A variety of multidimensional visualization methods are applied for the qualitative analysis of multidimensional data. One of the multidimensional data visualization methods is a method using autoassociative neural networks. In order to perform visualizations of n-dimensional data, such a network has n inputs, n outputs and one of the interlayers consisting of two outputs whose values represent coordinates of the analyzed sample’s image on the screen. Such a criterion for the network’s learning consists in that the same value as the one at the ith input appears at each ith output. If the network is trained in this way, the whole information from n inputs was compressed to two outputs of the interlayer and then decompressed to n network outputs. The paper shows the application of different learning criteria can be more beneficial from the point of view of the results’ readability. Overall analysis was conducted on seven-dimensional real data representing three coal classes, five-dimensional data representing printed characters, 216-dimensional data representing hand-written digits and, additionally, in order to illustrate additional explanations using artificially generated seven-dimensional data. Readability of results of the qualitative analysis of these data was compared using the multidimensional visualization utilizing neural networks for different learning criteria. Also, the obtained results of applying all analyzed criteria on 20 randomly selected sets of multidimensional data obtained from one of the publicly available repositories are presented.

中文翻译：

---

检验神经网络学习准则对多维数据定性分析有效性的影响

多种多维可视化方法可用于多维数据的定性分析。多维数据可视化方法之一是使用自缔合神经网络的方法。为了执行n维数据的可视化，这样的网络具有n个输入，n个输出以及由两个输出组成的中间层之一，其值表示屏幕上分析的样本图像的坐标。这种用于网络学习的标准在于，与第i个输入处的值相同的值出现在每个第i个输出处。如果以这种方式训练网络，则来自n的全部信息输入被压缩为中间层的两个输出，然后解压缩为n网络输出。本文显示，从结果的可读性角度来看，应用不同的学习标准可能会更加有益。对代表三个煤种的七维真实数据，代表印刷字符的五维数据，代表手写数字的216维数据进行了全面分析，此外，为了说明使用人工生成的七维数据的其他解释。使用针对不同学习标准的神经网络多维可视化，比较了对这些数据进行定性分析的结果的可读性。此外，还提供了将所有分析的标准应用于从一个公共可用存储库之一获得的20个随机选择的多维数据集所获得的结果。