Dimensionality reduction by self organizing maps that preserve distances in output space
Dimensionality reduction by self organizing maps that preserve distances in output space
复制标题
通过自组织映射来降维，保留输出空间中的距离
DOI：
10.1109/ijcnn.2009.5179009
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
P. Campoy
中科院分区：
文献类型：
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作者：
P. Campoy
在许多科学问题中，高维向量是一个非常重要的问题，而这些高维向量又都位于一个更少维的流形上。因此，它们可以由减少数量的值表示，这些值参数化它们在所提到的非线性流形上的位置。这种降维不仅对于表示和管理数据至关重要，而且对于在高解释水平上理解数据也至关重要，类似于哺乳动物皮层执行的方式。本文提出了一种算法，用于表示的数据，躺在非线性流形上的减少数量的坐标沿着网格或地图的神经元扩展到这个流形上。该映射是由自组织学习过程生成的，其关键特征是选择获胜的神经元，以便在输出映射中用其坐标表示输入数据时保留输入数据的距离。与其他方法不同的是，该算法具有重要的特点，即在学习过程本身中同时获得内在维度，它不需要长时间的课程定位阶段，并且它试图从一开始就保持数据结构，而不是将其作为一个不可告人的事实来证明。该算法已被证明可以有效地解决经典的降维问题，也表明它可以用于现实问题，如人脸图像分类或文档索引。
Dimensionality Reduction is a key issue in many scientific problems, in which data is originally given by high dimensional vectors, all of which lie however over a fewer dimensional manifold. Therefore, they can be represented by a reduced number of values that parametrize their position over the mentioned non-linear manifold. This dimensionality reduction is essential not only for representing and managing data, but also for its understanding at a high interpretation level, similar to the way it is performed by the mammal cortex. This paper presents an algorithm for representing the data that lie on a non-linear manifold by the reduced number of their coordinates along a grid or map of neurons extended over this manifold. This map is generated by a Self-organization learning process whose key feature is the fact that the winning neuron is selected in order to preserve distances of input data when they are represented by their coordinates in the output map. Unlike other methods, the proposed algorithm has important features, that namely the intrinsic dimensionality is obtained simultaneously in the learning process itself, it doesn't require a long course positioning phase, and it seeks to maintain the data structure from the beginning, not leaving it as an ulterior fact to be proven. The algorithm has proven to efficiently solve classical dimensionality reduction problems, and has also showed that it can be useful for realistic problems, such as face images classification or document indexing.