Novel Circular-Shift Invariant Clustering

Several important pattern recognition applications are based on feature extraction and vector clustering. Directional patterns may be represented by rotation-variant directional vectors, formed from M features uniformly extracted in M directions. It is often required that pattern recognition algorithms are invariant under pattern rotation or, equivalently, invariant under circular shifts of such directional vectors. This paper introduces a K-means based algorithm (Circular K-means) to cluster vectors in a circular-shift invariant manner. Thus, the algorithm is appropriate for rotation invariant pattern recognition applications. An efficient Fourier domain implementation of the proposed technique is presented to reduce computational complexity. An index-based approach is proposed to estimate the correct number of clusters in the dataset. Experiments illustrate the superiority of CKmeans for clustering directional vectors, compared to the alternative approach that uses the original K-means and rotation-invariant vectors transformed from rotationvariant ones.