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Minimal Size of Basic Families ∗
, 2009
"... A family Φ of continuous realvalued functions on a space X is said to be basic if every f ∈ C(X) can be represented f = Pn gi ◦ φi for some i=1 φi ∈ Φ and gi ∈ C(R) (i = 1,..., n). Define basic (X) = min{Φ  : Φ is a basic family for X}. If X is separable metrizable X then either X is locally com ..."
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compact and finite dimensional, and basic (X) < ℵ0, or basic (X) = c. If K is compact and either w(K) (the minimal size of a basis for K) has uncountable cofinality or K has a discrete subset D with D  = w(K) then either K is finite dimensional, and basic (K) = cof([w(K)] ℵ0, ⊆), or basic (K
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 633 (38 self)
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optimization problem: specifically, minimizing the ℓ¹ norm of the coefficients γ. In this paper, we obtain parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems. We introduce the Spark, ameasure of linear dependence
Sequential minimal optimization: A fast algorithm for training support vector machines
 Advances in Kernel MethodsSupport Vector Learning
, 1999
"... This paper proposes a new algorithm for training support vector machines: Sequential Minimal Optimization, or SMO. Training a support vector machine requires the solution of a very large quadratic programming (QP) optimization problem. SMO breaks this large QP problem into a series of smallest possi ..."
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Cited by 461 (3 self)
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This paper proposes a new algorithm for training support vector machines: Sequential Minimal Optimization, or SMO. Training a support vector machine requires the solution of a very large quadratic programming (QP) optimization problem. SMO breaks this large QP problem into a series of smallest
A LinearTime Heuristic for Improving Network Partitions
, 1982
"... An iterative mincut heuristic for partitioning networks is presented whose worst case computation time, per pass, grows linearly with the size of the network. In practice, only a very small number of passes are typically needed, leading to a fast approximation algorithm for mincut partitioning. To d ..."
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Cited by 524 (0 self)
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An iterative mincut heuristic for partitioning networks is presented whose worst case computation time, per pass, grows linearly with the size of the network. In practice, only a very small number of passes are typically needed, leading to a fast approximation algorithm for mincut partitioning
The Cache Performance and Optimizations of Blocked Algorithms
 In Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems
, 1991
"... Blocking is a wellknown optimization technique for improving the effectiveness of memory hierarchies. Instead of operating on entire rows or columns of an array, blocked algorithms operate on submatrices or blocks, so that data loaded into the faster levels of the memory hierarchy are reused. This ..."
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Cited by 574 (5 self)
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given cache size, the block size that minimizes the expected number of cache misses is very small. Tailoring the block size according to the matrix size and cache parameters can improve the average performance and reduce the variance in performance for different matrix sizes. Finally, whenever possible
Inference by Minimizing Size, Divergence, or their Sum
"... We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; mi ..."
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denoising and to three different types of NLP parsing models, this technique performs marginal inference up to 11 times faster than loopy BP, with graph sizes reduced up to 98%—at comparable error in marginals and parsing accuracy. We also show that minimizing the weighted sum of divergence and size
Detection and Tracking of Point Features
 International Journal of Computer Vision
, 1991
"... The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade i ..."
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Cited by 629 (2 self)
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in 1981. The method defines the measure of match between fixedsize feature windows in the past and current frame as the sum of squared intensity differences over the windows. The displacement is then defined as the one that minimizes this sum. For small motions, a linearization of the image intensities
Storage management and caching in PAST, a largescale, persistent peertopeer storage utility
, 2001
"... This paper presents and evaluates the storage management and caching in PAST, a largescale peertopeer persistent storage utility. PAST is based on a selforganizing, Internetbased overlay network of storage nodes that cooperatively route file queries, store multiple replicas of files, and cache a ..."
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Cited by 803 (23 self)
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balances the number of files stored on each node. However, nonuniform storage node capacities and file sizes require more explicit storage load balancing to permit graceful behavior under high global storage utilization; likewise, nonuniform popularity of files requires caching to minimize fetch distance
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