We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.

翻译：我们提出角度均匀平行坐标，这是一种数据无关的平行坐标图像平面变形技术，使得两个变量之间线性关系的角度能够沿平行坐标图的水平轴线性映射。尽管平行坐标是可视化多维数据的常用方法，但由于正相关结构对应的平行坐标点可能位于图像平面无穷远处，且负相关与正相关的不对称编码会导致不可靠的估计，该方法在揭示正相关关系方面效果不佳。为解决这一问题，我们引入一种变换：通过角度均匀映射将所有点水平约束在有限范围内，并以保持结构的方式垂直压缩；折线变为平滑曲线，从而实现数据相关性的对称表示。我们进一步提出结合子采样与密度可视化的方法，以缓解过度绘制造成的视觉杂乱。本方法能够准确解读数据相关性的视觉模式，其数据无关特性使其适用于所有多维数据集。通过合成数据集与真实数据集的实例验证了本方法的实用性。