A bottleneck to detecting distance and density based outliers is that a nearest-neighbor search is required for each of the data points, resulting in a quadratic number of pairwise distance evaluations. In this paper, we propose a new method that uses the relative degree of density with respect to a fixed set of reference points to approximate the degree of density defined in terms of nearest neighbors of a data point. The running time of our algorithm based on this approximation is 0(Rn log n) where n is the size of dataset and R is the number of reference points. Candidate outliers are ranked based on the outlier score assigned to each data point. Theoretical analysis and empirical studies show that our method is effective, efficient, and highly scalable to very large datasets.

The utility of optical tomography as a practical imaging modality has, thus far, been limited by its intrinsically low spatial resolution and quantitative accuracy. Recently, we have argued that a broad range of physiological phenomena might be accurately studied by adopting this technology to investigate dynamic states (Schmitz et al., 2000; Barbour et al., 2000; Graber et al., 2000; Barbour et aL, 2001; and Barbour et aL, 1999). One such phenomenon holding considerable significance is the dynamics of the vasculature, which has been well characterized as being both spatially and temporally heterogeneous. In this paper, we have modeled such heterogeneity in the limiting case of spatiotemporal coincident behavior involving optical contrast features, in an effort to define the expected limits with which dynamic states can be characterized using two newly described reconstruction methods that evaluate normalized detector data: the normalized difference method (NDM) and the normalized constraint method (NCM). Influencing the design of these studies is the expectation that spatially coincident temporal variations in both the absorption and scattering properties of tissue can occur in vivo. We have also chosen to model dc illumination techniques, in recognition of their favorable performance and cost for practical systems. This choice was made with full knowledge of theoretical findings arguing that separation of the optical absorption and scattering coefficients under these conditions is not possible. Results obtained show that the NDM algorithm provides for good spatial resolution and excellent characterization of the temporal behavior of optical properties but is subject to interparameter crosstalk. The NCM algorithm, while also providing excellent characterization of temporal behavior, provides for improved spatial resolution, as well as for improved separation of absorption and scattering coefficients. A discussion is provided to reconcile these findings with theoretical expectations.