現時常見的分群演算法通常需要使用者指定參數，如分群數量。基於密度的分群演算法則不需要類似的參數，但是不適合用在高維空間的資料。近年的研究開始探索深度相似度學習，並把分群任務融合一起。在本研究中，我們提出一個創新的演算法，利用類神經網絡模型直接學習資料的相似度，加上使用座標學習的模型，從高維空間投影到兩維空間。我們同時提出點陣分群方法，用來把兩維空間的資訊進行分群和資料預測。這個機制能適用於高維空間資料分群，包括圖片資料；同時能把未有的測試資料無需整合在訓練資料中，穩定地進行群別預測。

Commonly used clustering algorithms usually requires user parameters such as the number of clusters to be divided. Density based algorithms do not have such requirements but are not suitable for high dimensional data. Recent studies have merged cluster assignment task with deep similarity learning. In this paper, we propose a novel algorithm to learn data similarity from scratch using neural network models, followed by a coordinate learning model to project high dimensional data onto a two-dimensional space. A new clustering algorithm, raster clustering, is also proposed to evaluate and classify the projected data. This mechanism can be applied in high dimensional data clustering including image data; and it allows prediction of unseen data in a consistent way without consolidating with training data.

[1] Abdelkarim Ben Ayed, Mohamed Ben Halima, and Adel M. Alimi, “Survey on clustering methods: Towards fuzzy clustering for big data," 2014 6th International Conference of Soft Computing and Pattern Recognition (SoCPaR), Tunis, pp. 331-336, 2014.
[2] Affix Mareta, Indah Soesanti, and Oyas Wahyunggoro, "Herbal leaf classification using images in natural background," 2018 International Conference on Information and Communications Technology (ICOIACT), Yogyakarta, pp. 612-616, 2018.
[3] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton, “ImageNet classification with deep convolutional neural networks,” Neural Information Processing Systems, vol. 141, no. 5, pp. 1097–1105, 2012.
[4] Amit Saxena, Mukesh Prasad, Akshansh Gupta, Neha Bharill, Om Prakash Patel, Aruna Tiwari, Meng Joo Er, Weiping Ding, and Chin-Teng Lin, “A review of clustering techniques and developments,” Neurocomputing, vol. 267, pp. 664–681, 2017.
[5] Andrew Y. Ng, Michael I. Jordan, and Yair Weiss, “On spectral clustering: Analysis and an algorithm,” Advances in Neural Information Processing Systems 14, pp. 849–856, 2001.
[6] Binyu Wang, Wenfen Liu, Zijie Lin, Xuexian Hu, Jianghong Wei, and Chun Liu, "Text clustering algorithm based on deep representation learning," in The Journal of Engineering, vol. 2018, no. 16, pp. 1407-1414, 11 2018.
[7] Bo Yang, Xiao Fu, Nicholas D. Sidiropoulos, and Mingyi Hong, “Towards K-means-friendly spaces: Simultaneous deep learning and clustering,” International Conference on Machine Learning, pp. 3861–3870, 2017.
[8] Chris H. Q. Ding, and Xiaofeng He, “K-means clustering via principal component analysis.” Proceedings of the Twenty-First International Conference on Machine Learning, p. 29, 2004.
[9] D. Sculley, “Web-scale k-Means clustering,” Proceedings of the 19th International Conference on World Wide Web, pp. 1177–1178, 2010.
[10] David Arthur, and Sergei Vassilvitskii, “K-Means++: The advantages of careful seeding,” Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1027–1035, 2007.
[11] Dejiao Zhang, Yifan Sun, Brian Eriksson, and Laura Balzano, “Deep unsupervised clustering using mixture of autoencoders,” ArXiv Preprint ArXiv:1712.07788, 2017.
[12] Erich Schubert, Jörg Sander, Martin Ester, Hans Peter Kriegel, and Xiaowei Xu, “DBSCAN revisited, revisited: Why and how you should (still) use DBSCAN,” International Conference on Management of Data, vol. 42, no. 3, p. 19, 2017.
[13] Erxue Min, Xifeng Guo, Qiang Liu, Gen Zhang, Jianjing Cui, and Jun Long, "A survey of clustering with deep learning: From the perspective of network architecture," in IEEE Access, vol. 6, pp. 39501-39514, 2018.
[14] Fengfu Li, Hong Qiao, and Bo Zhang, “Discriminatively boosted image clustering with fully convolutional auto-encoders,” Pattern Recognition, vol. 83, pp. 161–173, 2018.
[15] Gang Chen, “Deep learning with nonparametric clustering,” ArXiv Preprint ArXiv:1501.03084, 2015.
[16] Gang Chen, “Deep learning with nonparametric clustering,” ArXiv Preprint ArXiv:1501.03084, 2015.
[17] Gholamhosein Sheikholeslami, Surojit Chatterjee, and Aidong Zhang, “WaveCluster: A multi-resolution clustering approach for very large spatial databases,” Very Large Data Bases, pp. 428–439, 1998.
