Face Identification by a Cascade of Rejection Classifiers

Nearest neighbor search is commonly employed in face recognition but it does not scale well to large dataset sizes. A strategy to combine rejection classifiers into a cascade for face identification is proposed in this paper. A rejection classifier for a pair of classes is defined to reject at least one of the classes with high confidence. These rejection classifiers are able to share discriminants in feature space and at the same time have high confidence in the rejection decision. In the face identification problem, it is possible that a pair of known individual faces are very dissimilar. It is very unlikely that both of them are close to an unknown face in the feature space. Hence, only one of them needs to be considered. Using a cascade structure of rejection classifiers, the scope of nearest neighbor search can be reduced significantly. Experiments on Face Recognition Grand Challenge (FRGC) version 1 data demonstrate that the proposed method achieves significant speed up and an accuracy comparable with the brute force Nearest Neighbor method. In addition, a graph cut based clustering technique is employed to demonstrate that the pairwise separability of these rejection classifiers is capable of semantic grouping.National Science Foundation (EIA-0202067, IIS-0329009); Office of Naval Research (N00014-03-1-0108

An Efficient Dual Approach to Distance Metric Learning

Distance metric learning is of fundamental interest in machine learning because the distance metric employed can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to the problem, but typically requires solving a semidefinite programming (SDP) problem, which is computationally expensive. Standard interior-point SDP solvers typically have a complexity of $O(D^{6.5})$ (with $D$ the dimension of input data), and can thus only practically solve problems exhibiting less than a few thousand variables. Since the number of variables is $D (D+1) / 2$, this implies a limit upon the size of problem that can practically be solved of around a few hundred dimensions. The complexity of the popular quadratic Mahalanobis metric learning approach thus limits the size of problem to which metric learning can be applied. Here we propose a significantly more efficient approach to the metric learning problem based on the Lagrange dual formulation of the problem. The proposed formulation is much simpler to implement, and therefore allows much larger Mahalanobis metric learning problems to be solved. The time complexity of the proposed method is $O (D ^ 3)$, which is significantly lower than that of the SDP approach. Experiments on a variety of datasets demonstrate that the proposed method achieves an accuracy comparable to the state-of-the-art, but is applicable to significantly larger problems. We also show that the proposed method can be applied to solve more general Frobenius-norm regularized SDP problems approximately

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Max-margin Metric Learning for Speaker Recognition

Probabilistic linear discriminant analysis (PLDA) is a popular normalization approach for the i-vector model, and has delivered state-of-the-art performance in speaker recognition. A potential problem of the PLDA model, however, is that it essentially assumes Gaussian distributions over speaker vectors, which is not always true in practice. Additionally, the objective function is not directly related to the goal of the task, e.g., discriminating true speakers and imposters. In this paper, we propose a max-margin metric learning approach to solve the problems. It learns a linear transform with a criterion that the margin between target and imposter trials are maximized. Experiments conducted on the SRE08 core test show that compared to PLDA, the new approach can obtain comparable or even better performance, though the scoring is simply a cosine computation

Scalable Nonlinear Embeddings for Semantic Category-based Image Retrieval

We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on similar and dissimilar pairs while training. The proposed method is derived by an approximate kernelization of a linear Mahalanobis-like distance metric learning algorithm and can also be seen as a kernel neural network. The number of model parameters and test time evaluation complexity of the proposed method are O(dD) where D is the dimensionality of the input features and d is the dimension of the projection space - this is in contrast to the usual kernelization methods as, unlike them, the complexity does not scale linearly with the number of training examples. We propose a stochastic gradient based learning algorithm which makes the method scalable (w.r.t. the number of training examples), while being nonlinear. We train the method with up to half a million training pairs of 4096 dimensional CNN features. We give empirical comparisons with relevant baselines on seven challenging datasets for the task of low dimensional semantic category based image retrieval.Comment: ICCV 2015 preprin

Positive Semidefinite Metric Learning Using Boosting-like Algorithms

The success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data. It is often beneficial to learn such a metric from the input training data, instead of using a default one such as the Euclidean distance. In this work, we propose a boosting-based technique, termed BoostMetric, for learning a quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance metric requires enforcing the constraint that the matrix parameter to the metric remains positive definite. Semidefinite programming is often used to enforce this constraint, but does not scale well and easy to implement. BoostMetric is instead based on the observation that any positive semidefinite matrix can be decomposed into a linear combination of trace-one rank-one matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting methods are easy to implement, efficient, and can accommodate various types of constraints. We extend traditional boosting algorithms in that its weak learner is a positive semidefinite matrix with trace and rank being one rather than a classifier or regressor. Experiments on various datasets demonstrate that the proposed algorithms compare favorably to those state-of-the-art methods in terms of classification accuracy and running time.Comment: 30 pages, appearing in Journal of Machine Learning Researc

Low-Rank Discriminative Least Squares Regression for Image Classification

Latest least squares regression (LSR) methods mainly try to learn slack regression targets to replace strict zero-one labels. However, the difference of intra-class targets can also be highlighted when enlarging the distance between different classes, and roughly persuing relaxed targets may lead to the problem of overfitting. To solve above problems, we propose a low-rank discriminative least squares regression model (LRDLSR) for multi-class image classification. Specifically, LRDLSR class-wisely imposes low-rank constraint on the intra-class regression targets to encourage its compactness and similarity. Moreover, LRDLSR introduces an additional regularization term on the learned targets to avoid the problem of overfitting. These two improvements are helpful to learn a more discriminative projection for regression and thus achieving better classification performance. Experimental results over a range of image databases demonstrate the effectiveness of the proposed LRDLSR method