As the Netflix Prize competition has demonstrated, matrix factorization models are superior to classic nearest-neighbor techniques for producing product recommendations, allowing the incorporation of additional information such as implicit feedback, temporal effects, and confidence levels. Modern

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information

In this paper, we present the problem of allocating processors for matrix products. First, we consider how many processors should be allocated for computing one matrix product on a parallel system. Then, we discuss how to allocate processors for a number of independent matrix products

Abstract. A new type of diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product states and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automata that “generates

We propose a decoding algorithm for the (u | u+ v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error correction capability of the code. 1

. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums

signals. We prove that there is no point in making the number of transmitter antennas greater than the length of the coherence interval: the capacity for M> Tis equal to the capacity for M = T. Capacity is achieved when the T M transmitted signal matrix is equal to the product of two statistically

bone marrow cultures Extracellular matrix production by the adherent cells of long-term murine

matrix). That is, our lower bound is super-linear in the number of inputs and is applied for circuits that use addition gates, product gates and products with field elements of absolute value up to 1.

Introduction Computing the square root of the product of two matrices can be used in model reduction methods based on the cross-Gramians; see [1] and the references therein. This lead us to consider the more general problem of computing the kth root of a matrix product W = A 1 A 2 \Delta \Delta