Recursive neural networks for processing graphs with labelled edges: theory and applications

In this paper, we introduce a new recursive neural network model able to process directed acyclic graphs with labelled edges. The model uses a state transition function which considers the edge labels and is independent both from the number and the order of the children of each node. The computational capabilities of the new recursive architecture are assessed. Moreover, in order to test the proposed architecture on a practical challenging application, the problem of object detection in images is also addressed. In fact, the localization of target objects is a preliminary step in any recognition system. The proposed technique is general and can be applied in different detection systems, since it does not exploit any a priori knowledge on the particular problem. Some experiments on face detection, carried out on scenes acquired by an indoor camera, are reported, showing very promising results.

[1]  Franco Scarselli,et al.  BackPropagation through Cyclic Structures , 2003, AI*IA.

[2]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[3]  Reiner Lenz,et al.  Optimal filters for the detection of linear patterns in 2-D and higher dimensional images , 1987, Pattern Recognit..

[4]  Din-Chang Tseng,et al.  Invariant handwritten Chinese character recognition using fuzzy min-max neural networks , 1997, Pattern Recognit. Lett..

[5]  Marco Gori,et al.  Similarity learning for graph-based image representations , 2003, Pattern Recognit. Lett..

[6]  Barbara Hammer,et al.  Neural networks can approximate mappings on structured objects , 1997 .

[7]  Timo Honkela,et al.  Connectionism in a Broad Perspective , 1995 .

[8]  Jeffrey Adams,et al.  Representation Theory of Groups and Algebras , 1993 .

[9]  Marco Gori,et al.  A recursive neural network model for processing directed acyclic graphs with labeled edges , 2003, Proceedings of the International Joint Conference on Neural Networks, 2003..

[10]  Lawrence D. Jackel,et al.  Backpropagation Applied to Handwritten Zip Code Recognition , 1989, Neural Computation.

[11]  Pietro Perona,et al.  Probabilistic affine invariants for recognition , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[12]  Jouko Lampinen,et al.  Improved rotational invariance for statistical inverse in electrical impedance tomography , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[13]  Franco Turini,et al.  AI*IA 2003: Advances in Artificial Intelligence , 2003, Lecture Notes in Computer Science.

[14]  Reiner Lenz.  A group theoretical approach to filter design , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[15]  G. Lewicki,et al.  Approximation by Superpositions of a Sigmoidal Function , 2003 .

[16]  Franco Scarselli,et al.  Face Spotting in Color Images using Recursive Neural Networks , 2003 .

[17]  Franco Scarselli,et al.  Recursive neural networks learn to localize faces , 2005, Pattern Recognit. Lett..

[18]  Christoph Goller,et al.  Inductive Learning in Symbolic Domains Using Structure-Driven Recurrent Neural Networks , 1996, KI.

[19]  Alessandro Sperduti,et al.  A general framework for adaptive processing of data structures , 1998, IEEE Trans. Neural Networks.

[20]  Marco Gori,et al.  Adaptive graphical pattern recognition for the classification of company logos , 2001, Pattern Recognit..

[21]  Alex Pentland,et al.  Probabilistic Visual Learning for Object Representation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Narendra Ahuja,et al.  Detecting Faces in Images: A Survey , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Alessandro Sperduti,et al.  Supervised neural networks for the classification of structures , 1997, IEEE Trans. Neural Networks.

[24]  Lars Asplund,et al.  Neural networks for admission control in an ATM network , 1994 .

[25]  M. Maggini,et al.  Recursive neural networks for object detection , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[26]  Shaogang Gong,et al.  Tracking colour objects using adaptive mixture models , 1999, Image Vis. Comput..

[27]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[28]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[29]  Joe Harris,et al.  Representation Theory: A First Course , 1991 .

[30]  Takeo Kanade,et al.  A statistical method for 3D object detection applied to faces and cars , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[31]  W. Schempp,et al.  Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory , 1986 .

[32]  Andrew Zisserman,et al.  Applications of Invariance in Computer Vision , 1993, Lecture Notes in Computer Science.

[33]  C. De Mauro,et al.  Similarity learning for graph based image representation , 2003 .

[34]  Franco Scarselli,et al.  Processing directed acyclic graphs with recursive neural networks , 2001, IEEE Trans. Neural Networks.

[35]  Barbara Hammer,et al.  Learning with recurrent neural networks , 2000 .

[36]  Barbara Hammer,et al.  Approximation capabilities of folding networks , 1999, ESANN.

[37]  Tomaso A. Poggio,et al.  A general framework for object detection , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[38]  Horst Bunke,et al.  Graph Edit Distance with Node Splitting and Merging, and Its Application to Diatom Idenfication , 2003, GbRPR.