Uncertainty-Aware Multidimensional Scaling

We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty. With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.