Abstract
Missing values in data are common in real world applications. There are several methods that deal with this problem. In this research we developed a new version of the mean shift clustering algorithm that deals with datasets with missing values. We use a weighted distance function that deals with datasets with missing values, that was defined in our previous work. To compute the distance between two points that may have attributes with missing values, only the mean and the variance of the distribution of the attribute are required. Thus, after they have been computed, the distance can be computed in O(1). Furthermore, we use this distance to derive a formula for computing the mean shift vector for each data point, showing that the mean shift runtime complexity is the same as the Euclidian mean shift runtime. We experimented on six standard numerical datasets from different fields. On these datasets we simulated missing values and compared the performance of the mean shift clustering algorithm using our distance and the suggested mean shift vector to other three basic methods. Our experiments show that mean shift using our distance function outperforms mean shift using other methods for dealing with missing values.
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References
AbdAllah, L., Shimshoni, I.: A distance function for data with missing values and its applications on knn and kmeans algorithms. Submitted to Int. J. Advances in Data Analysis and Classification
Batista, G., Monard, M.C.: An analysis of four missing data treatment methods for supervised learning. Applied Artificial Intelligence 17(5-6), 519–533 (2003)
Cheng, Y.: Mean shift, mode seeking, and clustering. IEEE Trans. PAMI 17(8), 790–799 (1995)
Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE Trans. PAMI 24(5), 603–619 (2002)
Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based Object Tracking. IEEE Trans. PAMI 25(5), 564–577 (2003)
DeMenthon, D., Megret, R.: Spatio-temporal segmentation of video by hierarchical mean shift analysis. Computer Vision Laboratory, Center for Automation Research, University of Maryland (2002)
Fukunaga, K., Hostetler, L.: The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Transactions on Information Theory 21(1), 32–40 (1975)
Georgescu, B., Shimshoni, I., Meer, P.: Mean shift based clustering in high dimensions: A texture classification example. In: Proceedings of the 9th International Conference on Computer Vision, pp. 456–463 (2003)
Grzymała-Busse, J.W., Hu, M.: A comparison of several approaches to missing attribute values in data mining. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 378–385. Springer, Heidelberg (2001)
Magnani, M.: Techniques for dealing with missing data in knowledge discovery tasks. Obtido 15(01), 2007 (2004), http://magnanim.web.cs.unibo.it/index.html
Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)
Suguna, N., Thanushkodi, K.G.: Predicting missing attribute values using k-means clustering. Journal of Computer Science 7(2), 216–224 (2011)
Tao, W., Jin, H., Zhang, Y.: Color image segmentation based on mean shift and normalized cuts. IEEE Trans. on Systems, Man, and Cybernetics, Part B 37(5), 1382–1389 (2007)
Speech University of Eastern Finland and Image Processing Unit. Clustering dataset, http://cs.joensuu.fi/sipu/datasets/
Zhang, S., Qin, Z., Ling, C.X., Sheng, S.: “Missing is useful”: missing values in cost-sensitive decision trees. IEEE Trans. on Knowledge and Data Engineering 17(12), 1689–1693 (2005)
Zhang, S.: Shell-neighbor method and its application in missing data imputation. Applied Intelligence 35(1), 123–133 (2011)
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AbdAllah, L., Shimshoni, I. (2014). Mean Shift Clustering Algorithm for Data with Missing Values. In: Bellatreche, L., Mohania, M.K. (eds) Data Warehousing and Knowledge Discovery. DaWaK 2014. Lecture Notes in Computer Science, vol 8646. Springer, Cham. https://doi.org/10.1007/978-3-319-10160-6_38
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DOI: https://doi.org/10.1007/978-3-319-10160-6_38
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