Limited Rank Matrix Learning, discriminative dimension reduction and visualization
Limited Rank Matrix Learning, discriminative dimension reduction and visualization
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DOI：
10.1016/j.neunet.2011.10.001
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发表时间：
2012-02-01
期刊：
影响因子：
7.8
通讯作者：
Biehl, Michael
中科院分区：
文献类型：
--
作者：
Bunte, Kerstin;Schneider, Petra;Biehl, Michael
我们提出了一个扩展最近推出的广义矩阵学习矢量量化算法。在原始方案中，相关因子的自适应方阵参数化了区分距离度量。我们将该计划扩展到对应于数据的低维表示的有限秩矩阵。这允许将先验知识的内在维，并有效地减少自适应参数的数量。特别是，对于非常大的维度的数据，秩的限制可以减少计算时间和内存需求显着。此外，二维或三维表示构成了标记数据集的有效可视化方法。合适的投影的识别不被视为预处理步骤，而是作为监督训练的组成部分。几个真实的世界的数据集作为一个例子，并证明所提出的方法的实用性。(c)2011爱思唯尔有限公司保留所有权利。
We present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices of relevance factors parameterize a discriminative distance measure. We extend the scheme to matrices of limited rank corresponding to low-dimensional representations of the data. This allows to incorporate prior knowledge of the intrinsic dimension and to reduce the number of adaptive parameters efficiently.In particular, for very large dimensional data, the limitation of the rank can reduce computation time and memory requirements significantly. Furthermore, two- or three-dimensional representations constitute an efficient visualization method for labeled data sets. The identification of a suitable projection is not treated as a pre-processing step but as an integral part of the supervised training. Several real world data sets serve as an illustration and demonstrate the usefulness of the suggested method. (c) 2011 Elsevier Ltd. All rights reserved.