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Alistair Moffat - One of the best experts on this subject based on the ideXlab platform.
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Incremental Calculation of Minimum-Redundancy Length-Restricted Codes
IEEE Transactions on Communications, 2007Co-Authors: Michael Liddell, Alistair MoffatAbstract:The length-restricted code-construction problem arises when using prefix codes for large messages and also for search-tree depth minimization. A problem instance comprises an ordered set of input probabilities which in this paper are assumed, without loss of generality, to be a set of unnormalized integer frequencies {f1 , f2,..., fn}, and a maximum codeword length L bits. The package-merge algorithm of Larmore and Hirschberg constructs a Minimum-Redundancy length-restricted code in O(nL) time. Here we present an algorithm which computes a Minimum-Redundancy length-restricted code in O((H L + 1)n) time, by starting with a Minimum-Redundancy (Huffman) code with a maximum codeword length of H, and then refining it to meet the length limit L. The new algorithm is suited to problems where H - L is small; and when H - L > L - [log n], the new algorithm outperforms all previous methods. Experimental results confirm the behavior of the new algorithm
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Incremental calculation of Minimum-Redundancy length-restricted codes
Proceedings DCC 2002. Data Compression Conference, 2002Co-Authors: Michael Liddell, Alistair MoffatAbstract:The prefix-free code construction problem is to take a message containing n unique symbols and produce a set of n codewords which can be used to create a reversible encoding of the message. The Minimum-Redundancy code construction problem adds the requirement that the code produced must minimise the cost of transmission (or storage) of the message. Adding another constraint, the Minimum-Redundancy length-restricted code construction problem is to create a Minimum-Redundancy code in which no codeword has a length greater than L bits. The solution to the Minimum-Redundancy code construction problem is due to Huffman (1952). The package-merge strategy of Larmore and Hirschberg (1990) is a two-stage mechanism for creating Minimum-Redundancy length-restricted codes. Their implementation, here called ORIGINAL-PM, requires O(nL) time and space. ORIGINAL-PM follows the underlying strategy closely and the following is a description of both the principle and that first implementation. Different implementation methods are discussed.
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efficient construction of Minimum Redundancy codes for large alphabets
IEEE Transactions on Information Theory, 1998Co-Authors: Alistair Moffat, Andrew TurpinAbstract:We consider the problem of calculating Minimum-Redundancy codes for alphabets in which there is significant repetition of symbol weights. On a sorted-by-weight alphabet of, n symbols and r distinct symbol weights we show that a Minimum-Redundancy prefix code can be constructed in O(r+r log(n/r)) time, and that a Minimum Redundancy L-bit length-limited prefix code can be constructed in O(Lr+Lrlog(n/r)) time. When r is small relative to n-which is necessarily the case for most practical coding problems on large alphabets-these bounds represent a substantial improvement upon the best previous algorithms for these two problems, which consumed O(n) time and O(nL) time, respectively. The improved algorithms are also space-efficient.
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On the implementation of Minimum Redundancy prefix codes
IEEE Transactions on Communications, 1997Co-Authors: Alistair Moffat, Andrew TurpinAbstract:Minimum Redundancy coding (also known as Huffman coding) is one of the enduring techniques of data compression. Many efforts have been made to improve the efficiency of Minimum Redundancy coding, the majority based on the use of improved representations for explicit Huffman trees. In this paper, we examine how Minimum Redundancy coding can be implemented efficiently by divorcing coding from a code tree, with emphasis on the situation when n is large, perhaps on the order of 10/sup 6/. We review techniques for devising Minimum Redundancy codes, and consider in detail how encoding and decoding should be accomplished. In particular, we describe a modified decoding method that allows improved decoding speed, requiring just a few machine operations per output symbol (rather than for each decoded bit), and uses just a few hundred bytes of memory above and beyond the space required to store an enumeration of the source alphabet.
