Local feature based tensor kernel for image manifold learning

![CDATA[In this paper, we propose a tensor kernel on images which are described as set of local features and then apply a novel dimensionality reduction algorithm called Twin Kernel Embedding (TKE) [1] on it for images manifold learning. The local features of the images extracted by some feature extraction methods like SIFT [2] are represented as tuples in the form of coordinates and feature descriptor which are regarded as highly structured data. In [3], different kernels were used for intra and inter images similarity. This is problematic because different kernels refer to different feature spaces and hence they are representing different measures. This heterogeneity embedded in the kernel Gram matrix which was input to a dimensionality reduction algorithm has been transformed to the image embedding space and therefore led to unclear understanding of the embedding. We address this problem by introducing a tensor kernel which treats different sources of information in a uniform kernel framework. The kernel Gram matrix generated by tensor kernel is homogeneous, that is all elements are from the same measurement. Image manifold learned from this kernel is more meaningful. Experiments on image visualization are used to show the effectiveness of this method.]]