Diversity in training data density and environment locality is intrinsic in the real-world deployment of indoor localization systems and has a major impact on the performance of existing localization approaches. In this paper, through micro-benchmarks, we find that fingerprint-based approaches are preferable in scenarios where a dense database is available; while model-based approaches are the method of choice in the case of sparse data. It should be noted, however, that practical situations are complex. A single deployment often features both sparse and dense sampled areas. Furthermore, the internal layout affects the propagation of radio signals and exhibits environmental impacts. A certain number of measurement samples may be sufficient for one part of the building, but entirely insufficient for another. Thus, finding the right indoor localization algorithm for a given large-scale deployment is challenging, if not impossible; there is no one-size-fits-all indoor localization approach.

A memory-based learning system is an extended memory management system that decomposes the input space either statically or dynamically into subregions for the purpose of storing and retrieving functional information. The main generalization techniques employed by memory-based learning systems are the nearest-neighbor search, space decomposition techniques, and clustering. Research on memory-based learning is still in its early stage. In particular, there are very few rigorous theoretical results regarding memory requirement, sample size, expected performance, and computational complexity. In this paper, we propose a model for memory-based learning and use it to analyze several methods— ε-covering, hashing, clustering, tree-structured clustering, and receptive-fields— for learning smooth functions. The sample size and system complexity are derived for each method. Our model is built upon the generalized PAC learning model of Haussler and is closely related to the method of vector quantization in data compression. Our main result is that we can build memory-based learning systems using new clustering algorithms [LiVb] to PAC-learn in polynomial time using only polynomial storage in typical situations.

The authors present new vector quantization algorithms. The new approach is to formulate a vector quantization problem as a 0-1 integer linear program. They first solve its relaxed linear program by linear programming techniques. Then they transform the linear program solution into a provably good solution for the vector quantization problem. These methods lead to the first known polynomial-time full-search vector quantization codebook design algorithm and tree pruning algorithm with provable worst-case performance guarantees. They also introduce the notion of pseudorandom pruned tree-structured vector quantizers. Initial experimental results on image compression are very encouraging.>

We present efficient new randomized and deterministic methods for transforming optimal solutions for a type of relaxed integer linear program into provably good solutions for the corresponding NP-hard discrete optimization problem. Without any constraint violation, the ε-approximation problem for many problems of this type is itself NP-hard. Our methods provide polynomial-time ε-approximations while attempting to minimize the packing constraint violation.