Generalized Kernel-based Visual Tracking

In this work we generalize the plain MS trackers and attempt to overcome standard mean shift trackers' two limitations. It is well known that modeling and maintaining a representation of a target object is an important component of a successful visual tracker. However, little work has been done on building a robust template model for kernel-based MS tracking. In contrast to building a template from a single frame, we train a robust object representation model from a large amount of data. Tracking is viewed as a binary classification problem, and a discriminative classification rule is learned to distinguish between the object and background. We adopt a support vector machine (SVM) for training. The tracker is then implemented by maximizing the classification score. An iterative optimization scheme very similar to MS is derived for this purpose.Comment: 12 page

A scalable algorithm for learning a Mahalanobis distance metric

A distance metric that can accurately re°ect the intrinsic characteristics of data is critical for visual recognition tasks. An e®ective solution to de¯ning such a metric is to learn it from a set of training sam- ples. In this work, we propose a fast and scalable algorithm to learn a Ma- halanobis distance. By employing the principle of margin maximization to secure better generalization performances, this algorithm formulates the metric learning as a convex optimization problem with a positive semide¯nite (psd) matrix variable. Based on an important theorem that a psd matrix with trace of one can always be represented as a convex combination of multiple rank-one matrices, our algorithm employs a dif- ferentiable loss function and solves the above convex optimization with gradient descent methods. This algorithm not only naturally maintains the psd requirement of the matrix variable that is essential for met- ric learning, but also signi¯cantly cuts down computational overhead, making it much more e±cient with the increasing dimensions of fea- ture vectors. Experimental study on benchmark data sets indicates that, compared with the existing metric learning algorithms, our algorithm can achieve higher classi¯cation accuracy with much less computational load

Positive Semidefinite Metric Learning with Boosting

The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive 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 method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.Comment: 11 pages, Twenty-Third Annual Conference on Neural Information Processing Systems (NIPS 2009), Vancouver, Canad

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

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

Efficient and scalable approaches to Mahalanobis distance metric learning

The development of an appropriate data-dependent distance metric is a compelling goal for many visual recognition tasks. This thesis proposes three efficient and scalable distance learning algorithms by employing the principle of margin maximization to secure better generalization performances. The proposed algorithms formulate metric learning as a convex optimization problem with a positive semidefinite (psd) matrix variable. A standard interior-point semidefinite programming (SDP) solver has a complexity of O(n to the power of 6.5) where n is the number of variables, and can only solve problems with up to a few thousand variables. Since the number of variables is D ( D+1 ) / 2, where D is the dimensionality of the input data, this corresponds to a limit of around D < 100. This high complexity hampers the application of metric learning to high-dimensional problems. Compared with conventional methods such as standard interior-point algorithms or the special solver used in the large-margin nearest neighbor (LMNN), our algorithms are much more efficient and perform better in terms of scalability. The first algorithm, SDPmetric is based on an important theorem in which a psd matrix with a trace of one can always be represented as a convex combination of multiple rank-one matrices. The algorithm not only naturally maintains the psd requirement of the matrix variable that is essential for metric learning but also significantly cuts down the computational overhead, making it much more efficient with increasing the dimensions of feature vectors. In brief, only the leading eigendecomposition is required for metric learning; hence, the time complexity is O ( t times D squared ) , where t is the number of iterations and D is the dimensionality of the feature vectors. The second algorithm, BoostMetric is based on a boosting technique to learn the Mahalanobis distance metric. One of the primary difficulties in learning this metric is ensuring that the Mahalanobis matrix remains psd. SDP is sometimes used to enforce this constraint but does not scale well. Similar to SDPMetric, BoostMetric is instead based on a key observation that any psd matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. BoostMetric thus uses rank-one psd matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. The last algorithm, FrobMetric is designed for a very efficient approach to this metric learning problem. A Lagrange dual approach is formulated that is much simpler to optimize and we therefore be used to solve much larger Mahalanobis metric learning problems. In general, the proposed approach had a time complexity of O ( t times the cube of D ) with t = 20 ~ 30 for most problems in our experiments. As presented in each chapter, our experiments on various datasets in several applications showed that our algorithms can achieve comparable classification accuracy as state-of-the-art metric learning algorithms with reduced computational complexity

An face-based visual fixation system for prosthetic vision

Recent studies have shown the success of face recognition using low resolution prosthetic vision, but it requires a zoomed-in and stably-fixated view, which will be challenging for a user with the limited resolution of current prosthetic vision devices. We propose a real-time object detection and tracking system capable of fixating human faces. By integrating both static and temporal information, we are able to improve the robustness of face localization so that it can fixate on faces with large pose variations. Our qualitative and quantitative results demonstrate the viability of supplementing visual prosthetic devices with the ability to visually fixate objects automatically, and provide a stable zoomed-in image stream to facilitate face and expression recognition

A Scalable Dual Approach to Semidefinite Metric Learning

Distance metric learning plays an important role in many vision problems. Previous work of quadratic Maha-lanobis metric learning usually needs to solve a semidefinite programming (SDP) problem. A standard interior-point SDP solver has a complexity of O(D6.5) (with D the dimension of input data), and can only solve problems up to a few thousand variables. Since the number of variables is D(D +l)/2, this corresponds to a limit around D < 100. This high complexity hampers the application of metric learning to high-dimensional problems. In this work, we propose a very efficient approach to this metric learning problem. We formulate a Lagrange dual approach which is much simpler to optimize, and we can solve much larger Mahalanobis metric learning problems. Roughly, the proposed approach has a time complexity of O(t ̇ D3) with t ≈ 20 ∼ 30 for most problems in our experiments. The proposed algorithm is scalable and easy to implement. Experiments on various datasets show its similar accuracy compared with state-of-the-art. We also demonstrate that this idea may also be able to be applied to other SDP problems such as maximum variance unfolding

Adversarial Robustness on Image Classification With <italic>k</italic>-Means

Attacks and defences in adversarial machine learning literature have primarily focused on supervised learning. However, it remains an open question whether existing methods and strategies can be adapted to unsupervised learning approaches. In this paper we explore the challenges and strategies in attacking a $k$ -means clustering algorithm and in enhancing its robustness against adversarial manipulations. We evaluate the vulnerability of clustering algorithms to adversarial attacks on two datasets (MNIST and Fashion-MNIST), emphasising the associated security risks. Our study investigates the impact of incremental attack strength on training, introduces the concept of transferability between supervised and unsupervised models, and highlights the sensitivity of unsupervised models to sample distributions. We additionally introduce and evaluate an adversarial training method that improves testing performance in adversarial scenarios, and we highlight the importance of various parameters in the proposed training method, such as continuous learning, centroid initialisation, and adversarial step-count. Overall, our study emphasises the vulnerability of unsupervised learning and clustering algorithms to adversarial attacks and provides insights into potential defence mechanisms