[18] Guang Ouyang, Dipak K. Dey, and Panpan Zhang, “Clique-based method for social network clustering,” Journal of Classification, pp. 1–21, 2019.
[19] Han Zhai, Hongyan Zhang, Liangpei Zhang, Pingxiang Li, and Antonio Plaza, "A new sparse subspace clustering algorithm for hyperspectral remote sensing imagery," in IEEE Geoscience and Remote Sensing Letters, vol. 14, no. 1, pp. 43-47, Jan. 2017.
[20] Hanan Al-Jubouri, Hongbo Du, and Harin Sellahewa, “Adaptive clustering based segmentation for image classification,” 2013 5th Computer Science and Electronic Engineering Conference (CEEC), Colchester, pp. 128-133, 2013.
[21] James C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, 1981.
[22] Jianlong Chang, Gaofeng Meng, Lingfeng Wang, Shiming Xiang, and Chunhong Pan, “Deep self-evolution clustering,” IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 1–1, 2019.
[23] Jianlong Chang, Lingfeng Wang, Gaofeng Meng, Shiming Xiang, and Chunhong Pan, “Deep adaptive image clustering,” 2017 IEEE International Conference on Computer Vision (ICCV), pp. 5880–5888, 2017.
[24] Jianlong Chang, Lingfeng Wang, Gaofeng Meng, Shiming Xiang, and Chunhong Pan, “Deep adaptive image clustering,” 2017 IEEE International Conference on Computer Vision (ICCV), pp. 5880–5888, 2017.
[25] Jost Tobias Springenberg, “Unsupervised and semi-supervised learning with categorical generative adversarial networks,” International Conference on Learning Representations, 2016.
[26] Junyuan Xie, Ross B. Girshick, and Ali Farhadi, “Unsupervised deep embedding for clustering analysis,” International Conference on Machine Learning, pp. 478–487, 2016.
[27] Khalid Raza, and Nripendra Kumar Singh, “A tour of unsupervised deep learning for medical image analysis,” ArXiv Preprint ArXiv:1812.07715, 2018.
[28] Li He, Nilanjan Ray, Yisheng Guan, and Hong Zhang, "Fast large-scale spectral clustering via explicit feature mapping," in IEEE Transactions on Cybernetics, vol. 49, no. 3, pp. 1058-1071, March 2019.
[29] Martin Ester, Hans-Peter Kriegel, Jiirg Sander, and Xiaowei Xu, “A density-based algorithm for discovering clusters in large spatial databases with noise,” Proc. 1996 Int. Conf. Knowledg Discovery and Data Mining (KDD ’96), pp. 226–231, 1996.
[30] Nat Dilokthanakul, Pedro A. M. Mediano, Marta Garnelo, Matthew C. H. Lee, Hugh Salimbeni, Kai Arulkumaran, and Murray Shanahan, “Deep unsupervised clustering with gaussian mixture variational autoencoders,” ArXiv Preprint ArXiv:1611.02648, 2017.
[31] Nikhil R. Pal, Kuhu Pal, James M. Keller, and James C. Bezdek, "A possibilistic fuzzy c-means clustering algorithm," in IEEE Transactions on Fuzzy Systems, vol. 13, no. 4, pp. 517-530, Aug. 2005.
[32] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, and Michael S. Bernstein, “ImageNet large scale visual recognition challenge,” International Journal of Computer Vision, vol. 115, no. 3, pp. 211–252, 2015.
[33] Pascal Vincent, Hugo Larochelle, Isabelle Lajoie, Yoshua Bengio, and Pierre-Antoine Manzagol, “Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion.” Journal of Machine Learning Research 11: 3371–3408, 2010.
[34] Peihao Huang, Yan Huang, Wei Wang, and Liang Wei Wang, "Deep embedding network for clustering," 2014 22nd International Conference on Pattern Recognition, Stockholm, pp. 1532-1537, 2014.
[35] Peilin Li, Sang-Heon Lee, and Jae-Sam Park, "Development of a global batch clustering with gradient descent and initial parameters in colour image classification," in IET Image Processing, vol. 13, no. 1, pp. 161-174, 10 1 2019.
[36] Qi Wang, Zequn Qin, Feiping Nie, and Xuelong Li, "Spectral embedded adaptive neighbors clustering," in IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 4, pp. 1265-1271, April 2019.
[37] Rakesh Agrawal, Johannes Ernst Gehrke, Dimitrios Gunopulos, and Prabhakar Raghavan, “Automatic subspace clustering of high dimensional data for data mining applications,” Proceedings of the 1998 ACM SIGMOD International Conference on Management of Data, vol. 27, no. 2, pp. 94–105, 1998.
[38] René Vidal, "Subspace clustering," in IEEE Signal Processing Magazine, vol. 28, no. 2, pp. 52-68, March 2011.
[39] Rui Xu, and Donald C. Wunsch. “Survey of clustering algorithms,” IEEE Transactions on Neural Networks, vol. 16, no. 3, pp. 645–678, 2005.
