Indoor localization via ℓ1-graph regularized semi-supervised manifold learning

In this paper, a new ℓ1-graph regularized semi-supervised manifold learning (LRSML) method is proposed for indoor localization. Due to noise corruption and non-linearity of received signal strength (RSS), traditional approaches always fail to deliver accurate positioning results. The ℓ1-graph is constructed by sparse representation of each sample with respect to remaining samples. Noise factor is considered in the construction process of ℓ1-graph, leading to more robustness compared to traditional k-nearest-neighbor graph (KNN-graph). The KNN-graph construction is supervised, while the ℓ1-graph is assumed to be unsupervised without harnessing any data label information and uncovers the underlying sparse relationship of each data. Combining KNN-graph and ℓ1-graph, both labeled and unlabeled information are utilized, so the LRSML method has the potential to convey more discriminative information compared to conventional methods. To overcome the non-linearity of RSS, kernel-based manifold learning method (K-LRSML) is employed through mapping the original signal data to a higher dimension Hilbert space. The efficiency and superiority of LRSML over current state of art methods are verified with extensive experiments on real data.