Abstract
Two-Dimensional Neural Network (2D CNN) has become an alternative method for one-dimensional data classification. Previous studies are focused either only on sequence or vector data. In this paper, we proposed a new 2D CNN classification method that suitable for both, sequence and vector data. The Hilbert space-filling curve was used as a 1D to 2D transfer function in the proposed method. It is used for two reasons: (i) to preserve the spatial locality of 1D data and (ii) to reduce the distance of far-flung data elements. Furthermore, a 1D convolution layer was added in the first stage of our proposed method. It can capture the correlation information of neighboring elements, which is effective for sequence data classification. Consequently, the trainable property of 1D convolutions is very helpful in extracting relevant information for vector data classification. Finally, the performance of the proposed Hilbert Vector Convolutional Neural Network (HVCNN) was compared with two 2D CNN based methods and two non-CNN based methods. Experimental results showed that the proposed HVCNN method delivers better numerical accuracy and generalization property than the other competitive methods. We also did weight distribution analysis to support this claim.
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References
Elbayad, M., Besacier, L., Verbeek, J.: Pervasive attention: 2D convolutional neural networks for sequence-to-sequence prediction. In: Conference on Computational Natural Language Learning (2018). https://arxiv.org/abs/1808.03867
GoogleResearch: TensorFlow: a system for large-scale machine learning. GoogleResearch (2015). http://dl.acm.org/citation.cfm?id=3026877.3026899
Hearst, M.A., Dumais, S.T., Osuna, E., Platt, J., Scholkopf, B.: Support vector machines. IEEE Intell. Syst. Appl. 13(4), 18–28 (1998). https://doi.org/10.1109/5254.708428
Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735–1780 (1997). https://doi.org/10.1162/neco.1997.9.8.1735
Kavitha, M., Kurita, T., Park, S.Y., Chien, S.I., Bae, J.S., Ahn, B.C.: Deep vector-based convolutional neural network approach for automatic recognition of colonies of induced pluripotent stem cells. PLoS ONE 12(12), 1–18 (2017). https://doi.org/10.1371/journal.pone.0189974
Kiranyaz, S., Ince, T., Gabbouj, M.: Real-time patient-specific ECG classification by 1-D convolutional neural networks. IEEE Trans. Biomed. Eng. 63(3), 664–675 (2016). https://doi.org/10.1109/TBME.2015.2468589
Krizhevsky, A., Sutskever, I., Hinton, G.E.: ImageNet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1–9 (2012). https://doi.org/10.1016/j.protcy.2014.09.007
LeCun, Y.: Generalization and network design strategies (1989). http://yann.lecun.com/exdb/publis/pdf/lecun-89.pdf
Mark, H., Erik, R., George, F., Jaap, S.: UCI Machine Learning Repository (1999). https://archive.ics.uci.edu/ml/datasets/spambase
Moon, B., Jagadish, H.V., Faloutsos, C., Saltz, J.H.: Analysis of the clustering properties of the Hilbert space-filling curve. IEEE Trans. Knowl. Data Eng. 13(1), 124–141 (2001). https://doi.org/10.1109/69.908985
Nair, V., Hinton, G.E.: Rectified linear units improve restricted boltzmann machines. In: Proceedings of the 27th International Conference on Machine Learning (ICML) (2010). https://doi.org/10.1.1.165.6419
Redmon, J., Divvala, S., Girshick, R., Farhadi, A.: You only look once: unified, real-time object detection. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2015). https://doi.org/10.1109/CVPR.2016.91
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Scherer, D., Müller, A., Behnke, S.: Evaluation of pooling operations in convolutional architectures for object recognition. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010. LNCS, vol. 6354, pp. 92–101. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15825-4_10
Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. In: ICLR, pp. 1–14 (2014). https://doi.org/10.1016/j.infsof.2008.09.005
Towell, G., Noordewier, M., Shavlik, J.: UCI Machine Learning Repository (1992). https://archive.ics.uci.edu/ml/datasets/Molecular+Biology+(Splice-junction+Gene+Sequences)
Yin, B., Balvert, M., Zambrano, D., Schönhuth, A., Bohte, S.M.: An Image Representation based Convolutional Network for DNA Classification. CoRR abs/1806.04931 (2018). http://arxiv.org/abs/1806.04931
Acknowledgment
This work was partly supported by JSPS KAKENHI Grant Number 16K00239. The authors also thank the Institute of Education Fund Management (LPDP) of the Ministry of Finance of Indonesia, which has provided scholarship support for the first author to undertake the master program.
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Loka, N.R.B.S., Kavitha, M., Kurita, T. (2019). Hilbert Vector Convolutional Neural Network: 2D Neural Network on 1D Data. In: Tetko, I., Kůrková, V., Karpov, P., Theis, F. (eds) Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. ICANN 2019. Lecture Notes in Computer Science(), vol 11727. Springer, Cham. https://doi.org/10.1007/978-3-030-30487-4_36
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