Cosine Similarity-Based Classifiers for Functional Data

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.