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on the implementation of Minimum Redundancy prefix codes
Data Compression Conference, 1996Co-Authors: Alistair Moffat, Andrew TurpinAbstract:Minimum-Redundancy coding (also known as Huffman (1952) coding) is one of the enduring techniques of data compression. We examine how best Minimum-Redundancy coding can be implemented, with particular emphasis on the situation when n is large, perhaps of the order of 10/sup 6/. We review techniques for devising Minimum-Redundancy codes, and consider in detail how encoding and decoding should be accomplished. In particular, we describe a modified decoding method that allows improved decoding throughput, requiring just a few machine operations per output symbol (rather than for each decoded bit), and uses just a few hundred bytes of memory above and beyond the space required to store an enumeration of the source alphabet. We review methods for calculating codeword lengths, show how those codeword lengths should be used to derive a Minimum-Redundancy code that has the alphabetic sequence property, and describes a memory-compact method for decoding such canonical codes. An improved method for decoding canonical codes is also presented.
Andrew Turpin - One of the best experts on this subject based on the ideXlab platform.
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efficient construction of Minimum Redundancy codes for large alphabets
IEEE Transactions on Information Theory, 1998Co-Authors: Alistair Moffat, Andrew TurpinAbstract:We consider the problem of calculating Minimum-Redundancy codes for alphabets in which there is significant repetition of symbol weights. On a sorted-by-weight alphabet of, n symbols and r distinct symbol weights we show that a Minimum-Redundancy prefix code can be constructed in O(r+r log(n/r)) time, and that a Minimum Redundancy L-bit length-limited prefix code can be constructed in O(Lr+Lrlog(n/r)) time. When r is small relative to n-which is necessarily the case for most practical coding problems on large alphabets-these bounds represent a substantial improvement upon the best previous algorithms for these two problems, which consumed O(n) time and O(nL) time, respectively. The improved algorithms are also space-efficient.
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On the implementation of Minimum Redundancy prefix codes
IEEE Transactions on Communications, 1997Co-Authors: Alistair Moffat, Andrew TurpinAbstract:Minimum Redundancy coding (also known as Huffman coding) is one of the enduring techniques of data compression. Many efforts have been made to improve the efficiency of Minimum Redundancy coding, the majority based on the use of improved representations for explicit Huffman trees. In this paper, we examine how Minimum Redundancy coding can be implemented efficiently by divorcing coding from a code tree, with emphasis on the situation when n is large, perhaps on the order of 10/sup 6/. We review techniques for devising Minimum Redundancy codes, and consider in detail how encoding and decoding should be accomplished. In particular, we describe a modified decoding method that allows improved decoding speed, requiring just a few machine operations per output symbol (rather than for each decoded bit), and uses just a few hundred bytes of memory above and beyond the space required to store an enumeration of the source alphabet.
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on the implementation of Minimum Redundancy prefix codes
Data Compression Conference, 1996Co-Authors: Alistair Moffat, Andrew TurpinAbstract:Minimum-Redundancy coding (also known as Huffman (1952) coding) is one of the enduring techniques of data compression. We examine how best Minimum-Redundancy coding can be implemented, with particular emphasis on the situation when n is large, perhaps of the order of 10/sup 6/. We review techniques for devising Minimum-Redundancy codes, and consider in detail how encoding and decoding should be accomplished. In particular, we describe a modified decoding method that allows improved decoding throughput, requiring just a few machine operations per output symbol (rather than for each decoded bit), and uses just a few hundred bytes of memory above and beyond the space required to store an enumeration of the source alphabet. We review methods for calculating codeword lengths, show how those codeword lengths should be used to derive a Minimum-Redundancy code that has the alphabetic sequence property, and describes a memory-compact method for decoding such canonical codes. An improved method for decoding canonical codes is also presented.
Jian Dong - One of the best experts on this subject based on the ideXlab platform.
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Minimum Redundancy mimo array synthesis with a hybrid method based on cyclic difference sets and aco
International Journal of Microwave and Wireless Technologies, 2017Co-Authors: Jian Dong, Ronghua Shi, Ying GuoAbstract:As a recently proposed concept, multiple-input multiple-output (MIMO) radars exhibit much higher spatial resolution than traditional transmitter based radars because of the synthesized virtual array. In this paper, the problem of Minimum Redundancy (MR)-MIMO array synthesis is addressed, which seeks to maximize the virtual array aperture of MIMO radars for a given number of transmitting and receiving elements. A hybrid method combining autocorrelation property of cyclic difference sets (CDSs) and global search characteristics of ant colony optimization (ACO) is proposed for a rapid and numerically-effective exploration of MR-MIMO array configurations. Numerical experiments validate the proposed method, showing improvements in convergence rate and computational cost with respect to bare ACO-based search as well as improvements in the generality and configuration variety with respect to the CDS-based method.
