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Label Propagation through Linear Neighborhoods
January 2008 (vol. 20 no. 1)
pp. 55-67
In many practical data mining applications such as text classification, unlabeled training examples are readily available but labeled ones are fairly expensive to obtain. Therefore, semi-supervised learning algorithms have aroused considerable interests from the data mining and machine learning fields. In recent years, graph based semi-supervised learning has been becoming one of the most active research area in semi-supervised learning community. In this paper, a novel graph based semi-supervised learning approach is proposed based on a linear neighborhood model, which assumes that each data point can be linearly reconstructed from its neighborhood. Our algorithm, named Linear Neighborhood Propagation (LNP), can propagate the labels from the labeled points to the whole dataset using these linear neighborhoods with sufficient smoothness. Theoretical analysis of the properties of LNP are presented in this paper. Furthermore, we also derive an easy way to extend LNP to out-of-sample data. Promising experimental results are presented for synthetic data, digit and text classification tasks.

[1] M.-F. Balcan, A. Blum, P.P. Choi, J. Lafferty, B. Pantano, M.R. Rwebangira, and X. Zhu, “Person Identification in Webcam Images: An Application of Semi-Supervised Learning,” Proc. ICML Workshop Learning with Partially Classified Training Data, 2005.
[2] M. Belkin and P. Niyogi, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation,” Neural Computation, vol. 15, no. 6, pp. 1373-1396, 2003.
[3] M. Belkin, I. Matveeva, and P. Niyogi, “Regularization and Semi-Supervised Learning on Large Graphs,” Proc. 17th Ann. Conf. Learning Theory (COLT '04), pp. 624-638, 2004.
[4] M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples,” J. Machine Learning Research, vol. 7, pp.2399-2434, Nov. 2006.
[5] Y. Bengio, M. Monperrus, and H. Larochelle, “Nonlocal Estimation of Manifold Structure,” Neural Computation, vol. 18, no. 10, pp.2509-2528, 2006.
[6] A. Blum and T. Mitchell, “Combining Labeled and Unlabeled Data with Co-Training,” Proc. 11th Ann. Conf. Computational Learning Theory (COLT '98), pp. 92-100, 1998.
[7] A. Blum and S. Chawla, “Learning from Labeled and Unlabeled Data Using Graph Mincuts,” Proc. 18th Int'l Conf. Machine Learning (ICML '01), pp. 19-26, 2001.
[8] M.A. Carreira-Perpinan and R.S. Zemel, “Proximity Graphs for Clustering and Manifold Learning,” Advances in Neural Information Processing Systems 17, L.K. Saul, Y. Weiss, and L. Bottou, eds., pp.225-232, MIT Press, 2005.
[9] O. Chapelle, J. Weston, and B. Schölkopf, “Cluster Kernels for Semi-Supervised Learning,” Advances in Neural Information Processing Systems 15, S. Becker, S. Thrun, and K. Obermayer, eds., pp.601-608, MIT Press, 2003.
[10] O. Chapelle, B. Schölkopf, and A. Zien, Semi-Supervised Learning, p. 371. MIT Press, 2006.
[11] O. Delalleu, Y. Bengio, and N. Le Roux, “Non-Parametric Function Induction in Semi-Supervised Learning,” Proc. 10th Int'l Workshop Artificial Intelligence and Statistics (AISTAT '05), pp. 96-103, 2005.
[12] A.P. Dempster, N.M. Laird, and D.B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. Royal Statistical Soc., Series B, vol. 39, no. 1, pp. 1-38, 1977.
[13] F.R.K. Chung, “Spectral Graph Theory,” CBMS Regional Conf. Series in Mathematics, vol. 92, published for the Conf. Board of the Mathematical Sciences, Washington, DC. 1997.
[14] G.H. Golub and C.F Van Loan, Matrix Computation, second ed., 1989.
[15] A.K. Jain and R.C Dubes, Algorithms for Clustering Data, Prentice Hall Advanced Reference Series. Prentice Hall, 1988.
[16] T. Joachims, “Transductive Inference for Text Classification Using Support Vector Machines,” Proc. 16th Int'l Conf. Machine Learning (ICML '99), pp. 200-209, 1999.
[17] T. Joachims, “Transductive Learning via Spectral Graph Partitioning,” Proc. 20th Int'l Conf. Machine Learning (ICML '03), pp. 290-297, 2003.
[18] N. Kambhatla and T.K. Leen, “Dimension Reduction by Local Principal Component Analysis,” Neural Computation, vol. 9, no. 7, pp. 1493-1516, 1997.
