Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.     

一种欠定盲源分离中混合矩阵的估计方法

欠定盲源分离问题中基于源信号稀疏性的两阶段法中,混合矩阵估计的准确与否,直接影响源信号的恢复效果。文中提出了一种在稀疏域估计混合矩阵的新方法。该方法通过搜索稀疏域中同一直线附近的点,利用这些点重构出混合矩阵,避免了远离直线周边的点对估计混合矩阵的干扰,从而大大降低了计算量。仿真表明该算法性能良好。     

MATLAB在通信系统仿真中的若干应用

在通信系统的设计与仿真中经常会碰到一些相似的基本问题，它们都可以建立相似的数学模型，并且用数学工具或仿真工具加以解决。文中以实际项目中3个不同的通信系统模型为例，说明了建立数学模型的过程并具体阐述了如何利用MATLAB设计语言所提供的各种函数加以实现。     

改进仿射投影算法及其在电子回声消除中的应用

在电子回声消除应用中,为提高自适应算法的收敛速度,提出一种改进的仿射投影算法及其快速实现形式.新算法利用回声路径的稀疏结构特征,通过收敛步长控制矩阵,按滤波器各系数幅值大小,等比例地为其指定相应收敛步长,以加快大系数收敛,最终达到加快滤波器整体收敛速度的目的.对新算法进行的统计学分析,为其快速收敛于目标系统的算法特性提供了理论依据.仿真实验表明与传统自适应算法相比,新算法能减小稳态失调并大幅提高收敛速度,其低计算复杂度亦保证了系统的实时性.     

基于欠定盲分离的多目标微多普勒特征提取

连续波雷达多目标回波中多种微多普勒特征分离问题采用独立成分分析方法实现,该方法在使用中存在较大局限性,要求待分离的微多普勒特征之间必须是统计独立的,且仅局限于恰定和超定的方程组求解问题。然而,在多目标雷达观测场景下,雷达接收的混叠回波的个数通常少于目标的个数,各目标的微多普勒特征可能存在相关性。为此,提出了一种基于欠定盲分离的多目标回波微多普勒特征分离方法。该方法可以从少数原始混叠回波中分离出多个目标的微多普勒特征,对待分离的微多普勒特征限制性弱。通过数值仿真,证实了该方法的可行性。     

基于时间序列分析的动态分布平滑方法

 统计语言模型在实际应用中显示出了不俗的效果,但由于语言的灵活性,模型的数据稀疏问题始终不能避免,现有的平滑方法只考虑了模型中元素出现的频数,没有考虑到语言的使用是随着时间变化的.本文分析了模型中词语随着时间的变化而出现的频数变化情况,利用时间序列模型分析中的预测方法获得下一个阶段的数据来估计模型的参数,提出了一种对在时间线上频数增加的词语增加概率值,对频数减少的则降低概率值的动态分布平滑方法.实验数据显示,本平滑方法具有一定的优越性.     

Dictionary-based histogram packing technique for lossless image compression

This paper proposes a dictionary-based histogram packing technique for lossless image compression. It is used to improve the performance of the state-of-the-art lossless image compression standards and methods when compressing sparse and locally sparse histogram images. The proposed method leverages inter-block correlations and similarities not only within the neighborhood but also across the entire image, thereby effectively reducing the block boundary artifacts commonly observed in block-based histogram packing techniques. To achieve this, a dictionary is employed to represent highly correlated blocks using a key that captures the union of their active symbol sets. Experimental results have demonstrated that the proposed method, when applied to sparse and locally sparse histogram images, enhances the performance of various state-of-the-art lossless image compression techniques. Notably, improvements were observed in standards and methods such as JPEG-2000, JPEG-LS, JPEG-XL, PNG, and CALIC.     

Poisson limits for a hard-core clustering model

Let X_1n,…,X_>nn denote the locations of n points in a bounded, γ-dimensional, Euclidean region D_n which has positive γ-dimensional Lebesgue measure μ(D_n). Let {Y_n(r): r > 0} be the interpoint distance process for these points where Y_n(r) is the number of pairs of points(X_in, X_in) which with i < j have Euclidean distance 6X_in ? X_>in6 < r. In this article we study the limiting distribution of Y_n(r) when n → ∞ and μ(D_n) → ∞, and the joint density of X_1n,…,X_nnis of the form

where r₀ is a positive constant and C_n is a normalizing constant. These joint densities modify the Strauss [11] clustering model densities by introducing a hard-core component (no two points can have 6X_in ? X_in6 < r₀) found in the Matérn [4] models. In our main result we show that the interpoint distance process converges to a non-homogeneous Poisson process for r values in a bounded interval 0 < r₀ < r < r₀₀ provided sparseness conditions discussed by Saunders and Funk [9] hold. The sparseness conditions which require $\text{μ(D}{}_{\mathrm{n}}\text{)}\text{n}{}^2$ converges to a positive constant and the boundary of D_n is negligible are essentially equivalent to requiring that although the number of points n is large the region is large enough so that the points are sparse in this region. That is, it is rare for a point to have another point close to it. These results extend results for v ? 0 given by Saunders and Funk [9] where it is shown that without the hard core component such results do not hold for v > 0. Statistical applications are discussed.     

基于独立分量分析的图像边缘特征提取

本文探讨了一种新的多元统计分析方法——独立分量分析在图像边缘特征提取方面的应用．采用基于信息最大算法的无监督神经网络对自然图像进行迭代学习, 获得ICA所需的基函数。提取的基函数在空间频率上具有方向性和局部性,很好地描述了输入自然景物图像的边缘特征。实验结果表明,即使在有噪声的条件下,ICA也可以较好地获得图像的边缘特征信息。     

基于子主题选择与三级分层结构的Web文本挖掘方法

针对用户和查询之间的意图差距导致的查询模糊宽泛和数据稀疏问题,根据流行性和多样性返回可能子主题的排名列表,利用子主题选择与排序的分层结构进行Web 文本挖掘。首先,在名词性短语和可替代部分查询的基础上,使用简单模式提取各种相关的短语作为候选子主题;然后,使用网页文档集合中的相关文档构建候选子主题的三级层次结构;最后,综合考虑流行性和多样性,利用该结构和估计的流行度进行排序。实验使用了NTCIR-9库的100个日文查询和来自TREC 2009库的100个英文查询以及网络跟踪多样性任务,实验结果验证了本文方法可有效应用于各种搜索,对于高排名的子主题挖掘优于外部资源。