IJDAR (1999) 2: 30–36 International Journal on IJDAR Document Analysis and Recognition c  Springer-Verlag 1999 Recognition of handwritten numerals by Quantum Neural Network with fuzzy features Jie Zhou 1 , Qiang Gan 2 , Adam Krzy˙ zak 1 , Ching Y. Suen 1 1 Center for Pattern Recognition and Machine Intelligence, Concordia University, Montreal, Canada H3G 1M8 2 ISIS Research Group, University of Southampton, Southampton SO17 1BJ, UK Received October 26, 1998 / Revised January 9, 1999 Abstract. This paper describes a new kind of neural network — Quantum Neural Network (QNN) — and its application to the recognition of handwritten numer- als. QNN combines the advantages of neural modelling and fuzzy theoretic principles. Novel experiments have been designed for in-depth studies of applying the QNN to both real data and confusing images synthesized by morphing. Tests on synthesized data examine QNN’s fuzzy decision boundary with the intention to illustrate its mechanism and characteristics, while studies on real data prove its great potential as a handwritten numeral classifier and the special role it plays in multi-expert sys- tems. An effective decision-fusion system is proposed and a high reliability of 99.10% has been achieved. Key words: Quantum Neural Network – Handwritten numeral recognition – Fuzzy classification – Morphing – Decision-fusion system 1 Introduction The subject of handwritten numeral recognition has been intensively studied for many years. However, the intrinsic varieties and ambiguities of handwritten char- acters make it hard for practical applications to meet the high expectations of industrial reality. In particular, how to bridge the “reliability” gap between machine and human being are among the most important concerns. Parallel multi-expert combinations [1-4] and hierar- chical verification systems [5] have been introduced in recent years in this regard. However, the effects of these methods are somehow limited by the same weaknesses which exist in conventional classifiers on recognizing con- fusing characters. For example, conventional feedforward neural networks do not perform satisfactorily on confus- ing handwritten digits due to their crisp decision bound- aries. A possible way to improve this is to modify the neural network so that a fuzzy boundary can be created. Correspondence to : J. Zhou Some researchers then try to exploit the fuzzy feed- forward neural network with the intention to improve its generalization ability when recognizing confusing char- acters. In [6], an alternative neural network architecture to standard feedforward NNs was proposed showing in- herently fuzzy classification ability and was applied to recognize handwritten numerals with valid generaliza- tion performance. In [7], a similar network architecture further proved to have fuzzier decision boundaries com- pared with conventional neural networks and was named Quantum Neural Network (QNN). In this paper, the properties of the QNN are studied in greater depth in recognizing handwritten numerals. Novel experiments are designed to study QNN’s response to confusing numeral patterns, which are synthesized images with ambiguous identities. Experimental evalu- ation shows QNN’s capability of generating multilevel partitions on the decision boundary. Its performance on handwritten numeral recognition is then tested on the CENPARMI database. Error distribution analysis and the high reliability of a proposed decision-fusion system show two distinguishing advantages of QNN when ap- plied to handwritten numeral recognition: 1. QNN performs better on recognizing confusing digits, which makes it a desirable candidate for verification and combination tasks, resulting in an improvement of the reliability of the whole recognition system. 2. Due to its fuzzy decision ability, QNN does not incur high rejection when we try to reduce the error rate, i.e., it can maintain high reliability with a reasonable rejection rate. This paper is organized as follows: In Sect. 2, the mechanism of the QNN is introduced and the training al- gorithm for it is given. In Sect. 3, QNN’s multilevel fuzzy decision ability is studied by its response to overlapping inputs. Morphing and spline methods are used in our ex- periments to synthesize the confusing numeral patterns. Comparison is done with a standard back-propagation (BP) network. In Sect. 4, we present the performance of QNN based on the CENPARMI database. Its error dis- tribution on confusing numeral pairs is given and is com- pared to that of a BP net. An effective decision-fusion