如何制作U矩阵? [英] How do I make a U-matrix?

问题描述

为了可视化自组织映射?更具体地说，假设我有一个3x3节点的输出网格(已经训练过)，如何从中构造一个U矩阵?您可以例如假设神经元(和输入)的维数为4.

我在网上找到了几种资源，但是它们不清楚或矛盾.例如，原始纸充满了错字.

解决方案

U矩阵是输入数据维度空间中神经元之间距离的直观表示.即，您使用相邻神经元的训练向量来计算它们之间的距离.如果您输入的维数为4，则经过训练的映射中的每个神经元也对应于一个4维向量.假设您有一张3x3的六边形地图.

U矩阵将是一个5x5矩阵，其中像这样的两个神经元之间的每个连接都有内插元素

{x，y}元素是神经元x和y之间的距离，{x}元素中的值是周围值的平均值.例如，{4,5} =距离(4,5)，{4} =平均值({1,4}，{2,4}，{4,5}，{4,7}).为了计算距离，您使用了每个神经元的训练过的4维矢量以及用于训练地图的距离公式(通常是欧几里得距离).因此，U矩阵的值仅是数字(不是向量).然后，您可以将浅灰色分配给这些值中的最大值，将深灰色分配给这些值中的最小值，将其他值分配给相应的灰色阴影.您可以使用这些颜色绘制U矩阵的细胞，并直观地表示神经元之间的距离.

还可以查看此网络文章.

How exactly is an U-matrix constructed in order to visualise a self-organizing-map? More specifically, suppose that I have an output grid of 3x3 nodes (that have already been trained), how do I construct a U-matrix from this? You can e.g. assume that the neurons (and inputs) have dimension 4.

I have found several resources on the web, but they are not clear or they are contradictory. For example, the original paper is full of typos.

解决方案

A U-matrix is a visual representation of the distances between neurons in the input data dimension space. Namely you calculate the distance between adjacent neurons, using their trained vector. If your input dimension was 4, then each neuron in the trained map also corresponds to a 4-dimensional vector. Let's say you have a 3x3 hexagonal map.

The U-matrix will be a 5x5 matrix with interpolated elements for each connection between two neurons like this

The {x,y} elements are the distance between neuron x and y, and the values in {x} elements are the mean of the surrounding values. For example, {4,5} = distance(4,5) and {4} = mean({1,4}, {2,4}, {4,5}, {4,7}). For the calculation of the distance you use the trained 4-dimensional vector of each neuron and the distance formula that you used for the training of the map (usually Euclidian distance). So, the values of the U-matrix are only numbers (not vectors). Then you can assign a light gray colour to the largest of these values and a dark gray to the smallest and the other values to corresponding shades of gray. You can use these colours to paint the cells of the U-matrix and have a visualized representation of the distances between neurons.

Have also a look at this web article.

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