Ieee Transactions on Visualization and Computer Graphics Robust Linear Dimensionality Reduction
Ieee Transactions on Visualization and Computer Graphics Robust Linear Dimensionality Reduction
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通讯作者：
Y. Koren;L. Carmel
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作者：
Y. Koren;L. Carmel
- 我们提出了一个新的家庭的数据驱动的线性变换，旨在寻找低维嵌入的多元数据，以最佳的方式保持数据的结构。研究良好的PCA和Fisher的LDA被证明是特殊的成员在这个家庭的变换，我们演示了如何推广这两种方法，如提高其性能。此外，据我们所知，我们的技术是唯一一种在结果嵌入中反映数据坐标和数据元素之间的成对相似性和/或不相似性的技术。更重要的是，当数据的聚类（标记）分解信息已知时，这些信息也可以集成到线性变换中，从而产生清晰显示聚类之间的分离及其内部结构的嵌入。所有这些都使我们的技术非常灵活和强大，并让我们能够科普其他技术无法正确描述的数据。
— We present a novel family of data-driven linear transformations, aimed at finding low dimensional embeddings of multivariate data, in a way that optimally preserves the structure of the data. The well-studied PCA and Fisher's LDA are shown to be special members in this family of transformations, and we demonstrate how to generalize these two methods such as to enhance their performance. Furthermore, our technique is the only one, to the best of our knowledge, that reflects in the resulting embedding both the data coordinates and pairwise similarities and/or dissimilarities between the data elements. Even more so, when information on the clustering (labeling) decomposition of the data is known, this information can also be integrated in the linear transformation, resulting in embeddings that clearly show the separation between the clusters, as well as their internal structure. All this makes our technique very flexible and powerful, and lets us cope with kinds of data that other techniques fail to describe properly.