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Spatial Neighborhood-Constrained linear coding for Visual Object Tracking

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2014年第1期10卷 469-480页

作者： Liu, Huaping Yuan, Mingyi Sun, Fuchun Zhang, Jianwei Tsinghua Univ Dept Comp Sci & Technol State Key Lab Intelligent Technol & Syst TNLIST Beijing 100084 Peoples R China Univ Hamburg Dept Informat Grp TAMS D-20148 Hamburg Germany

In this paper, a new spatial neighborhood-constrained linear coding strategy which realizes sparse representation is proposed for visual object tracking. Unlike conventional sparse and locality-constrained linear coding approaches that need an extra post-processing stage to incorporate the spatial layout information, the proposed coding strategy intrinsically embeds the spatial layout information into the coding stage. The proposed coding strategy can also be used to effectively realize joint sparse representation for different feature descriptors. In addition, based on the distance to the "ideal point" in the reconstruction error space, a new multicue integration approach for robust tracking is proposed and a co-learning approach is developed to update the dictionaries. Finally, the proposed tracking algorithm is compared with other state-of-the-art trackers on some challenging video sequences and shows promising results.

关键词： linear coding particle filter visual tracking

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RGB-D action recognition using linear coding

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NEUROCOMPUTING 2015年第PartA期149卷 79-85页

作者： Liu, Huaping Yuan, Mingyi Sun, Fuchun Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China State Key Lab Intelligent Technol & Syst Beijing Peoples R China Tsinghua Natl Lab Informat Sci & Technol Beijing Peoples R China

In this paper, we investigate action recognition using an inexpensive RGB-D sensor (Microsoft Kinect). First, a depth spatial-temporal descriptor is developed to extract the interested local regions in depth image. Such descriptors are very robust to the illumination and background clutter. Then the intensity spatial-temporal descriptor and the depth spatial-temporal descriptor are combined and feeded into a linear coding framework to get an effective feature vector, which can be used for action classification. Finally, extensive experiments are conducted on a publicly available RGB-D action recognition dataset and the proposed method shows promising results. (C) 2014 Elsevier B.V. All rights reserved.

关键词： RGB-D Action recognition linear coding

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Computing linear Functions by linear coding Over Networks

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第1期60卷 422-431页

作者： Appuswamy, Rathinakumar Franceschetti, Massimo IBM Res Almaden San Jose CA 95120 USA Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

We consider the scenario in which a set of sources generates messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can compute linear functions using linear codes. We identify a class of linear functions that can be computed using linear codes in every network that satisfies a natural cut-based condition. Conversely, for another class of linear functions, we show that the cut-based condition does not guarantee the existence of a linear coding solution. For linear functions over the binary field, the two classes are complements of each other.

关键词： Function computation linear coding network coding network computing

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Stability of MMSE state estimators over lossy networks using linear coding

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AUTOMATICA 2015年 51卷 167-174页

作者： Sui, Tianju You, Keyou Fu, Minyue Marelli, Damian Zhejiang Univ Dept Control Sci & Engn Hangzhou 310013 Zhejiang Peoples R China Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310013 Zhejiang Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Univ Newcastle Sch Elect Engn & Comp Sci Callaghan NSW 2308 Australia Austrian Acad Sci Acoust Res Inst A-1040 Vienna Austria

This paper studies the state estimation problem for a stochastic discrete-time system over a lossy channel where the packet loss is modeled as an independent and identically distributed binary process. To counter the effect of random packet loss, we propose a linear coding method to preprocess the measured output, and prove that the coded output is information preserving when packet loss is void and is information enhancing when packet loss is present. An optimal state estimator under the minimum mean square error (MMSE) criterion is derived for the coded output when subject to packet loss. The maximum packet loss rate for ensuring a stable estimator is then derived and shown to be very close to a well-known lower bound. Also considered is a compressed linear coding method where the measured output is first compressed onto a lower dimensional space before encoding, and it is shown that the similar packet rate condition for stability holds. Crown Copyright (C) 2014 Published by Elsevier Ltd. All rights reserved.

关键词： Stochastic systems Networked systems State estimation Kalman filter Packet loss linear coding

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linear coding for Network Computing

Linear Coding for Network Computing

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IEEE International Symposium on Information Theory (ISIT)

作者： Appuswamy, Rathinakumar Franceschetti, Massimo Karamchandani, Nikhil Zeger, Kenneth Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

ISBN: (纸本)9781457705953

We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, and semi-injective target functions. Computing capacity bounds are given with respect to these target function classes for network codes that use routing, linear coding, or nonlinear coding.

关键词： Gain linear code Network coding Receivers Routing linear codes linear coding network coding network computing routing semi injective target functions single-receiver networks source messages telecommunication network routing

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Insufficiency of linear coding in network information flow

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第8期51卷 2745-2759页

作者： Dougherty, R Freiling, C Zeger, K Ctr Commun Res San Diego CA 92121 USA Calif State Univ San Bernardino Dept Math San Bernardino CA 92407 USA Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite-field alphabet. It is also known that this result does not generalize to arbitrary networks. There are several examples in the literature of solvable networks with no scalar linear solution over any finite field. However, each example has a linear solution for some vector dimension greater than one. It has been conjectured that every solvable network has a linear solution over some finite-field alphabet and some vector dimension. We provide a counterexample to this conjecture. We also show that if a network has no linear solution over any finite field, then it has no linear solution over any finite commutative ring with identity. Our counterexample network has no linear solution even in the more general algebraic context of modules, which includes as special cases all finite rings and Abelian groups. Furthermore, we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field (exactly 10% greater), so the network is not even asymptotically linearly solvable. It follows that, even for more general versions of linearity such as convolutional coding, filter-bank coding, or linear time sharing, the network has no linear solution.

