  Modern machine learning-based recognition approaches require large-scale
datasets with large number of labelled training images. However, such datasets
are inherently difficult and costly to collect and annotate. Hence there is a
great and growing interest in automatic dataset collection methods that can
leverage the web. % which are collected % in a cheap, efficient and yet
unreliable way. Collecting datasets in this way, however, requires robust and
efficient ways for detecting and excluding outliers that are common and
prevalent. % Outliers are thus a % prominent treat of using these dataset. So
far, there have been a limited effort in machine learning community to directly
detect outliers for robust classification. Inspired by the recent work on
Pre-conditioned LASSO, this paper formulates the outlier detection task using
Pre-conditioned LASSO and employs \red{unsupervised} transductive diffusion
component analysis to both integrate the topological structure of the data
manifold, from labeled and unlabeled instances, and reduce the feature
dimensionality. Synthetic experiments as well as results on two real-world
classification tasks show that our framework can robustly detect the outliers
and improve classification.