[40] Santosh K. Bethi, Vir V. Phoha, and Yenumula B. Reddy, "CLIQUE clustering approach to detect denial-of-service attacks," Proceedings from the Fifth Annual IEEE SMC Information Assurance Workshop, 2004., West Point, NY, pp. 447-448, 2004.
[41] Siew Cheng Lai, and Phooi Yee Lau, "Upper body action classification for multiview images using K-means," 2018 International Workshop on Advanced Image Technology (IWAIT), Chiang Mai, pp. 1-4, 2018.
[42] Sitthichok Chaichulee, Mauricio Villarroel, Joao Jorge, Carlos Arteta, Gabrielle Green, Kenny McCormick, Andrew Zisserman, and Lionel Tarassenko, “Multi-task convolutional neural network for patient detection and skin segmentation in continuous non-contact vital sign monitoring,” 2017 12th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2017), pp. 266–272, 2017.
[43] Sohil Atul Shah, and Vladlen Koltun, “Deep continuous clustering,” ArXiv Preprint ArXiv:1803.01449, 2018.
[44] Suman Saini, and Pinki Rani, “A survey on STING and CLIQUE grid based clustering methods,” International Journal of Advanced Research in Computer Science, vol. 8, no. 5, pp. 1510–1512, 2017.
[45] Sumit Chopra, Raia Hadsell, and Yann LeCun, “Learning a Similarity Metric Discriminatively, with Application to Face Verification,” 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, pp. 539–546, 2005.
[46] Susanto B. Sulistyo, Di Wu, Wai Lok Woo, Satnam Singh Dlay, and Bin Gao, “Computational deep intelligence vision sensing for nutrient content estimation in agricultural automation,” IEEE Transactions on Automation Science and Engineering, vol. 15, no. 3, pp. 1243–1257, 2018.
[47] Tao Li, and Chris H. Q. Ding, “The relationships among various nonnegative matrix factorization methods for clustering,” Sixth International Conference on Data Mining (ICDM’06), pp. 362–371, 2006.
[48] Tarun Yellamraju, and Mireille Boutin, “Clusterability and clustering of images and other ‘real’ high-dimensional data,” IEEE Transactions on Image Processing, vol. 27, no. 4, pp. 1927–1938, 2018
[49] Ulrike von. Luxburg, “A tutorial on spectral clustering,” Statistics and Computing, vol. 17, no. 4, pp. 395–416, 2007.
[50] Warith Harchaoui, Pierre-Alexandre Mattei, and Charles Bouveyron, “Deep adversarial gaussian mixture autoencoder for clustering,” in Proceedings of the International Conference on Learning Representations (ICLR), Toulon, France, 24–26 April 2017.
[51] Wei Wang, Jiong Yang, and Richard R. Muntz, “STING: A statistical information grid approach to spatial data mining,” Very Large Data Bases, pp. 186–195, 1997.
[52] Weihua Hu, Takeru Miyato, Seiya Tokui, Eiichi Matsumoto, and Masashi Sugiyama, “Learning discrete representations via information maximizing self-augmented training,” International Conference on Machine Learning, pp. 1558–1567, 2017.
[53] Weng-Tai Su, Chih-Chung Hsu, Ziling Huang, Chia-Wen Lin, and Gene Cheung, “Joint Pairwise Learning and Image Clustering Based on a Siamese CNN.” 2018 25th IEEE International Conference on Image Processing (ICIP), pp. 1992–1996, 2018.
[54] Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, and Pieter Abbeel, “InfoGAN: Interpretable representation learning by information maximizing generative adversarial nets,” Neural Information Processing Systems, pp. 2180–2188, 2016.
[55] Yang Fan, Liu Gongshen, Meng Kui, and Sun Zhaoying, "Neural feedback text clustering with BiLSTM-CNN-Kmeans," in IEEE Access, vol. 6, pp. 57460-57469, 2018.
[56] Yanxin Pan, Alexander Burnap, Jeffrey Hartley, Richard Gonzalez, and Panos Y. Papalambros, “Deep design: Product aesthetics for heterogeneous markets,” Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1961–1970, 2017.
[57] Yoshua Bengio, Pascal Lamblin, Dan Popovici, and Hugo Larochelle, “Greedy layer-wise training of deep networks,” Advances in Neural Information Processing Systems 19, pp. 153–160, 2006.
[58] Zara Alaverdyan, Julien Jung, Romain Bouet, and Carole Lartizien, “Regularized Siamese Neural Network for Unsupervised Outlier Detection on Brain Multiparametric Magnetic Resonance Imaging: Application to Epilepsy Lesion Screening,” 2018.
[59] Zhuxi Jiang, Yin Zheng, Huachun Tan, Bangsheng Tang, and Hanning Zhou, “Variational deep embedding: An unsupervised and generative approach to clustering,” Twenty-Sixth International Joint Conference on Artificial Intelligence, pp. 1965–1972, 2017.