Dimensionality reduction is an essential step in high-dimensional data analysis. Many dimensionality reduction algorithms have been applied successfully to multi-class and multi-label problems. They are commonly applied as a separate data preprocessing step before classification algorithms. In this paper, we study a joint learning framework in which we perform dimensionality reduction and multi-label classification simultaneously. We show that when the least squares loss is used in classification, this joint learning decouples into two separate components, i.e., dimensionality reduction followed by multi-label classification. This analysis partially justifies the current practice of a separate application of dimensionality reduction for classification problems. We extend our analysis using other loss functions, including the hinge loss and the squared hinge loss. We further extend the formulation to the more general case where the input data for different class labels may differ, overcoming the limitation of traditional dimensionality reduction algorithms. Experiments on benchmark data sets have been conducted to evaluate the proposed joint formulations.

This paper deals with evolutionary clustering, which refers to the problem of clustering data with distribution drifting along time. Starting from a density estimation view to clustering problems, we propose two general on-line frameworks. In the first framework, i.e., historical data dependent (HDD), current model distribution is designed to approximate both current and historical data distributions. In the second framework, i.e., historical model dependent (HMD), current model distribution is designed to approximate both current data distribution and historical model distribution. Both frameworks are based on the general exponential family mixture (EFM) model. As a result, all conventional clustering algorithms based on EFMs can be extended to evolutionary setting under the two frameworks. Empirical results validate the two frameworks.

Most of the existing metric learning methods are accomplished by exploiting pairwise constraints over the labeled data and frequently suffer from the insufficiency of training examples.  To learn a robust distance metric from few labeled examples, prior knowledge from unlabeled examples as well as the metrics previously derived from auxiliary data sets can be useful.  In this paper, we propose to leverage such auxiliary knowledge to assist distance metric learning, which is formulated following the regularized loss minimization principle.  Two algorithms are derived on the basis of manifold regularization and log-determinant divergence regularization technique, respectively, which can simultaneously exploit label information (i.e., the pairwise constraints over labeled data), unlabeled examples, and the metrics derived from auxiliary data sets.  The proposed methods directly manipulate the auxiliary metrics and require no raw examples from the auxiliary data sets, which make them efficient and flexible.  We conduct extensive evaluations to compare our approaches with a number of competing approaches on face recognition task.  The experimental results show that our approaches can derive reliable distance metrics from limited training examples and thus are superior in terms of accuracy and labeling efforts.

In this paper, we formulate the problem of early classification of time series data, which is important in some time-sensitive applications such as health-informatics. We introduce a novel concept of MPL (Minimum Prediction Length) and develop ECTS (Early Classification on Time Series), an effective 1-nearest neighbor classification method. ECTS makes early predictions and at the same time retains the accuracy comparable to that of a 1NN classifier using the full-length time series. Our empirical study using benchmark time series data sets shows that ECTS works well on the real data sets where 1NN classification is effective.

Kernel methods have been applied successfully in many applications. The kernel matrix plays an important role in kernel-based learning methods, but the ideal kernel matrix is usually unknown in practice and needs to be estimated. In this paper, we propose to directly learn the ideal kernel matrix (called the optimal neighborhood kernel matrix) from a pre-specified kernel matrix for improved classification performance. We assume that the pre-specified kernel matrix generated from the specific application is a noisy observation of the ideal one. The resulting optimal neighborhood kernel matrix is shown to be the summation of the pre-specified kernel matrix and a rank-one matrix. We formulate the problem of learning the optimal neighborhood kernel as a constrained quartic problem, and propose to solve it using two methods: level method and constrained gradient descent. Empirical results on several benchmark data sets demonstrate the efficiency and effectiveness of the proposed algorithms.

Robots operating in home environments must be able to interact with articulated objects such as doors or drawers.  Ideally, robots are able to autonomously infer articulation models by observation.  In this paper, we present an approach to learn kinematic models by inferring the connectivity of rigid parts and the articulation models for the corresponding links.  Our method uses a mixture of parameterized and parameter-free (Gaussian process) representations and finds low-dimensional manifolds that provide the best explanation of the given observations.  Our approach has been implemented and evaluated using real data obtained in various realistic home environment settings.

These existing algorithms discover projections policies in very high dimensional state spaces. of the training data under which nearby points are likely We propose a linear dimensionality reduction algorithm to have the same class label or similar regression targets. The that discovers predictive projections: projections algorithm described in this paper makes use of the same machinery in which accurate predictions of future states but attempts to find low-dimensional projections under can be made using simple nearest neighbor style which current state vectors accurately predict future states learning. The goal of this work is to extend the in the projected space. The intuition is that projections which reach of existing reinforcement learning algorithms capture the state dynamics in this way are likely to contain to domains where they would otherwise be inapplicable information that will be useful for control.

In this work we propose gRegress, a new algorithm which given set of labeled graphs and a real value associated with each graph extracts the complete set of subgraphs such that a) each subgraph in this set has correlation with the real value above a user-specified threshold and b) each subgraph in this set has correlation with any other subgraph in the set below a user-specified threshold. gRegress incorporates novel pruning mechanisms based on correlation of a subgraph feature with the output and correlation with other subgraph features. These pruning mechanisms lead to significant speedup. Experimental results indicate that in terms of runtime, gRegress substantially outperforms gSpan, often by an order of magnitude while the regression models produced by both approaches have comparable accuracy.

We propose a probabilistic transfer learning model that uses task-level features to control the task mixture selection in a hierarchical Bayesian model. These task-level features, although rarely used in existing approaches, can provide additional information to model complex task distributions and allow effective transfer to new tasks especially when only limited number of data are available. To estimate the model parameters, we develop an empirical Bayes method based on variational approximation techniques. Our experiments on information retrieval show that the proposed model achieves significantly better performance compared with other transfer learning methods.

Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features within a kernel with a sparse set of weights that are estimated in conjunction with the original classification or regression problem. The iterative algorithm, KNIFE, alternates between finding the coefficients of the original problem and finding the feature weights through kernel linearization. In addition, a slight modification of KNIFE yields an efficient algorithm for finding feature regularization paths, or the paths of each feature's weight. Simulation results demonstrate the utility of KNIFE for both kernel regression and support vector machines with a variety of kernels. Feature path realizations also reveal important non-linear correlations among features that prove useful in determining a subset of significant variables. Results on vowel recognition data, Parkinson's disease data, and microarray data are also given.