We present a path algorithm for the generalized lasso problem. This problem penalizes the `1 norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which facilitates computation and conceptual understanding of the path. For D = I (the usual lasso), we draw a connecti...

When (φn) is a sequence of positive functions in L1(R) such that the convolutions φn ? f converge in L1-norm to f for all f ∈ L1(R), then these convolutions may or may not converge almost everywhere too. There is always a subsequence (φnk ) such that at least φnk ? f converges almost everywhere to f for all f ∈ Lp(R), 1 < p < ∞. A special case of this is when the functions φn are the dilations ...

In this paper, we propose a novel shape description method for mobile retrieval of leaf images. In this method, termed multiscale arch height (MARCH), hierarchical arch height features at different chord spans are extracted from each contour point to provide a compact, multiscale shape descriptor. Both the global and detailed features of the leaf shape can be effectively captured by the propose...

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We consider the flow of gas in an N-dimensional porous medium with initial density v0(x) ≥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = ∆vm where m > 1 is a physical constant. Assuming that ∫ (1 + |x|2)v0(x)dx < ∞, we prove that v(x, t) behaves asymptotically, as t → ∞, like the Barenblatt-Pattle solution V(|x|, t). We prove that the L1-distance decays ...

This paper introduces DEVIATION, a soft global constraint to obtain balanced solutions. A violation measure of the perfect balance can be defined as the Lp norm of the vector variables minus their mean. SPREAD constraints the sum of square deviations to the mean [5, 7] i.e. the L2 norm. The L1 norm is considered here. Neither criterion subsumes the other but the design of a propagator for L1 is...

We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuousdomain regularization. We derive the parametric form of the solution (representer theorems) for Tikhonov (quadratic) and generalized total-variation (gTV) regulariza...

© 2 0 0 1 m a s s a c h u s e t t s i n s t i t u t e o f t e c h n o l o g y, c a m b r i d g e , m a 0 2 1 3 9 u s a — w w w. a i. m i t. e d u m a s s a c h u s e t t s i n s t i t u t e o f t e c h n o l o g y — a r t i f i c i a l i n t e l l i g e n c e l a b o r a t o r y 1 ABSTRACT The image comparison operation – assessing how well one image matches another – forms a critical component...

Abstract. Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ R|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form x Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not th...

The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of lattices. These lattices, in turn, are obtained from Construction A applied to binary codes and Z4−codes. A lower bound on the size of our codes for the Manhattan di...