Performance Analysis of l_0 Norm Constraint Least Mean Square Algorithm

As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The performance of $l_0$-LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents all-around and throughout theoretical performance analysis of $l_0$-LMS for white Gaussian input data based on some reasonable assumptions. Expressions for steady-state mean square deviation (MSD) are derived and discussed with respect to algorithm parameters and system sparsity. The parameter selection rule is established for achieving the best performance. Approximated with Taylor series, the instantaneous behavior is also derived. In addition, the relationship between $l_0$-LMS and some previous arts and the sufficient conditions for $l_0$-LMS to accelerate convergence are set up. Finally, all of the theoretical results are compared with simulations and are shown to agree well in a large range of parameter setting.Comment: 31 pages, 8 figure

部分范数约束的稀疏恢复算法及其在单载波水声数据遥测中的应用

对于单载波水声数据压缩与恢复问题,压缩感知能以较低能耗获得信号压缩与恢复效果。但压缩感知核心目标是直接求最小l0范数,该问题表现为NP难问题,因此,常将其转化为求l1范数约束最小化问题,而求l1范数约束最小化的稀疏解精度有限。基于此,推导出基于部分范数约束的稀疏信号恢复算法,该算法通过部分范数约束在拉格朗日求解中增加一个零吸引项,从而动态分配稀疏抽头的软阈值。同时,该算法用于实际海上数据的遥测,结合离散余弦变换（DCT）,可将单载波水声数据恢复精度提高。国家自然科学基金资助项目(No.61701405);;中央高校基本科研业务费专项资金资助项目(No.3102017OQD007);;中国博士后科学基金资助项目(No.2017M613208)~

Change of support problemへの新たな空間統計モデルの開発

筑波大学 (University of Tsukuba)201

Tune your brown clustering, please

Brown clustering, an unsupervised hierarchical clustering technique based on ngram mutual information, has proven useful in many NLP applications. However, most uses of Brown clustering employ the same default configuration; the appropriateness of this configuration has gone predominantly unexplored. Accordingly, we present information for practitioners on the behaviour of Brown clustering in order to assist hyper-parametre tuning, in the form of a theoretical model of Brown clustering utility. This model is then evaluated empirically in two sequence labelling tasks over two text types. We explore the dynamic between the input corpus size, chosen number of classes, and quality of the resulting clusters, which has an impact for any approach using Brown clustering. In every scenario that we examine, our results reveal that the values most commonly used for the clustering are sub-optimal