Classification and data acquisition with incomplete data
Authors: Lawrence Carin
Venue:  (2006)

In remote-sensing applications, incomplete data can result when only a subset of sensors (e.g., radar, infrared, acoustic) are deployed at certain regions. The limitations of single sensor systems have spurred interest in employing multiple sensor modalities simultaneously. For example, in land mine detection tasks, different sensor modalities are better-suited to capture different aspects of the underlying physics of the mines. Synthetic aperture radar sensors may be better at detecting surface mines, while infrared sensors may be better at detecting buried mines. By employing multiple sensor modalities to address the detection task, the strengths of the disparate sensors can be exploited in a synergistic manner to improve performance beyond that which would be achievable with either single sensor alone. When multi-sensor approaches are employed, however, incomplete data can be manifested. If each sensor is located on a separate platform ( e.g., aircraft), each sensor may interrogate---and hence collect data over---only partially overlapping areas of land. As a result, some data points may be characterized by data (i.e., features) from only a subset of the possible sensors employed in the task. Equivalently, this scenario implies that some data points will be missing features. Increasing focus in the future on using---and fusing data from---multiple sensors will make such incomplete-data problems commonplace. In many applications involving incomplete data, it is possible to acquire the missing data at a cost. In multi-sensor remote-sensing applications, data is acquired by deploying sensors to data points. Acquiring data is usually an expensive, time-consuming task, a fact that necessitates an intelligent data acquisition process. Incomplete data is not limited to remote-sensing applications, but rather, can arise in virtually any data set. In this dissertation, we address the general problem of classification when faced with incomplete data. We also address the closely related problem of active data acquisition, which develops a strategy to acquire missing features and labels that will most benefit the classification task. We first address the general problem of classification with incomplete data, maintaining the view that all data (i.e., information) is valuable. We employ a logistic regression framework within which we formulate a supervised classification algorithm for incomplete data. This principled, yet flexible, framework permits several interesting extensions that allow all available data to be utilized. One extension incorporates labeling error, which permits the usage of potentially imperfectly labeled data in learning a classifier. A second major extension converts the proposed algorithm to a semi-supervised approach by utilizing unlabeled data via graph-based regularization. Finally, the classification algorithm is extended to the case in which (image) data---from which features are extracted---are available from multiple resolutions. Taken together, this family of incomplete-data classification algorithms exploits all available data in a principled manner by avoiding explicit imputation. Instead, missing data is integrated out analytically with the aid of an estimated conditional density function (conditioned on the observed features). This feat is accomplished by invoking only mild assumptions. We also address the problem of active data acquisition by determining which missing data should be acquired to most improve performance. Specifically, we examine this data acquisition task when the data to be acquired can be either labels or features. The proposed approach is based on a criterion that accounts for the expected benefit of the acquisition. This approach, which is applicable for any general missing data problem, exploits the incomplete-data classification framework introduced in the first part of this dissertation. This data acquisition approach allows for the acquisition of both labels and features. Moreover, several types of feature acquisition are permitted, including the acquisition of individual or multiple features for individual or multiple data points, which may be either labeled or unlabeled. Furthermore, if different types of data acquisition are feasible for a given application, the algorithm will automatically determine the most beneficial type of data to acquire. Experimental results on both benchmark machine learning data sets and real (i.e., measured) remote-sensing data demonstrate the advantages of the proposed incomplete-data classification and active data acquisition algorithms.