A generalized (k, m)-segment mean algorithm for long term modeling of traversable environments

Abstract

We present an ecient algorithm for computing semantic environment models and activity patterns in terms of those models from long-term value trajectories defined as sensor data streams. We use an expectation-maximization approach to calculate a locally optimal set of path segments with minimal total error from the given data signal. This process reduces the raw data stream to an approximate semantic representation. The algorithm's speed is greatly improved by the use of lossless coresets during the iterative update step, as they can be calculated in constant amortized time to perform operations with otherwise linear runtimes. We evaluate the algorithm for two types of data, GPS points and video feature vectors, on several data sets collected from robots and human-directed agents. These experiments demonstrate the algorithm's ability to reliably and quickly produce a model which closely ts its input data, at a speed which is empirically no more than linear relative to the size of that data set. We analyze several topological maps and representative feature sets produced from these data sets.