An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We exten...An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.展开更多
In the extension matrix approach of inductive learning, the minimum formula (MFL) ofa positive example (e^+) against a set of negative examples (NE) and tbe optimal covering(MCV) of a set of positive examples (PE) aga...In the extension matrix approach of inductive learning, the minimum formula (MFL) ofa positive example (e^+) against a set of negative examples (NE) and tbe optimal covering(MCV) of a set of positive examples (PE) against NE are two striking optimization prob-lems. They have been proved to be NP-hard in Ref. [1]. This paper presents four algorithms,named MFL, HFL, MCV and HCV respectively. Algorithms MFL and MCV are complete forsolving the problems MFL and MCV but they opelate in exponential time on the number ofattributes in an example space and polynomial time on the number of examples. AlgorithmsHFL and HCV are two heuristic algorithms homologous to Algorithms MFL and MCV buttheir time complexities are polynomial.展开更多
A two-dimensional direction-of-arrival(DOA) estimation method for non-uniform two-L-shaped array is presented in which the element spacing is larger than half-wavelength. To extract automatically paired low-variance c...A two-dimensional direction-of-arrival(DOA) estimation method for non-uniform two-L-shaped array is presented in which the element spacing is larger than half-wavelength. To extract automatically paired low-variance cyclically ambiguous direction cosines and high-variance unambiguous direction cosines from the sub-blocks, the proposed method constructs and partitions the cross-correlation matrices. Then, the low-variance unambiguous direction cosines are obtained using the ambiguity resolved technique. Simulation results demonstrate that the proposed method has lower computation complexity and higher resolution than the existing methods especially when the elevation angles are between 70 and 90 degrees.展开更多
This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.
The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the co...The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.展开更多
Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedur...Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh poly- nomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11（6） （2013）, 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.展开更多
In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight fra...In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.展开更多
Extension matrix（EM）and ID3 are two main algorithms with wide applicationin the field of machine learning,but analysis shows EM may Cause false diagnosis and ID3may cause fail diagnosis.This paper presents a new com...Extension matrix（EM）and ID3 are two main algorithms with wide applicationin the field of machine learning,but analysis shows EM may Cause false diagnosis and ID3may cause fail diagnosis.This paper presents a new combination of these two methods toachieve a new method called entropy extension matrix（EEM）and a new concept ofgeneralization association ability（GAA）.Results show that this algorithm has propertiesbetter than those of EM and ID3.展开更多
基金Acknowledgements The authors express their gratitude to the anonymous referees for their kind suggestions and useful comments on the original manuscript, which resulted in this final version. This work was supported by the National Natural Science Foundation of China （No. 61071189）, the Natural Science Foundation for the Education Department of Henan Province of China （No. 13A110072）, and the Natural Science Foundation of Henan University （No. 2011YBZR001）.
文摘An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.
基金Project supported by the National Natural Science Foundation of China.
文摘In the extension matrix approach of inductive learning, the minimum formula (MFL) ofa positive example (e^+) against a set of negative examples (NE) and tbe optimal covering(MCV) of a set of positive examples (PE) against NE are two striking optimization prob-lems. They have been proved to be NP-hard in Ref. [1]. This paper presents four algorithms,named MFL, HFL, MCV and HCV respectively. Algorithms MFL and MCV are complete forsolving the problems MFL and MCV but they opelate in exponential time on the number ofattributes in an example space and polynomial time on the number of examples. AlgorithmsHFL and HCV are two heuristic algorithms homologous to Algorithms MFL and MCV buttheir time complexities are polynomial.
基金supported by the Joint Laboratory for Ocean Observation and Detectionthe National Laboratory for Marine Science and Technology
文摘A two-dimensional direction-of-arrival(DOA) estimation method for non-uniform two-L-shaped array is presented in which the element spacing is larger than half-wavelength. To extract automatically paired low-variance cyclically ambiguous direction cosines and high-variance unambiguous direction cosines from the sub-blocks, the proposed method constructs and partitions the cross-correlation matrices. Then, the low-variance unambiguous direction cosines are obtained using the ambiguity resolved technique. Simulation results demonstrate that the proposed method has lower computation complexity and higher resolution than the existing methods especially when the elevation angles are between 70 and 90 degrees.
基金supported in part Professor Yuesheng Xu under the program of"One Hundred Outstanding Young Chinese Scientists" of the Chinese Academy of Sciencesthe Graduate Innovation Foundation of the Chinese Academy of Sciences
文摘This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.
基金The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P.1/85/42.
文摘The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.
文摘Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh poly- nomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11（6） （2013）, 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.
文摘In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.
文摘Extension matrix（EM）and ID3 are two main algorithms with wide applicationin the field of machine learning,but analysis shows EM may Cause false diagnosis and ID3may cause fail diagnosis.This paper presents a new combination of these two methods toachieve a new method called entropy extension matrix（EEM）and a new concept ofgeneralization association ability（GAA）.Results show that this algorithm has propertiesbetter than those of EM and ID3.
