Classification problems involving a categorical class label Y and a functional predictor X(t) are becoming increasingly common. Since X(t) is essentially infinite dimensional some form of dimensionality reduction is essential in these problems. Conventional data reduction techniques for functional data can be categorized into functional principal component analysis and filtering methods. Howeve...

In common binary classification scenarios, the presence of both positive and negative examples in training data is needed to build an efficient classifier. Unfortunately, in many domains, this requirement is not satisfied and only one class of examples is available. To cope with this setting, classification algorithms have been introduced that learn from Positive and Unlabeled (PU) data. Origin...

Under reasonable assumptions on the data u, v and the function f , we show that the nonlinear periodic Goursat problem ∂u ∂x∂y (x, y) = f(x, y, u(x, y)); u(x, 0) = v(x); u(0, y) = w(y) which cannot be posed in the general theory of distributions, may be studied and solved in a differential algebra of periodic new generalized functions on R2. This algebra contains, in a canonical way, the space ...