The problem of outlier detection has been widely studied in existing literature because of its numerous applications in fraud detection, medical diagnostics, fault detection, and intrusion detection. A large category of outlier analysis algorithms have been proposed, such as proximity-based methods and local density-based methods. These methods are effective in finding outliers distributed along linear manifolds. Spectral methods, however, are particularly well suited to finding outliers when the data is distributed along manifolds of arbitrary shape. In practice, the underlying manifolds may have varying density, as a result of which a direct use of spectral methods may not be effective. In this paper, we show how to combine spectral techniques with local density-based methods in order to discover interesting outliers. We present experimental results demonstrating the effectiveness of our approach with respect to well-known competing methods.