scholarly journals Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Juhe Sun ◽  
Xiao-Ren Wu ◽  
B. Saheya ◽  
Jein-Shan Chen ◽  
Chun-Hsu Ko
Keyword(s):  
Neural Network ◽  
Second Order ◽  
Merit Functions ◽  
Second Order Cone ◽  
The Neural Network ◽  
Complementarity Functions ◽  
Type Classes ◽  
Quadratic Programming Problems ◽  
Numerical Performance ◽  
Discrete Type

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.

ARTIFICIAL NEURAL NETWORK BASED CLASSIFICATION OF MAMMOGRAPHIC MICROCALCIFICATIONS USING IMAGE STRUCTURE FEATURES

1993 ◽  
Vol 07 (06) ◽  
pp. 1377-1401 ◽  
Author(s):  
YATEEN CHITRE ◽  
ATAM P. DHAWAN ◽  
MYRON MOSKOWITZ
Keyword(s):  
Neural Network ◽  
Correlation Study ◽  
Second Order ◽  
Breast Cancers ◽  
Grey Level ◽  
K Nearest Neighbor ◽  
Image Structure ◽  
The Neural Network ◽  
Grey Level Histogram

Mammography associated with clinical breast examination and breast self-examination is the only effective and viable method for mass breast screening. Most of the minimal breast cancers are detected by the presence of microcalcifications. It is however difficult to distinguish between benign and malignant microcalcifications associated with breast cancer. Most of the techniques used in the computerized analysis of mammographic microcalcifications segment the digitized grey-level image into regions representing microcalcifications. Since mammographic images usually suffer from poorly defined microcalcification features, the extraction of microcalcification features based on segmentation process is not reliable and accurate. We present a second-order grey-level histogram based feature extraction approach which does not require the segmentation of microcalcifications into binary regions to extract features to be used in classification. The image structure features, computed from the second-order grey-level histogram statistics, are used for classification of microcalcifications. Several image structure features were computed for 100 cases of “difficult to diagnose” microcalcification cases with known biopsy results. These features were analyzed in a correlation study which provided a set of five best image structure features. A feedforward backpropagation neural network was used to classify mammographic microcalcifications using the image structure features. Four networks were trained for different combinations of training and test cases, and number of nodes in hidden layers. False Positive (FP) and True Positive (TP) rates for microcalcification classification were computed to compare the performance of the trained networks. The results of the neural network based classification were compared with those obtained using multivariate Baye’s classifiers, and the k-nearest neighbor classifier. The neural network yielded good results for classification of “difficult-to-diagnose” micro-calcifications into benign and malignant categories using the selected image structure features.

Information-Geometric Measures as Robust Estimators of Connection Strengths and External Inputs

2009 ◽  
Vol 21 (8) ◽  
pp. 2309-2335 ◽  
Author(s):  
Masami Tatsuno ◽  
Jean-Marc Fellous ◽  
Shun-ichi Amari
Keyword(s):  
Neural Network ◽  
Linear Model ◽  
Information Geometry ◽  
Second Order ◽  
System Level ◽  
Biophysical Model ◽  
Order Information ◽  
Close Link ◽  
The Neural Network ◽  
Log Linear

Information geometry has been suggested to provide a powerful tool for analyzing multineuronal spike trains. Among several advantages of this approach, a significant property is the close link between information-geometric measures and neural network architectures. Previous modeling studies established that the first- and second-order information-geometric measures corresponded to the number of external inputs and the connection strengths of the network, respectively. This relationship was, however, limited to a symmetrically connected network, and the number of neurons used in the parameter estimation of the log-linear model needed to be known. Recently, simulation studies of biophysical model neurons have suggested that information geometry can estimate the relative change of connection strengths and external inputs even with asymmetric connections. Inspired by these studies, we analytically investigated the link between the information-geometric measures and the neural network structure with asymmetrically connected networks of N neurons. We focused on the information-geometric measures of orders one and two, which can be derived from the two-neuron log-linear model, because unlike higher-order measures, they can be easily estimated experimentally. Considering the equilibrium state of a network of binary model neurons that obey stochastic dynamics, we analytically showed that the corrected first- and second-order information-geometric measures provided robust and consistent approximation of the external inputs and connection strengths, respectively. These results suggest that information-geometric measures provide useful insights into the neural network architecture and that they will contribute to the study of system-level neuroscience.

scholarly journals The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoni Chi ◽  
Zhongping Wan ◽  
Zijun Hao
Keyword(s):  
Directional Derivative ◽  
Second Order ◽  
Smoothing Function ◽  
Smoothing Methods ◽  
Second Order Cone ◽  
Complementarity Functions ◽  
Computable Formula ◽  
Smoothing Functions ◽  
The One ◽  
Parametric Class

Second-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity functions, propose its smoothing function, and derive the computable formula for the Jacobian of the smoothing function. Based on these results, we prove the Jacobian consistency of the one-parametric class of smoothing functions, which will play an important role for achieving the rapid convergence of smoothing methods. Moreover, we estimate the distance between the subgradient of the one-parametric class of the SOC complementarity functions and the gradient of its smoothing function, which will help to adjust a parameter appropriately in smoothing methods.

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