[19] A. Kapoor, Y. Qi, H. Ahn, and R.W. Picard, “Hyperparameter and Kernel Learning for Graph Based Semi-Supervised Classification,” Advances in Neural Information Processing Systems, 2005.
[20] N.D. Lawrence and M.I. Jordan, “Semi-Supervised Learning via Gaussian Processes,” Advances in Neural Information Processing Systems 17, L.K. Saul, Y. Weiss, and L. Bottou, eds., MIT Press, 2005.
[21] D.J. Miller and U.S. Uyar, “A Mixture of Experts Classifier with Learning Based on Both Labelled and Unlabelled Data,” Advances in Neural Information Processing Systems 9, M. Mozer, M.I. Jordan, and T.Petsche, eds., pp. 571-577, MIT Press, 1997.
[22] K. Nigam, A.K. McCallum, S. Thrun, and T. Mitchell, “Text Classification from Labeled and Unlabeled Documents Using EM,” Machine Learning, vol. 39, no. 2-3, pp. 103-134, 2000.
[23] J.R. Quinlan, “Introduction to Decision Trees,” Machine Learning, vol. 1, no. 1, pp. 81-106, 1986.
[24] S.T. Roweis and L.K. Saul, “Nonlinear Dimensionality Reduction by Locally Linear Embedding,” Science, vol. 290, pp. 2323-2326, 2000.
[25] L.K. Saul, K.Q. Weinberger, J.H. Ham, F. Sha, and D.D. Lee, “Spectral Methods for Dimensionality Reduction,” Semisupervised Learning, O. Chapelle, B. Schölkopf, and A. Zien, eds. MIT Press, 2006.
[26] B. Schölkopf and A.J. Smola, Learning with Kernels. MIT Press, 2002.
[27] B. Shahshahani and D. Landgrebe, “The Effect of Unlabeled Samples in Reducing the Small Sample Size Problem and Mitigating the Hughes Phenomenon,” IEEE Trans. Geoscience and Remote Sensing, vol. 32, no. 5, pp. 1087-1095, 1994.
[28] M. Szummer and T. Jaakkola, “Partially Labeled Classification with Markov Random Walks,” Advances in Neural Information Processing Systems 14, T.G. Dietterich, S. Becker, and Z. Ghahramani, eds., pp. 945-952, 2002.
[29] J.B. Tenenbaum, V. Silva, and J.C. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction,” Science, vol. 290, pp. 2319-2323, 2000.
[30] V.N. Vapnik, The Nature of Statistical Learning Theory. Springer, 1995.
[31] F. Wang and C. Zhang, “Label Propagation through Linear Neighborhoods,” Proc. 23rd Int'l Conf. Machine Learning (ICML '06), pp. 985-992, 2006.
[32] D. Zhou, O. Bousquet, T.N. Lal, J. Weston, and B. Schölkopf, “Learning with Local and Global Consistency,” Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B.Schölkopf, eds., pp. 321-328, 2004.
[33] D. Zhou and B. Schölkopf, “Learning from Labeled and Unlabeled Data Using Random Walks,” Proc. 26th Pattern Recognition Symp. (DAGM '04), 2004.
[34] D. Zhou, B. Schölkopf, and T. Hofmann, “Semi-Supervised Learning on Directed Graphs,” Advances in Neural Information Processing Systems 17, L.K., Saul, Y. Weiss, and L. Bottou, eds., pp.1633-1640, MIT Press, 2005.
[35] X. Zhu, Z. Ghahramani, and J. Lafferty, “Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions,” Proc. 20th Int'l Conf. Machine Learning (ICML '03), 2003.
[36] X. Zhu and Z. Ghahramani, “Learning from Labeled and Unlabeled Data with Label Propagation,” Technical Report CMU-CALD-02-107, Carnegie Mellon Univ., 2002.
[37] X. Zhu and Z. Ghahramani, “Towards Semi-Supervised Classification with Markov Random Fields,” Technical Report CMU-CALD-02-106, Carnegie Mellon Univ., 2002.
[38] X. Zhu, J. Lafferty, and Z. Ghahramani, “Semi-Supervised Learning: From Gaussian Fields to Gaussian Processes,” Technical Report CMU-CS-03-175, Carnegie Mellon Univ., 2003.
[39] X. Zhu, “Semi-Supervised Learning Literature Survey,” Computer Sciences Technical Report 1530, Univ. of Wisconsin, Madison, 2006.

Index Terms:
Data mining, Mining methods and algorithms, Machine learning, Graph labeling
Fei Wang, Changshui Zhang, "Label Propagation through Linear Neighborhoods," IEEE Transactions on Knowledge and Data Engineering, vol. 20, no. 1, pp. 55-67, Jan. 2008, doi:10.1109/TKDE.2007.190672
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