Object and Face Recognition with Image Set (Jun. 2007 - Present)
Publication:
Manifold Discriminant Analysis (MDA)
To solve the problem of image set classification, we model each image set as a manifold, and formulate the problem as classification-oriented multi-manifolds learning. Aiming at maximizing "manifold margin", MDA seeks to learn an embedding space, where manifolds with different class labels are better separated, and local data compactness within each manifold is enhanced. As a result, new testing manifold can be more reliably classified in the learned embedding space.
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Manifold-Manifold Distance (MMD)
We address the problem of classifying image sets, each of which contains images belonging to the same class but covering large variations. We innovatively formulate the problem as the computation of Manifold-Manifold Distance (MMD). To compute MMD, we propose a novel manifold learning approach, which expresses a manifold by a collection of local linear models, each depicted by a subspace. MMD is then converted to integrating the distances between pair of subspaces respectively from one of the involved manifolds.
Dimensionality Reduction and Manifold Learning (Nov. 2005 - May. 2007)
Publication:
Maximal Linear Embedding (MLE)
We propose a simple but effective nonlinear dimensionality reduction algorithm, named Maximal Linear Embedding (MLE). MLE learns a parametric mapping to recover a single global low-dimensional coordinate space and yields an isometric embedding for the manifold. Inspired by geometric intuition, we introduce a reasonable definition of locally linear patch, Maximal Linear Patch (MLP), which seeks to maximize the local neighborhood in which linearity holds. The input data are first decomposed into a collection of local linear models, each depicting an MLP. These local models are then aligned into a global coordinate space, which is achieved by applying MDS to some randomly selected landmarks. The proposed alignment method, called Landmarks-based Global Alignment (LGA), can efficiently produce a closed-form solution with no risk of local optima. It just involves some small-scale eigenvalue problems, while most previous aligning techniques employ time-consuming iterative optimization. Compared with traditional methods such as ISOMAP and LLE, our MLE yields an explicit modeling of the intrinsic variation modes of the observation data.
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Face Detection (Jul. 2004 - Dec. 2005)
The performance of a learning-based method highly depends on the quality of a training set. However, it is very challenging to collect an efficient and effective training set for training a good classifier, because of the high dimensionality of the feature space and the complexity of decision boundaries. In this research, we study the methodology of automatically obtaining an optimal training set for robust face detection by resampling the collected training set.
Publication:
Optimizing Training Set for Face Detection
We propose a genetic algorithm (GA) and manifold-based method to resample a given training set for more robust face detection. The motivations behind lie in two folds: (1) dynamic optimization, diversity, and consistency of the training samples are cultivated by the evolutionary nature of GA and (2) the desirable non-linearity of the training set is preserved by using the manifold-based resampling. We demonstrate the effectiveness of the proposed method through experiments and comparisons to other existing face detectors. The system trained from the training set by the proposed method has achieved 90.73% accuracy with no false alarm on MIT+CMU frontal face test set-the best result reported so far to our knowledge. Moreover, as a fully automatic technology, the proposed method can significantly facilitate the preparation of training sets for obtaining well-performed object detection systems in different applications.
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