hyperspectral sensors provide a large number of spectral bands. this massive and complex data structure of hyperspectral images presents a challenge to traditional data processing techniques. therefore, reducing the dimensionality of hyperspectral images without losing important information is a very important issue for the remote sensing community. we propose to use overlap-based feature weigh...

Canonical correlation analysis (CCA) is a technique to find statistical dependencies between pair of multivariate data. However, its application high dimensional data limited due the resulting time complexity. While conventional CCA algorithm requires polynomial time, we have developed an that approximates with computational proportional logarithm input dimensionality using quantum-inspired com...

Kernels for structured data are rapidly becoming an essential part of the machine learning toolbox. Graph kernels provide similarity measures for complex relational objects, such as molecules and enzymes. Graph kernels based on walks are popular due their fast computation but their predictive performance is often not satisfactory, while kernels based on subgraphs suffer from high computational ...

Kernel k-Means is a basis for many state of the art global clustering approaches. When the number of samples grows too big, however, it is extremely time-consuming to compute the entire kernel matrix and it is impossible to store it in the memory of a single computer. The algorithm of Approximate Kernel k-Means has been proposed, which works using only a small part of the kernel matrix. The com...

Convolution kernels for trees provide effective means for learning with treestructured data, such as parse trees of natural language sentences. Unfortunately, the computation time of tree kernels is quadratic in the size of the trees as all pairs of nodes need to be compared: large trees render convolution kernels inapplicable. In this paper, we propose a simple but efficient approximation tech...

Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model, produces relatively accurate approximations, but is inefficient on large square matrices. The Nyström method is highly efficient, but can only achieve low a...

We propose a new fast Gaussian summation algorithm for high-dimensional datasets with high accuracy. First, we extend the original fast multipole-type methods to use approximation schemes with both hard and probabilistic error. Second, we utilize a new data structure called subspace tree which maps each data point in the node to its lower dimensional mapping as determined by any linear dimensio...

One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance. By extending the notion of statistical leverage scores...