School of Science and Technology 科技學院
Computing Programmes 電腦學系

On Solving the Local Minimum Problem in Feed Forward Neural Networks

TSE Hau Ting Eric

ProgrammeBachelor of Computing with Honours in Internet Technology
SupervisorDr. Vanessa Ng
AreasNeural Networks, Algorithms
Year of Completion2011
Awards RecievedIEEE HK Section Student Paper Contest 2011 Undergraduate Champion

Objectives

The aim of this project is to investigate the local minimum problem in neural network and to design an algorithm to solve the problem. Neural network is widely used in pattern recognition and data classification accomplished by training. The training mainly involves comparing the output of neural network with the desire output and the difference is used to adjust the parameters to minimize the error. However, the performance of the training is always affected by the local minimum problem, or even fails in the training. The nature of the local minimum problem is illustrated in the following:

Background and Methodology

In this project, two approaches are used to solve the local minimum problem. The first approach is output monitoring and modification. In the early experiments, certain patterns are observed from the output indicating the occurrence of local minimum. For example, a wrong output is produced and remains unchanged for a period of time. The following shows the results for similar error group and extreme error group:

Since the training to escape from local minimum can be improved from monitoring the output of neural network and making corresponding modification, the second approach is based on Meta training. The training is learned to solve the local minimum by restarting the training with a different set of parameters to reach its destination by a different path. With these approaches, most of the training data are guaranteed to achieve over 90 percent of successful training. The detail of the methodology is described below:

Implementation

Concerned with the similar error group problem, this type of problem happens when a group of output value, which is two or more, has a similar error, with different signs of target value. According to the result of experiment, such problem is now solved using the Weight Update Rule (MGF) with details as shown in the following:

Regarding the extreme error problem, it occurs when one or more input nodes have an error which is an extreme value. Generally, since sigmoid function is used as activation function, the range of output value in neural network is 0 to 1, which are known as extreme values. Extreme error, on the other hand, states that an output node has obtained an extreme value but targeting on another extreme value. A new method is proposed particularly solving this type of error using output monitoring and modification, which is aimed to firstly identifying the extreme error output through monitoring and then produce a temperate value to significant the change of weight through modification. The detailed operation is shown below:

The extreme error is now solved by this integrated algorithm. The resulted graph is shown in the following using Rprop as learning algorithm to learn the patterns comparing with the algorithm of Meta training in 5-bit counting:

Evaluation

The integrated algorithm are used to learn all problem sets to examine the performance by comparing the result to other learning algorithm, including MGF, Quickprop and Rprop. The results are based on 100 different weight files, 100000 iterations are used for the training processes, to ensure that the only reason of training failed is the local minimum problem instead of not enough iteration to operate. The training is considered as successful if the error is smaller than 0.001. The results are show as follow:

Problem setLearning algorithmAverage convergence rateConvergence percentage
XORMGF1925.9199%
 Quickprop68.3655%
 Rprop53.1546%
 Integrated algorithm1970.23100%
ParityMGF6699.48100%
 Quickprop84.9100%
 Rprop117.3871%
 Integrated algorithm2522.97100%
RegressionMGF11850.62100%
 Quickprop6603.1199%
 Rprop2961.5596%
 Integrated algorithm3413.8100%
5 Bit CountingMGF684.52%
 Quickprop446.1941%
 Rprop441.628%
 Integrated algorithm1195.97100%
WineMGFN/A0%
 QuickpropN/A0%
 Rprop735.9149%
 Integrated algorithm9433.65100%
Breast CancerMGFN/A0%
 QuickpropN/A0%
 Rprop1130.01%
 Integrated algorithm1653.02100%
IrisMGFN/A0%
 QuickpropN/A0%
 Rprop3286.8111%
 Integrated algorithm16257.91100%
ThyroidMGFN/A0%
 QuickpropN/A0%
 Rprop327.0798%
 Integrated algorithm366.36100%

With the integrated algorithm, all problem set can have 100% percentage convergence since the local minimum problem is handled with focus. The average convergence rate is relatively large because some iteration during the training is used to locate the local minimum problem and to apply the corresponding optimization.

The integrated algorithm is evaluated by testing. Since it is possible that the training is completed by the Rprop itself without interrupting by the algorithm, the weights which have used the algorithm to complete the training will only be considered. Testing set included wine, breast cancer and Iris testing set are used. The results are measured by the correctness of the target output and the actual output. The results are shown below:

Testing setPercentage of correctness
Wine98.14%
Breast Cancer96.0%
Iris97.03%

From the result, the integrated algorithm can be concluded is a valid algorithm for neural network to help improving the performance of learning process.

