Axis Calibration for Improving Data Attribute Estimation in Star Coordinates Plots

Abstract

Star coordinates is a well-known multivariate visualization method that produces linear dimensionality reduction mappings through a set of radial axes defined by vectors in an observable space. One of its main drawbacks concerns the difficulty to recover attributes of data samples accurately, which typically lie in the [0], [1] interval, given the locations of the low-dimensional embeddings and the vectors. In this paper we show that centering the data can considerably increase attribute estimation accuracy, where data values can be read off approximately by projecting embedded points onto calibrated (i.e., labeled) axes, similarly to classical statistical biplots. In addition, this idea can be coupled with a recently developed orthonormalization process on the axis vectors that prevents unnecessary distortions. We demonstrate that the combination of both approaches not only enhances the estimates, but also provides more faithful representations of the data.

Linear Discriminative Star Coordinates for Exploring Class and Cluster Separation of High Dimensional Data

“…Recently, Lehmann and Theisel [LT13] extend these approaches to an orthography‐preserving star coordinates, they provide optimal and short data tours with them [LT15], and they generalize them in a concept of general projective maps [LT16]. To increase estimation accuracy, Sanchez and Sanchez [RSS14] suggest to combine data centering with the orthography‐preserving star coordinates [LT13].…”

Adaptable Radial Axes Plots for Improved Multivariate Data Visualization

“…The ℓ 1 norm is able to achieve accurate estimates on the variables, but at the expense of an even larger estimation error on Acceleration. Finally, note that these estimation errors could be visualized (e.g., through the size of the plotted points) in order to indicate which samples are represented well according to a particular layout of axis vectors (see [RSS14]).…”

“…Traditionally, the data has been often normalized so that its range becomes [0, 1] for every variable. However, centering the data allows to estimate original data values more accurately [RSS14].…”

“…This provides more faithful representations of the data since it avoids introducing distortions, and enhances preserving relative distances between samples. In addition, it helps reducing attribute estimation errors when approximating values through projections onto calibrated axes [RSS14]. A drawback of this approach concerns the possibility of choosing specific layouts for the axes.…”

“…Lastly, we have colored the points according to the values of MPG in order to show that the method indeed orders the data correctly. However, since the estimates for MPG along its axis are exact, color can be used to encode other information, such as the quality of the estimates (see [RSS14]). Thus, the approach provides an extra degree of freedom in the visualization that allows to include additional information.…”