A Common-Factor Approach for Multivariate Data Cleaning with an Application to Mars Phoenix Mission Data

Data quality is fundamentally important to ensure the reliability of data for stakeholders to make decisions. In real world applications, such as scientific exploration of extreme environments, it is unrealistic to require raw data collected to be perfect. As data miners, when it is infeasible to physically know the why and the how in order to clean up the data, we propose to seek the intrinsic structure of the signal to identify the common factors of multivariate data. Using our new data driven learning method, the common-factor data cleaning approach, we address an interdisciplinary challenge on multivariate data cleaning when complex external impacts appear to interfere with multiple data measurements. Existing data analyses typically process one signal measurement at a time without considering the associations among all signals. We analyze all signal measurements simultaneously to find the hidden common factors that drive all measurements to vary together, but not as a result of the true data measurements. We use common factors to reduce the variations in the data without changing the base mean level of the data to avoid altering the physical meaning.Comment: 12 pages, 10 figures, 1 tabl

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work