there were a total of 422 million cases of DM. Diabetes mellitus is a major cause of heart attacks, kidney failure, blindness and leg amputations. Diabetic foot ulcers are quite common and are estimated to affect nearly 15% of all diabetic patients during their lifetime. In long standing diabetic patients with chronic non-healing ulcers, bony changes or deformities are not uncommon. These bony changes can be identified using CT scans. Materials and Methods: An observational study was conducted on a total of 40 patients with chronic non-healing ulcer attending the surgery outpatient department of Saveetha Medical College, Chennai, Tamilnadu. The CT-scans of their foot were observed for deformities or bony changes. Results: Out of 40 patients, 67.5% were males and 32.5% were females. A maximum number of subjects fell under the age group of 51 - 60 years. The most common site of the ulcer was found to be in the plantar surface of big toe (53%). Among the 40 patients, 33 of them were found to have bony abnormalities on the CT scan of foot and no apparent changes were seen in the rest. Bone erosions (35%), osteopenic changes (22.5%), Charcot’s joint (2.5%), osteophyte formation (12.5) and reduced joint space (10%) were the predominant changes observed on the CT scans of the study population.

Reducing problem of multiplication operators on Bergman space

THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).

Identification of crack in a structural member using improved radial basis function(IRBF)neural networks

Purpose–The purpose of this paper is to provide an effective and simple technique to structural damage identification,particularly to identify a crack in a structure.Artificial neural networks approach is an alternative to identify the extent and location of the damage over the classical methods.Radial basis function(RBF)networks are good at function mapping and generalization ability among the various neural network approaches.RBF neural networks are chosen for the present study of crack identification.Design/methodology/approach–Analyzing the vibration response of a structure is an effective way to monitor its health and even to detect the damage.A novel two-stage improved radial basis function(IRBF)neural network methodology with conventional RBF in the first stage and a reduced search space moving technique in the second stage is proposed to identify the crack in a cantilever beam structure in the frequency domain.Latin hypercube sampling(LHS)technique is used in both stages to sample the frequency modal patterns to train the proposed network.Study is also conducted with and without addition of 5%white noise to the input patterns to simulate the experimental errors.Findings–The results show a significant improvement in identifying the location and magnitude of a crack by the proposed IRBF method,in comparison with conventional RBF method and other classical methods.In case of crack location in a beam,the average identification error over 12 test cases was 0.69 per cent by IRBF network compared to 4.88 per cent by conventional RBF.Similar improvements are reported when compared to hybrid CPN BPN networks.It also requires much less computational effort as compared to other hybrid neural network approaches and classical methods.Originality/value–The proposed novel IRBF crack identification technique is unique in originality and not reported elsewhere.It can identify the crack location and crack depth with very good accuracy,less computational effort and ease of implementation.