Semi-supervised clustering is an very important topic in machine learning and computer vision. The key challenge of this problem is how to learn a metric, such that the instances sharing the same label are more likely close to each other on the embedded space. However, little attention has been paid to learn better representations when the data lie on non-linear manifold. Fortunately, deep learning has led to great success on feature learning recently. Inspired by the advances of deep learning, we propose a deep transductive semi-supervised maximum margin clustering approach. More specifically, given pairwise constraints, we exploit both labeled and unlabeled data to learn a non-linear mapping under maximum margin framework for clustering analysis. Thus, our model unifies transductive learning, feature learning and maximum margin techniques in the semi-supervised clustering framework. We pretrain the deep network structure with restricted Boltzmann machines (RBMs) layer by layer greedily, and optimize our objective function with gradient descent. By checking the most violated constraints, our approach updates the model parameters through error backpropagation, in which deep features are learned automatically. The experimental results shows that our model is significantly better than the state of the art on semi-supervised clustering.
Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary issue of designing classification algorithms that can deal with more complex outputs, such as trees, sequences, or sets. More generally, we consider problems involving multiple dependent output variables, structured output spaces, and classification problems with class attributes. In order to accomplish this, we propose to appropriately generalize the well-known notion of a separation margin and derive a corresponding maximum-margin formulation. While this leads to a quadratic program with a potentially prohibitive, i.e. exponential, number of constraints, we present a cutting plane algorithm that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval extraction, and optical character recognition. Experiments from various domains involving different types of output spaces emphasize the breadth and generality of our approach. The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner. We describe and analyze an online algorithm for supervised learning of pseudo-metrics. The algorithm receives pairs of instances and predicts their similarity according to a pseudo-metric. The pseudo-metrics we use are quadratic forms parameterized by positive semi-definite matrices. The core of the algorithm is an update rule that is based on successive projections onto the positive semi-definite cone and onto half-space constraints imposed by the examples. We describe an efficient procedure for performing these projections, derive a worst case mistake bound on the similarity predictions, and discuss a dual version of the algorithm in which it is simple to incorporate kernel operators. The online algorithm also serves as a building block for deriving a large-margin batch algorithm. We demonstrate the merits of the proposed approach by conducting experiments on MNIST dataset and on document filtering.