Proportionality on Spatial Data with Context

More often than not, spatial objects are associated with some context, in the form of text, descriptive tags (e.g., points of interest, flickr photos), or linked entities in semantic graphs (e.g., Yago2, DBpedia). Hence, location-based retrieval should be extended to consider not only the locations but also the context of the objects, especially when the retrieved objects are too many and the query result is overwhelming. In this article, we study the problem of selecting a subset of the query result, which is the most representative. We argue that objects with similar context and nearby locations should proportionally be represented in the selection. Proportionality dictates the pairwise comparison of all retrieved objects and hence bears a high cost. We propose novel algorithms which greatly reduce the cost of proportional object selection in practice. In addition, we propose pre-processing, pruning, and approximate computation techniques that their combination reduces the computational cost of the algorithms even further. We theoretically analyze the approximation quality of our approaches. Extensive empirical studies on real datasets show that our algorithms are effective and efficient. A user evaluation verifies that proportional selection is more preferable than random selection and selection based on object diversification.