Data visualization with multidimensional scaling
Data visualization with multidimensional scaling
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DOI：
10.1198/106186008x318440
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发表时间：
2008-06-01
影响因子：
2.4
通讯作者：
Chen, Lisha
中科院分区：
文献类型：
--
作者：
Buja, Andreas;Swayne, Deborah F.;Chen, Lisha
我们讨论的方法，多维缩放（MDS）和它的实现在两个软件系统，GGvis和XGvis。MDS是一种用于邻近数据的可视化技术，邻近数据即呈N × N相异性矩阵形式的数据。MDS通过将相异解释为距离来构建Rk中的映射（“配置”、“嵌入”）。两个常见的差异来源是高维数据和图形。当不同点是高维对象之间的距离时，MDS充当（通常是非线性的）降维技术。当相异点是图中的最短路径距离时，MDS充当图布局技术。MDS最近在由图像数据库（“Isomap”）激发的机器学习中受到关注。由于受支持向量机启发的“核化”方法的流行，MDS也很有意义本文讨论了以下几个一般问题：（1）MDS解的稳定性和多重性，（2）在相异矩阵中具有缺失值模式的对象子集内和子集间的结构分析，（3）在非相似矩阵中具有缺失值模式的对象子集内和子集间的结构分析，（4）在非相似矩阵中具有缺失值模式的对象子集内和子集间的结构分析。（3）优化一般MDS损失函数的梯度下降法（“应变”和“应力”）;（4）经典的统一（基于应变）和距离（基于压力的）MDS.具体主题包括：（1）将自动优化与配置点的交互式位移混合以帮助搜索全局最优值;（2）利用交互式刷动形成对象组以在MDS损失函数中创建模式化缺失值;（3）优化MDS损失函数的大量对象相对于一个小的锚点集（“外部展开”）;（4）一个非度量版本的经典MDS。我们展示了应用程序的映射计算机使用数据，市场细分数据的降维，数学图形和社交网络的布局，最后的空间重构分子。
We discuss methodology for multidimensional scaling (MDS) and its implementation in two software systems, GGvis and XGvis. MDS is a visualization technique for proximity data, that is, data in the form of N x N dissimilarity matrices. MDS constructs maps ("configurations," "embeddings") in Rk by interpreting the dissimilarities as distances. Two frequent sources of dissimilarities are high-dimensional data and graphs. When the dissimilarities are distances between high-dimensional objects, MDS acts as a (often nonlinear) dimension-reduction technique. When the dissimilarities are shortest-path distances in a graph, MDS acts as a graph layout technique. MDS has found recent attention in machine learning motivated by image databases ("Isomap"). MDS is also of interest in view of the popularity of "kernelizing" approaches inspired by Support Vector Machines (SVMs; "kernel PCA").This article discusses the following general topics: (1) the stability and multiplicity of MDS solutions; (2) the analysis of structure within and between subsets of objects with missing value schemes in dissimilarity matrices; (3) gradient descent for optimizing general MDS loss functions ("Strain" and "Stress"); (4) a unification of classical (Strain-based) and distance (Stress-based) MDS.Particular topics include the following: (1) blending of automatic optimization with interactive displacement of configuration points to assist in the search for global optima; (2) forming groups of objects with interactive brushing to create patterned missing values in MDS loss functions; (3) optimizing MDS loss functions for large numbers of objects relative to a small set of anchor points ("external unfolding"); and (4) a non-metric version of classical MDS.We show applications to the mapping of computer usage data, to the dimension reduction of marketing segmentation data, to the layout of mathematical graphs and social networks, and finally to the spatial reconstruction of molecules.