We present a simultaneous generalization of the well-known Karhunen-Loéve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n = 0 we obtain the classical k-means, while for k = 1 we obtain PCA algorithm. Moreover, by our approach we can obtain clusters with different dimensionality which describe the structure...

A fast identification algorithm is proposed for systems with delayed inputs. It is based on a non-asymptotic distributional estimation technique initiated in the framework of systems without delay. Such technique leads to simple realization schemes, involving integrators, multipliers and piecewise polynomial or exponential time functions. Thus, it allows for a real time implementation. In order...

Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on Gn, the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic characterization of the closed H-orbits in Gn, generalizing work of Richardson which treats the case H = G. This characterization turns out to be a natural generalizati...

We propose a simultaneous spatiotemporal filter optimization algorithm for the single trial ElectroEncephaloGraphy (EEG) classification problem. The algorithm is a generalization of the Common Spatial Pattern (CSP) algorithm, which incorporates non-homogeneous weighting of the crossspectrum matrices. The spectral weighting coefficients and the spatial filter are alternately updated. The validat...

We address a generalization of the classical 1and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipul...

New fractional r -order seminorms, TGV r , r ∈ R , r ≥ 1 , are proposed in the one-dimensional (1D) setting, as a generalization of the integer order TGV k seminorms, k ∈ N . The fractional r -order TGV r -seminorms are shown to be intermediate between the integer order TGV k -seminorms. A bilevel training scheme is proposed, where under a box constraint a simultaneous optimization with respect...

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, de­ termination of liability, and policy analysis. We present a method for evaluating counter­ factuals when the underlying causal model is represented by structural models a nonlin­ ear generalization of the simultaneous equa­ tions models commonly used in econometr...

Abstract The Hopfield-Tank (1985) recurrent neural network architecture for the Traveling Salesman Problem is generalized to a fully interconnected “cellular” neural network of regular oscillators. Tours are defined by synchronization patterns, allowing the simultaneous representation of all cyclic permutations of a given tour. The network converges to local optima some of which correspond to s...

We derive a smoothing regularizer for recurrent network models by requiring robustness in prediction performance to perturbations of the training data. The regularizer can be viewed as a generalization of the first order Tikhonov stabilizer to dynamic models. The closed-form expression of the regularizer covers both time-lagged and simultaneous recurrent nets, with feedforward nets and onelayer...