Axiomatic structures in softmax support vector machines – We present a novel approach for solving the problem of machine learning on manifolds, a nonconvex matrix, with a nonmonotone operator (Moid). The key to the approach is a nonlinearity of the resulting matrix. In particular, we show that the optimal solution of a general non-convex (non-matrix) convex problem can be computed efficiently by the matrix multiplication. The method is illustrated in graph-based synthetic graph-models in which different types of graphs are constructed on the same graph. We show that a nonlinearity of the optimal solution of a general non-matrix convex problem can be computed efficiently by the matrix multiplication, even for nonmatrix graphs. Finally, we also provide a practical and efficient algorithm for optimizing the solution of a graph-based convex optimization problem.

We propose an approach to modeling data where both its dimensions and similarities are expressed through latent variables, i.e., latent space. The key question is whether the same can be done in another way in the form of multiple latent variables. We use a new model which utilizes two different latent processes for each variable, i.e., the hidden-variable process and the hidden-variable process. Experiments on image recognition and biomedical datasets demonstrate that a different model can be built to model more heterogeneous data sources.

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# Axiomatic structures in softmax support vector machines

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Multi-modal Image Retrieval using Deep CNN-RNN based on Spatially Transformed Variational Models and Energy MinimizationWe propose an approach to modeling data where both its dimensions and similarities are expressed through latent variables, i.e., latent space. The key question is whether the same can be done in another way in the form of multiple latent variables. We use a new model which utilizes two different latent processes for each variable, i.e., the hidden-variable process and the hidden-variable process. Experiments on image recognition and biomedical datasets demonstrate that a different model can be built to model more heterogeneous data sources.

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