Conclusion and Future Development

An integrated algorithm consists of Meta Training, solutions for both type of local minimum and deterministic optimization is proposed. Since both type of local minimum has handled respectively, the training process is capable to achieve 90% of successful training.

As the causes of local minimum problem have been exploited, the future development of neural network is recommended on developing an algorithm with local minimum problem free weight update rule. It can be done by preventing the calculation error which neglects the error of the training process. Also, the relationship of the patterns in the problem sets and the local minimum problem can be investigated to predict which type of local minimum problem will be happened.

Copyright Tse Hau Ting and Vanessa Ng 2011

Jonathan Chiu
Marketing Director
3DP Technology Limited

Jonathan handles all external affairs include business development, patents write up and public relations. He is frequently interviewed by media and is considered a pioneer in 3D printing products.

Krutz Cheuk
Biomedical Engineer
Hong Kong Sanatorium & Hospital

After graduating from OUHK, Krutz obtained an M.Sc. in Engineering Management from CityU. He is now completing his second master degree, M.Sc. in Biomedical Engineering, at CUHK. Krutz has a wide range of working experience. He has been with Siemens, VTech, and PCCW.

Hugo Leung
Software and Hardware Engineer
Innovation Team Company Limited

Hugo Leung Wai-yin, who graduated from his four-year programme in 2015, won the Best Paper Award for his ‘intelligent pill-dispenser’ design at the Institute of Electrical and Electronics Engineering’s International Conference on Consumer Electronics – China 2015.

The pill-dispenser alerts patients via sound and LED flashes to pre-set dosage and time intervals. Unlike units currently on the market, Hugo’s design connects to any mobile phone globally. In explaining how it works, he said: ‘There are three layers in the portable pillbox. The lowest level is a controller with various devices which can be connected to mobile phones in remote locations. Patients are alerted by a sound alarm and flashes. Should they fail to follow their prescribed regime, data can be sent via SMS to relatives and friends for follow up.’ The pill-dispenser has four medicine slots, plus a back-up with a LED alert, topped by a 500ml water bottle. It took Hugo three months of research and coding to complete his design, but he feels it was worth all his time and effort.

Hugo’s public examination results were disappointing and he was at a loss about his future before enrolling at the OUHK, which he now realizes was a major turning point in his life. He is grateful for the OUHK’s learning environment, its industry links and the positive guidance and encouragement from his teachers. The University is now exploring the commercial potential of his design with a pharmaceutical company. He hopes that this will benefit the elderly and chronically ill, as well as the society at large.

Soon after completing his studies, Hugo joined an automation technology company as an assistant engineer. He is responsible for the design and development of automation devices. The target is to minimize human labor and increase the quality of products. He is developing products which are used in various sections, including healthcare, manufacturing and consumer electronics.

Course CodeTitleCredits
 COMP S321FAdvanced Database and Data Warehousing5
 COMP S333FAdvanced Programming and AI Algorithms5
 COMP S351FSoftware Project Management5
 COMP S362FConcurrent and Network Programming5
 COMP S363FDistributed Systems and Parallel Computing5
 COMP S382FData Mining and Analytics5
 COMP S390FCreative Programming for Games5
 COMP S492FMachine Learning5
 ELEC S305FComputer Networking5
 ELEC S348FIOT Security5
 ELEC S371FDigital Forensics5
 ELEC S431FBlockchain Technologies5
 ELEC S425FComputer and Network Security5
 Course CodeTitleCredits
 ELEC S201FBasic Electronics5
 IT S290FHuman Computer Interaction & User Experience Design5
 STAT S251FStatistical Data Analysis5
 Course CodeTitleCredits
 COMPS333FAdvanced Programming and AI Algorithms5
 COMPS362FConcurrent and Network Programming5
 COMPS363FDistributed Systems and Parallel Computing5
 COMPS380FWeb Applications: Design and Development5
 COMPS381FServer-side Technologies and Cloud Computing5
 COMPS382FData Mining and Analytics5
 COMPS390FCreative Programming for Games5
 COMPS413FApplication Design and Development for Mobile Devices5
 COMPS492FMachine Learning5
 ELECS305FComputer Networking5
 ELECS363FAdvanced Computer Design5
 ELECS425FComputer and Network Security5