Abstract
Spacecrafts orbiting a selected suite of planets and moons of our solar system are continuously sending long sequences of data back to Earth. The availability of such data provides an opportunity to invoke tools from machine learning and pattern recognition to extract patterns that can help to understand geological processes shaping planetary surfaces. Due to the marked interest of the scientific community on this particular planet, we base our current discussion on Mars, where there are presently three spacecrafts in orbit (e.g., NASA’s Mars Odyssey Orbiter, Mars Reconnaissance Orbiter, ESA’s Mars Express). Despite the abundance of available data describing Martian surface, only a small fraction of the data is being analyzed in detail because current techniques for data analysis of planetary surfaces rely on a simple visual inspection and descriptive characterization of surface landforms (Wilhelms, 1990). The demand for automated analysis of Mars surface has prompted the use of machine learning and pattern recognition tools to generate geomorphic maps, which are thematic maps of landforms (or topographical expressions). Examples of landforms are craters, valley networks, hills, basins, etc. Machine learning can play a vital role in automating the process of geomorphic mapping. A learning system can be employed to either fully automate the process of discovering meaningful landform classes using clustering techniques; or it can be used instead to predict the class of unlabeled landforms (after an expert has manually labeled a representative sample of the landforms) using classification techniques. The impact of these techniques on the analysis of Mars topography can be of immense value due to the sheer size of the Martian surface that remains unmapped. While it is now clear that machine learning can greatly help in automating the detailed analysis of Mars’ surface (Stepinski et al., 2007; Stepinski et al., 2006; Bue and Stepinski, 2006; Stepinski and Vilalta, 2005), an interesting problem, however, arises when an automated data analysis has produced a novel classification of a specific site’s landforms. The problem lies on the interpretation of this new classification as compared to traditionally derived classifications generated through visual inspection by domain experts. Is the new classification novel in all senses? Is the new classification only partially novel, with many landforms matching existing classifications? This article discusses how to assess the value of clusters generated by machine learning tools as applied to the analysis of Mars’ surface.
TopBackground On Cluster Validation
We narrow our discussion to patterns in the form of clusters as produced by a clustering algorithm (a form of unsupervised learning). The goal of a clustering algorithm is to partition the data such that the average distance between objects in the same cluster (i.e., the average intra-distance) is significantly less than the distance between objects in different clusters (i.e., the average inter-distance). The goal is to discover how data objects gather into natural groups (Duda at el., 2001; Bishop, 2006). The application of clustering algorithms can be followed by a post-processing step, also known as cluster validation; this step is commonly employed to assess the quality and meaning of the resulting clusters (Theodoridis and Koutroumbas, 2003).
Cluster validation plays a key role in assessing the value of the output of a clustering algorithm by computing statistics over the clustering structure. Cluster validation is called internal when statistics are devised to capture the quality of the induced clusters using the available data objects only (Krishnapuran et al., 1995; Theodoridis and Koutroumbas, 2003). As an example, one can measure the quality of the resulting clusters by assessing the degree of compactness of the clusters, or the degree of separation between clusters.