摘要
V-系统是一类由分片多项式构成的L2[0,1]空间上的正交完备函数系,函数系中既有连续函数又有间断函数。0次V系统恰是Haar小波。对复杂的几何造型,可以用V级数的有限项精确表示。V系统还具有多分辨特性和局部性,这些性质在计算机图形学、计算机视觉、CAD/CAM、医学图像、科学计算等领域发挥重要的作用。本文利用V系统的特性,将其应用于Chernoff脸谱聚类问题。
Chernoff脸谱图是多元统计学中关于多变量图示的一种经典表示方法,也是一种有效的数据可视化技术。1973年,美国的统计学家Chernoff首先把脸谱用于聚类分析中,Chernoff脸谱能在平面上直观、形象地反映出多变量数据之间的信息特征,是平面上表示高维图的一种重要手段。多变量图示法也日益受到人们的关注,并且应用于多元分析的各种应用之中。Chemoff脸谱图的提出使多元统计分析图形化有了进一步的发展。
本文的主要工作如下：
(1)利用V系统的特性,对含有间断信息的chernoff脸谱精确重构。并与经典的Fourier函数系,连续小波等作了重构比较,当Fourier函数系,连续小波被用于重构带有间断的几何模型时,都不可避免地要引起Gibbs现象,而V系统只需要有限个函数就可以精确重构它们,消除Gibbs现象。
(2)利用V描述子对Chernoff脸谱进行特征量化,实现了Chernoff脸谱的计算机自适应聚类,避免了以往Chernoff脸谱聚类中人眼主观判断带来的误判,尤其当要处理的数据组较多时,这个方法更显优势。通过具体实例的检验,表明了该算法在Chernoff脸谱的聚类中简单、快捷、有效,聚类结果与统计学中的SAS软件聚类结果完全一致。
V-system is an orthogonal complete function on L_2[0,1], composed of piecewise polynomial, which includes not only continue functions, but also discontinue functions. The zero order V-system is just Haar wavelet. A complex geometric model can be expressed with finite terms of the V-series accurately. V-system has properties of multi-resolution and local support, which play an important role in computer graphics, computer vision, CAD/CAM, medical imaging, scientific calculation and so on. In this paper, the characteristic of V-system will be applied to cluster the Chernoff faces.
The Chernoff face is a classical method to display multidimensional data graphically in multivariate statistics and an effective data visualization technology. The Chernoff face reflects the information features of multi-variable data, and be used as an important tool representing high-dimensional data. In 1973, Chernoff, an American statistician, proposed Chernoff faces for clustering analysis firstly, and multi-variable expression in the plane is increasingly concerned from then on. The presentation of Chernoff faces has developed the graphical multivriate statistical Analysis. And it is an important mean for people to understand the multi-dimensional space visualizing
The central work of this paper is as follows:
(1)The Chernoff faces are reconstructed accurately via finite terms of the V-series. However, Fourier function systems, continuous wavelet and almost all well-known classical orthogonal continuous systems have inevitably caused Gibbs phenomenon when they are used to reconstruct the geometric model with discontinuous information.
(2)The V-descriptor is used to cluster analysis of the Cheronff faces. By quantifying the overall features of the Chernoff faces, we offer a new programmed clustering method for Chernoff faces. It can avoid misjudgment caused by human eyes. Especially when the number of data sets processing is very large, this approach is even more advantages. The concrete examples show that the clustering algorithm is a simple, fast, effective, and the clustering results are in line with the clustering results of the SAS statistical software.
引文
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