关键词： asymptotics flows linear coding network information theory routing

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Capacity and Achievable Rate Regions for linear Network coding Over Ring Alphabets

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第1期65卷 220-234页

作者： Connelly, Joseph Zeger, Kenneth Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets. For non-commutative rings, two-sided linearity is allowed. Specifically, we prove the following for directed acyclic networks. First, the linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field. Furthermore, any two fields with different characteristics yield different linear capacities for at least one network. Second, whenever the characteristic of a given finite field divides the size of a given finite ring, each network's linear rate region over the ring is contained in its linear rate region over the field. Thus, any network's linear capacity over a field is at least its linear capacity over any other ring of the same size. An analogous result also holds for linear network codes over module alphabets. Third, whenever the characteristic of a given finite field does not divide the size of a given finite ring, there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field. Thus, for any finite field, there always exist rings over which some networks have higher linear capacities than over the field.

关键词： linear coding capacity network coding modules (abstract algebra)

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linear Network coding Over Rings - Part II: Vector Codes and Non-Commutative Alphabets

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第1期64卷 292-308页

作者： Connelly, Joseph Zeger, Kenneth Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

In Part I, we studied linear network coding over finite commutative rings and made comparisons to the well-studied case of linear network coding over finite fields. Here, we consider the more general setting of linear network coding over finite (possibly non-commutative) rings and modules. We prove the following results regarding the linear solvability of directed acyclic networks over various finite alphabets. For any network, the following are equivalent: (i) vector linear solvability over some field, (ii) scalar linear solvability over some ring, and (iii) linear solvability over some module. Analogously, the following are equivalent: (a) scalar linear solvability over some field, (b) scalar linear solvability over some commutative ring, and (c) linear solvability over some module whose ring is commutative. Whenever any network is linearly solvable over a module, a smallest such module arises in a vector linear solution for that network over a field. If a network is scalar linearly solvable over some non-commutative ring but not over any commutative ring, then such a non-commutative ring must have size at least 16, and for some networks, this bound is achieved. An infinite family of networks is demonstrated, each of which is scalar linearly solvable over some non-commutative ring but not over any commutative ring. Whenever p is prime and 1 <= k <= 6, if a network is scalar linearly solvable over some ring of size p(k), then it is also k-dimensional vector linearly solvable over the field GF(p), but the converse does not necessarily hold. This result is extended to all k >= 1 when the ring is commutative.

关键词： linear coding network solvability network coding modules (abstract algebra)

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A Hypergraph Approach to linear Network coding in Multicast Networks

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2010年第7期21卷 968-982页

作者： Yang, Min Yang, Yuanyuan FalconStor Software Melville NY 11747 USA SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA

Network coding is a promising generalization of routing which allows a node to generate output messages by encoding its received messages. A typical scenario where network coding offers unique advantages is a multicast network where a source node generates messages and multiple receivers collect the messages. In a multicast network, linear network codes are preferred due to its sufficiency and simplicity. In this paper, we propose an approach to transforming the linear coding problem into a graph theory problem. By utilizing hypergraphs, we model the linear codes by constructing a pseudodual graph of the multicast network. Then, a valid linear code is equivalent to a cover in the pseudodual graph satisfying some constraints. By iterative refinements, an eligible cover can be found in polynomial time. Moreover, we propose several preprocessing algorithms to further reduce the computation time required by the iterative refinements by reducing the graph size before transformation. An important contribution of this work is that the proposed approach can be readily extended to solve many minimal network coding problems. By assigning different weights to edges, minimal network coding problems are reduced to the shortest path problem in the pseudodual graph. Our simulation results show that the proposed preprocessing algorithms can reduce the computation time by about 40-50 percent in a medium size multicast network compared to the scheme without preprocessing algorithms, and the throughput of the system with network coding is 25 percent higher than that with the traditional approach of multiple multicast trees.

关键词： Network coding linear coding multicast network hypergraph

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linear Network coding Over Rings - Part I: Scalar Codes and Commutative Alphabets

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第1期64卷 274-291页

作者： Connelly, Joseph Zeger, Kenneth Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

linear network coding over finite fields is a well-studied problem. We consider the more general setting of linear coding for directed acyclic networks with finite commutative ring alphabets. Our results imply that for scalar linear network coding over commutative rings, fields can always be used when the alphabet size is flexible, but other rings may be needed when the alphabet size is fixed. We prove that if a network has a scalar linear solution over some finite commutative ring, then the (unique) smallest such commutative ring is a field. We also show that fixed-size commutative rings are quasi-ordered, such that all the scalar linearly solvable networks over any given ring are also scalar linearly solvable over any higher-ordered ring. We study commutative rings that are maximal with respect to this quasi-order, as they may be considered the best commutative rings of a given size. We prove that a commutative ring is maximal if and only if some network is scalar linearly solvable over the ring, but not over any other commutative ring of the same size. Furthermore, we show that maximal commutative rings are direct products of certain fields specified by the integer partitions of the prime factor multiplicities of the ring's size. Finally, we prove that there is a unique maximal commutative ring of size m if and only if each prime factor of m has multiplicity in {1, 2, 3, 4, 6}. As consequences, 1) every finite field is such a maximal ring and 2) for each prime p, some network is scalar linearly solvable over a commutative ring of size p(k) but not over the field of the same size if and only if k is not an element of. {1, 2, 3, 4, 6}.

关键词： linear coding network solvability network coding modules (abstract algebra)

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