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Minimum Redundancy mimo array design using cyclic permutation of perfect distance cppd
URSI General Assembly and Scientific Symposium, 2014Co-Authors: Jian Dong, Fang Liu, Yi Jiang, Ronghua ShiAbstract:In this paper, Minimum Redundancy multiple-input multiple-output (MR-MIMO) arrays — a class of thinned antenna arrays — are discussed. The concepts of Minimum Redundancy array (MRA) and cyclic permutation of perfect distance (CPPD) are introduced, and an analytical method based on CPPD is proposed for MR-MIMO array designs. This method can quickly determine the locations of MR-MIMO arrays and require little computational cost. Numerical examples are presented, showing the advantages of the proposed method in spatial resolution performance and computational efficiency.
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Minimum Redundancy mimo array synthesis by means of cyclic difference sets
International Journal of Antennas and Propagation, 2013Co-Authors: Jian Dong, Ronghua Shi, Wentai Lei, Ying GuoAbstract:Antenna array synthesis is an important issue in MIMO radars. By judiciously designing antenna positions, one can create a very long virtual array steering vector with a small number of antennas and therefore achieve very high spatial resolution at a small cost. This paper presents a combinatorial methodology based on cyclic difference sets (CDSs) for Minimum Redundancy (MR) MIMO array synthesis which seeks to maximize the virtual array aperture for a given number of antennas. First, the key features of CDSs and the CDS-based MR-MIMO layouts are described. Then, the analytical expression of the maximum contiguous virtual array aperture is derived. Further, based on this expression, an enumerative shifting procedure is developed for identifying the optimal CDS-based MR-MIMO layout. Selected examples are analyzed to point out the computational effectiveness of the CDS-based MR-MIMO array synthesis.
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A combinatorial method for antenna array design in Minimum Redundancy MIMO radars
IEEE Antennas and Wireless Propagation Letters, 2009Co-Authors: Jian Dong, Qing-xia Li, Wei GuoAbstract:In this letter, the antenna array design problem in Minimum Redundancy (MR) multiple-input-multiple-output (MIMO) radars is addressed, which seeks to maximize the virtual array aperture for a given number of transmitting and receiving (Tx/Rx) elements. Based on difference bases and cyclic difference sets (CDSs), a combinatorial method is proposed for the optimal design of Tx/Rx antenna arrays. The theoretical limits of the Redundancy of MIMO virtual arrays constructed by the method for both one-dimensional and two-dimensional cases are derived. Numerical results are also presented, showing notable improvement in the spatial resolution of MIMO radar system over those reported in the literature.
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co array properties of Minimum Redundancy linear arrays with Minimum sidelobe level
International Symposium on Antennas Propagation and EM Theory, 2008Co-Authors: Jian Dong, Yaoting ZhuAbstract:Minimum Redundancy linear arrays (MRLA) are widely used in radio astronomy, microwave radiometry, radar and other fields. Based on the Fourier properties of arrays with optimal co-array properties, the co-array properties of MRLAs with Minimum sidelobe level are presented for the first time, validated by simulations of different MRLAs with 5~9 elements. The upper bound of the peak sidelobe level (PSL) of a MRLA is also derived.
Michael Liddell - One of the best experts on this subject based on the ideXlab platform.
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Incremental Calculation of Minimum-Redundancy Length-Restricted Codes
IEEE Transactions on Communications, 2007Co-Authors: Michael Liddell, Alistair MoffatAbstract:The length-restricted code-construction problem arises when using prefix codes for large messages and also for search-tree depth minimization. A problem instance comprises an ordered set of input probabilities which in this paper are assumed, without loss of generality, to be a set of unnormalized integer frequencies {f1 , f2,..., fn}, and a maximum codeword length L bits. The package-merge algorithm of Larmore and Hirschberg constructs a Minimum-Redundancy length-restricted code in O(nL) time. Here we present an algorithm which computes a Minimum-Redundancy length-restricted code in O((H L + 1)n) time, by starting with a Minimum-Redundancy (Huffman) code with a maximum codeword length of H, and then refining it to meet the length limit L. The new algorithm is suited to problems where H - L is small; and when H - L > L - [log n], the new algorithm outperforms all previous methods. Experimental results confirm the behavior of the new algorithm
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Incremental calculation of Minimum-Redundancy length-restricted codes
Proceedings DCC 2002. Data Compression Conference, 2002Co-Authors: Michael Liddell, Alistair MoffatAbstract:The prefix-free code construction problem is to take a message containing n unique symbols and produce a set of n codewords which can be used to create a reversible encoding of the message. The Minimum-Redundancy code construction problem adds the requirement that the code produced must minimise the cost of transmission (or storage) of the message. Adding another constraint, the Minimum-Redundancy length-restricted code construction problem is to create a Minimum-Redundancy code in which no codeword has a length greater than L bits. The solution to the Minimum-Redundancy code construction problem is due to Huffman (1952). The package-merge strategy of Larmore and Hirschberg (1990) is a two-stage mechanism for creating Minimum-Redundancy length-restricted codes. Their implementation, here called ORIGINAL-PM, requires O(nL) time and space. ORIGINAL-PM follows the underlying strategy closely and the following is a description of both the principle and that first implementation. Different implementation methods are discussed.
