U矩阵和自组织图 [英] U-matrix and self organizing maps

问题描述

我正在尝试了解SOM.我很困惑人们何时张贴代表 数据图像是我使用SOM将数据映射到地图空间的.据说使用了U矩阵.但是我们有一个有限的神经元网格，那么如何获得连续"图像呢? 例如，从40x40网格开始，有1600个神经元.现在计算U矩阵，但是现在如何绘制这些数字以获得可视化呢? 链接:

I am trying to understand SOMs. I am confused about when people post images representing the image of data gotten my using SOM to map data to the map space. It is said that the U-matrix is used. But we have a finite grid of neurons so how do you get a "continous" image ? For example starting with a 40x40 grid there are 1600 neurons. Now compute U-matrix but how do you plot these numbers now to get visualization ? Links:

具有可视化功能的SOM教程

来自维基百科的SOM

推荐答案

U矩阵代表统一距离，并且在每个单元格中包含相邻单元格之间(输入空间中)的欧氏距离.此矩阵中的较小值表示SOM节点在输入空间中靠近在一起，而较大值表示SOM节点相距较远，即使它们在输出空间中靠近也是如此.这样，U矩阵可以看作是二维空间中输入矩阵的概率密度函数的摘要.通常，这些距离值会根据强度进行离散化，颜色编码，并显示为热量图 .

The U-matrix stands for unified distance and contains in each cell the euclidean distance (in the input space) between neighboring cells. Small values in this matrix mean that SOM nodes are close together in the input space, whereas larger values mean that SOM nodes are far apart, even if they are close in the output space. As such, the U-matrix can be seen as summary of the probability density function of the input matrix in a 2D space. Usually, those distance values are discretized, color-coded based on intensity and displayed as a kind of heatmap.

引用Matlab SOM工具箱，

Quoting the Matlab SOM toolbox,

 Compute and return the unified distance matrix of a SOM. 
 For example a case of 5x1 -sized map:
            m(1) m(2) m(3) m(4) m(5)
 where m(i) denotes one map unit. The u-matrix is a 9x1 vector:
    u(1) u(1,2) u(2) u(2,3) u(3) u(3,4) u(4) u(4,5) u(5) 
 where u(i,j) is the distance between map units m(i) and m(j)
 and u(k) is the mean (or minimum, maximum or median) of the 
 surrounding values, e.g. u(3) = (u(2,3) + u(3,4))/2. 

除了SOM工具箱之外，您还可以查看 kohonen R程序包(请参见help(plot.kohonen)并使用type="dist.neighbours").

Apart from the SOM toolbox, you may have a look at the kohonen R package (see help(plot.kohonen) and use type="dist.neighbours").

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