Introduction Permit me to begin by telling you a little about the history of the book1 on which this talk2 is based. It will help you understand why I am so delighted to be presenting this talk. On the very day thirty-five years ago when my History of Vector Analysis was published, a good friend with the very best intentions helped me put the book in perspective by innocently asking: “Who was V...

We compare L1 and L2 soft margin support vector machines from the standpoint of positive definiteness, the number of support vectors, and uniqueness and degeneracy of solutions. Since the Hessian matrix of L2 SVMs is positive definite, the number of support vectors for L2 SVMs is larger than or equal to the number of L1 SVMs. For L1 SVMs, if there are plural irreducible sets of support vectors,...

In this paper we present the results of a detailed simulation study of the execution of vector programs on a single processor of a Convex C3480 machine, using a subset of the Perfect Club benchmarks. We are interested in evaluating several cost/performance tradeoos that the machine designers made in order to asses which features of the architecture severely limit the performance attainable. We ...

In this paper, we propose video classification using linear manifolds (affine subspaces). In our method, we represent videos belonging to a same class by several linear manifolds using k-varieties clustering. When a test video is given, each frame of it votes for the class to which its nearest linear manifold belongs. According to this voting, the test video is classified into the class that ac...

We show that the orientation and location of the separating hyperplane for 2-class supervised pattern classiication obtained by the Support Vector Machine (SVM) proposed by Vapnik and his colleagues, is equivalent to the solution obtained by Fisher's Linear Discriminant on the set of Support Vectors. In other words, SVM can be seen as a way to \sparsify" Fisher's Linear Discriminant in order to...

13] M. Krause and S. Waack. Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in. 22 Acknowledgments The authors would like to thank the referees for their detailed comments, and for strengthening the result presented in Theorem 6. A plc of the rows of the array that does not contain any row from the bottom N=16 rows will...

Usually in this type of calculations one does not write explicitly the unit vectors ei. This makes the notation more economical but is possible only either if the vectors are decomposed into the Cartesian unit vectors ex, ey, ez, or (for vectors decomposed into unit vectors e1(ξ), e2(ξ), e3(ξ) associated with some curvelinear coordinates ξ, ξ, ξ see below), or if no differentiations are involve...

Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic view is also quite effective for studying processes over structured state spaces, e.g. measurable, or continuous. In the present paper we consider coalgebras ...

The electromyography (EMG) signal is a bioelectrical signal variation, generated in muscles during voluntary or involuntary muscle activities. The muscle activities such as contraction or relaxation are always controlled by the nervous system. The EMG signal is a complicated biomedical signal due to anatomical/physiological properties of the muscles and its noisy environment. In this paper, a c...