Abstract
We propose a new family of vector similarity measures. Each measure is associated with a convex cost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the similarity measure. Convex cost function can be the negative entropy function, total variation (TV) function and filtered variation function constructed from wavelets. The convex cost functions need not to be differentiable everywhere. In general, we need to compute the gradient of the cost function to compute the surface normals. If the gradient does not exist at a given vector, it is possible to use the sub-gradients and the normal producing the smallest angle between the two vectors is used to compute the similarity measure. The proposed measures are compared experimentally to other nonlinear similarity measures and the ordinary cosine similarity measure. The TV-based vector product is more energy efficient than the ordinary inner product because it does not require any multiplications.
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References
Rajaraman, A., Ullman, J.D.: Mining of Massive Datasets. Cambridge University Press, Cambridge (2012)
Zadeh, R.B., Goel, A.: Dimension independent similarity computation. J. Mach. Learn. Res. 14(1), 1605–1626 (2013)
Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with bregman divergences. J. Mach. Learn. Res. 6, 1705–1749 (2005)
Bregman, L.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7(3), 200–217 (1967)
Censor, Y., Lent, A.: An iterative row-action method for interval convex programming. J. Optim. Theory Appl. 34(3), 321–353 (1981)
Çetin, A.E.: Reconstruction of signals from fourier transform samples. Signal Process. 16(2), 129–148 (1989)
Kose, K., Gunay, O., Çetin, A.E.: Compressive sensing using the modified entropy functional. Digit. Signal Process. 24, 63–70 (2014)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1–4), 259–268 (1992)
Akbaş, C.E., Bozkurt, A., Arslan, M., Aslanoglu, H., Çetin, A.E.: L1 norm based multiplication-free cosine similarity measures for big data analysis. In: 2014 International Workshop on Computational Intelligence for Multimedia Understanding (IWCIM), pp. 1–5 (2014)
Suhre, A., Keskin, F., Ersahin, T., Çetin Atalay, R., Ansari, R., Çetin, A.E.: A multiplication-free framework for signal processing and applications in biomedical image analysis. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1123–1127 (2013)
Tuna, H., Onaran, I., Çetin, A.E.: Image description using a multiplier-less operator. Signal Process. Lett. IEEE 16(9), 751–753 (2009)
Yorulmaz, O., Pearson, T.C., Çetin, A.E.: Detection of fungal damaged popcorn using image property covariance features. Comput. Electron. Agric. 84, 47–52 (2012)
Duman, K., Çetin, A.E.: Target Detection in Sar Images Using Codifference and Directional Filters, pp. 76,990S–76,990S-10 (2010)
Habiboglu, Y.H., Gunay, O., Çetin, A.E.: Covariance matrix-based fire and flame detection method in video. Mach. Vis. Appl. 23(6), 1103–1113 (2012)
Kleinberg, J., Tardos, E.: Approximation algorithms for classification problems with pairwise relationships: metric labeling and markov random fields. In: 40th Annual Symposium on Foundations of Computer Science, pp. 14–23 (1999)
Charikar, M.S.: Similarity estimation techniques from rounding algorithms. In: Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing, ser. STOC ’02.New York: ACM, pp. 380–388 (2002)
Madeo, R.C.B., Wagner, P.K., Peres, S.M.: UCI Machine Learning Repository (2014). [Online]. http://archive.ics.uci.edu/ml
Hayman, E., Caputo, B., Fritz, M., Eklundh, J.-O.: On the significance of real-world conditions for material classification. In: Pajdla, T., Matas, J. (Eds.) European Conference on Computer Vision (ECCV), pp. 253–266 (2004)
Selesnick, I., Baraniuk, R., Kingsbury, N.: The dual-tree complex wavelet transform. In: Zoltowski, M.D. (Ed.) IEEE Signal Processing Magazine, vol. 22, no. 6, pp. 123–151 (2005)
Ramos, J.: Using tf-idf to determine word relevance in document queries. In: Proceedings of the First Instructional Conference on Machine Learning (2003)
Baldi, P., Sadowski, P., Whiteson, D.: Searching for exotic particles in high-energy physics with deep learning. Nat. Commun. 5(4308), 1 (2014)
Blackard, J.A., Dean, D.J.: Comparative accuracies of artificial neural networks and discriminant analysis in predicting forest cover types from cartographic variables. Comput. Electron. Agric. 24, 131–151 (1999)
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Akbaş, C.E., Günay, O., Taşdemir, K. et al. Energy efficient cosine similarity measures according to a convex cost function. SIViP 11, 349–356 (2017). https://doi.org/10.1007/s11760-016-0949-7
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DOI: https://doi.org/10.1007/s11760-016-0949-7