Lin Sun - One of the best experts on this subject based on the ideXlab platform.
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feature selection with missing labels using multilabel fuzzy neighborhood rough sets and maximum relevance Minimum Redundancy
IEEE Transactions on Fuzzy Systems, 2021Co-Authors: Lin Sun, Tengyu Yin, Weiping Ding, Yuhua QianAbstract:Recently, multilabel classification has generated considerable research interest. However, the high dimensionality of multilabel data incurs high costs; moreover, in many real applications, a number of labels of training samples are randomly missed. Thus, multilabel classification can have great complexity and ambiguity, which means some feature selection methods exhibit poor robustness and yield low prediction accuracy. To solve these issues, this paper presents a novel feature selection method based on multilabel fuzzy neighborhood rough sets (MFNRS) and maximum relevance Minimum Redundancy (MRMR) that can be used on multilabel data with missing labels. First, to handle multilabel data with missing labels, a relation coefficient of samples, label complement matrix, and label-specific feature matrix are constructed and implemented in a linear regression model to recover missing labels. Second, the margin-based fuzzy neighborhood radius, fuzzy neighborhood similarity relationship, and fuzzy neighborhood information granule are developed. The MFNRS model is built based on multilabel neighborhood rough sets combined with fuzzy neighborhood rough sets. Based on algebra and information views, certain fuzzy neighborhood entropy-based uncertainty measures are proposed for MFNRS. The fuzzy neighborhood mutual information-based MRMR model with label correlation is improved to evaluate the performance of candidate features. Finally, a feature selection algorithm is designed to improve the performance for multilabel data with missing labels. Experiments on twenty datasets verify that our method is effective not only for recovering missing labels but also for selecting significant features with better classification performance.
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multilabel feature selection using relief and Minimum Redundancy maximum relevance based on neighborhood rough sets
IEEE Access, 2020Co-Authors: Miaomiao Huang, Lin Sun, Shiguang ZhangAbstract:Recently, multilabel classification is of increasing interest in machine learning and artificial intelligence. However, the distances of samples in most Relief methods easily result in heterogeneous or similar samples abnormal when the distances are very large. Besides, the classification margin as a neighborhood radius for some reduction algorithms may be meaningless when the margin is too large. To overcome these drawbacks, this paper presents a multilabel feature selection method using the improved Relief and Minimum Redundancy maximum relevance (MRMR) based on neighborhood rough sets. First, the number of heterogeneous and similar samples is introduced to improve the label weighting method which can eliminate the influence of the large distances of samples. By combining with the new label weighting, the distances between the sample and its nearest-neighbor heterogeneous sample and between the sample and its nearest-neighbor similar sample are presented to develop a new feature weighting method. Second, the number of heterogeneous and similar samples continues to be used to improve the classification margin, thereby constraining the neighborhood radius, based on which the neighborhood approximation accuracy is constructed to effectively measure the uncertainty of samples in the boundary region and the completeness of knowledge. Third, by integrating with the new neighborhood approximation accuracy, two types of mutual information between features and labels and among features are proposed, and then the mutual information-based MRMR model is investigated to evaluate the significance of features. Finally, a multilabel feature selection algorithm is designed for improving the classification performance of multilabel data. Experimental results on thirteen public datasets illustrate the effectiveness of our developed algorithm that can select the significant features and achieve great performance for multilabel datasets.