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Brijnesh Jain - IEEE Xplore Author Profile

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The sample mean is one of the most fundamental concepts in statistics with far-reaching implications for data mining and pattern recognition. Household load profiles are compared to the aggregated levels more intermittent and a specific error measure based on local permutations has been proposed to cope with this when comparing profiles. We formally describe a distance based on this error, the loc...Show More
This contribution extends linear classifiers to sub-linear classifiers for graphs and analyzes their properties. The results are (i) a geometric interpretation of sub linear classifiers, (ii) a generic learning rule based on the principle of empirical risk minimization, (iii) a convergence theorem for the margin perceptron in the separable case, and (iv) the VC-dimension of sub linear functions. E...Show More
The median and mean graph are basic building blocks for statistical graph analysis and unsupervised pattern recognition methods such as central clustering and graph quantization. This contribution provides sufficient conditions for consistent estimators of true but unknown central points of a distribution on graphs.Show More
We show that multiple structure alignment (MStA) using contact maps is equivalent to the problem of finding a sample mean of contact maps. From this result, we derive a subgradient method for solving the MStA method. Experiments show that the proposed algorithm is a flexible alignment method that provides an excellent tradeoff between accuracy and speed.Show More
Bimal, a fast method for approximately solving the maximum contact map overlap (maxCMO) problem is introduced. The method is based on an approximate model of the maxCMO-problem using the generic bipartite graph matching framework, which is then optimally solved by double dynamic programming. The performance of Bimal has been evaluated in an empirical comparative study including clustering of prote...Show More
We present an analytic and geometric view of the sample mean of graphs. The theoretical framework yields efficient subgradient methods for approximating a structural mean and a simple plug-in mechanism to extend existing central clustering algorithms to graphs. Experiments in clustering protein structures show the benefits of the proposed theory.Show More
We propose a multi-layer perceptron for learning on data represented in terms of attributed graphs. The approach is based on the idea to associate each simple perceptron with an attributed weight graph and to provide a concept similar to the inner product of vectors in the domain of graphs. This is achieved by the Schur-Hadamard inner product of graphs. To provide a supervised learning mechanism w...Show More
We develop a new mathematical framework, which embeds weighted graphs into quasi metric spaces. This concept establishes a theoretical basis to apply neural learning machines for structured data. To exemplarily illustrate the applicability of metric graph spaces, we propose and analyze a perceptron learning algorithm for graphs in its primal and dual form.Show More