Analysis of high dimensional data in modern applications, such as neuroscience, text mining, spectral analysis or chemometrices naturally requires tensor decomposition methods. The Tucker decompositions allow us to extract hidden factors (component matrices) with a different dimension in each mode and investigate interactions among various modes. The Alternating Least Squares (ALS) algorithms h...

The Kuhn-Tucker and envelope theorems can be used to characterize the solution to a wide range of constrained optimization problems: static or dynamic, under perfect foresight or featuring randomness and uncertainty. In addition, these same two results provide foundations for the work on the maximum principle and dynamic programming that we will do later on. For both of these reasons, the Kuhn-...

Analyses of array-valued datasets often involve reduced-rank array approximations, typically obtained via least-squares or truncations of array decompositions. However, least-squares approximations tend to be noisy in high-dimensional settings, and may not be appropriate for arrays that include discrete or ordinal measurements. This article develops methodology to obtain low-rank model-based re...

Train energy saving problem investigates how to control train's velocity such that the quantity of energy consumption is minimized and some system constraints are satis ed. On the assumption that the train's weights on different links are estimated by fuzzy variables when making the train scheduling strategy, we study the fuzzy train energy saving problem. First, we propose a fuzzy energy ...

Gated networks are that contain gating connections in which the output of at least two neurons multiplied. The basic idea a gated restricted Boltzmann machine (RBM) model is to use binary hidden units learn conditional distribution one image (the output) given another input). This allows RBM transformations between successive images. Inference consists extracting pair However, fully connected m...

This paper presents a constrained Tucker-3 model for blind beamforming. The constrained structure of this model is parameterized by two constraint matrices that capture the spatial and temporal structure of the channel. We first present a generalized Tucker-3 model that considers a multipath propagation scenario with large delay spread and different number of paths per source. This tensor model...

A matrix always has a full rank submatrix such that the of this is equal to submatrix. This property one corner stones theory. We call max-full-rank-submatrix property. Tensor ranks play crucial role in low tensor approximation, completion and recovery. However, their theory still not matured yet. Can we set an axiom system for ranks? extend tensors? explore these paper. first propose some axio...

Bakground: Phototherapy plays a significant role in the treatment and prevention of hyperbilirubinemia as well as the management of subsequent complications in the newborn. However, this treatment modality may itself result in the development of hypocalcaemia and create serious complications including convulsion and related condi-

In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.