In this paper, we will present a unified view for LDA. We will (1) emphasize that standard LDA solutions are not unique, (2) propose several new LDA formulations: St-orthonormal LDA, Sw-orthonormal LDA and orthogonal LDA which have unique solutions, and (3) show that with St-orthonormal LDA and Sw-orthonormal LDA formulations, solutions to all four major LDA objective functions are identical. Furthermore, we perform an indepth analysis to show that the LDA sometimes performs poorly due to over-fitting, i.e., it picks up PCA dimensions with small eigenvalues. From this analysis, we propose a stable LDA which uses PCA first to reduce to a small PCA subspace and do LDA in the subspace.

This paper presents a novel latent semantic learning algorithm for action recognition. Through efficient sparse coding, we can learn latent semantics (i.e. high-level features) from a large vocabulary of abundant mid-level features (i.e. visual keywords). More importantly, we can capture the manifold structure hidden among mid-level features by incorporating hypergraph regularization into sparse coding. The learnt latent semantics can further be readily used for action recognition by defining a histogram intersection kernel. Different from the traditional latent semantic analysis based on topic models, our sparse coding method with hypergraph regularization can exploit the manifold structure hidden among mid-level features for latent semantic learning, which results in compact but discriminative high-level features for action recognition. We have tested our method on the commonly used KTH action dataset and the unconstrained YouTube action dataset. The experimental results show the superior performance of our method.

Dependency networks are a compelling alternative to Bayesian networks for learning joint probability distributions from data and using them to compute probabilities. A dependency network consists of a set of conditional probability distributions, each representing the probability of a single variable given its Markov blanket. Running Gibbs sampling with these conditional distributions produces a joint distribution that can be used to answer queries, but suffers from the traditional slowness of sampling-based inference. In this paper, we observe that the mean field update equation can be applied to dependency networks, even though the conditional probability distributions may be inconsistent with each other. In experiments with learning and inference on 12 datasets, we demonstrate that mean field inference in dependency networks offers similar accuracy to Gibbs sampling but with orders of magnitude improvements in speed. Compared to Bayesian networks learned on the same data, dependency networks offer higher accuracy at greater amounts of evidence. Furthermore, mean field inference is consistently more accurate in dependency networks than in Bayesian networks learned on the same data.

Ordinal regression is an important research topic in machine learning. It aims to automatically determine the implied rating of a data item on a fixed, discrete rating scale. In this paper, we present a novel ordinal regression approach via manifold learning, which is capable of uncovering the embedded nonlinear structure of the data set according to the observations in the highdimensional feature space. By optimizing the order information of the observations and preserving the intrinsic geometry of the data set simultaneously, the proposed algorithm provides the faithful ordinal regression to the new coming data points. To offer more general solution to the data with natural tensor structure, we further introduce the multilinear extension of the proposed algorithm, which can support the ordinal regression of high order data like images. Experiments on various data sets validate the effectiveness of the proposed algorithm as well as its extension.

In this paper, we propose a novel method to select the most informativesubset of features, which has little redundancy andvery strong discriminating power. Our proposed approach automaticallydetermines the optimal number of features and selectsthe best subset accordingly by maximizing the averagepairwise informativeness, thus has obvious advantage overtraditional filter methods. By relaxing the essential combinatorialoptimization problem into the standard quadratic programmingproblem, the most informative feature subset canbe obtained efficiently, and a strategy to dynamically computethe redundancy between feature pairs further greatly acceleratesour method through avoiding unnecessary computationsof mutual information. As shown by the extensive experiments,the proposed method can successfully select the mostinformative subset of features, and the obtained classificationresults significantly outperform the state-of-the-art results onmost test datasets.

Semi-supervised support vector machines (S3VMs) are a kind of popular approaches which try to improve learning performance by exploiting unlabeled data. Though S3VMs have been found helpful in many situations, they may degenerate performance and the resultant generalization ability may be even worse than using the labeled data only. In this paper, we try to reduce the chance of performance degeneration of S3VMs. Our basic idea is that, rather than exploiting all unlabeled data, the unlabeled instances should be selected such that only the ones which are very likely to be helpful are exploited, while some highly risky unlabeled instances are avoided. We propose the S3VM- us method by using hierarchical clustering to select the unlabeled instances. Experiments on a broad range of data sets over eighty-eight different settings show that the chance of performance degeneration of S3VM- us is much smaller than that of existing S3VMs.

We describe the Fourier basis, a linear value function approximation scheme based on the Fourier series. We empirically demonstrate that it performs well compared to radial basis functions and the polynomial basis, the two most popular fixed bases for linear value function approximation, and is competitive with learned proto-value functions.

Multilabel classification is a central problem in many areas of data analysis, including text and multimedia categorization, where individual data objects need to be assigned multiple labels. A key challenge in these tasks is to learn a classifier that can properly exploit label correlations without requiring exponential enumeration of label subsets during training or testing. We investigate novel loss functions for multilabel training within a large margin framework---identifying a simple alternative that yields improved generalization while still allowing efficient training. We furthermore show how covariances between the label models can be learned simultaneously with the classification model itself, in a jointly convex formulation, without compromising scalability. The resulting combination yields state of the art accuracy in multilabel webpage classification.

We consider a learning setting of importance to large scale machine learning: potentially unlimited data arrives sequentially, but only a small fraction of it is labeled. The learner cannot store the data; it should learn from both labeled and unlabeled data, and it may also request labels for some of the unlabeled items. This setting is frequently encountered in real-world applications and has the characteristics of online, semi-supervised, and active learning. Yet previous learning models fail to consider these characteristics jointly. We present OASIS, a Bayesian model for this learning setting. The main contributions of the model include the novel integration of a semi-supervised likelihood function, a sequential Monte Carlo scheme for efficient online Bayesian updating, and a posterior-reduction criterion for active learning. Encouraging results on both synthetic and real-world optical character recognition data demonstrate the synergy of these characteristics in OASIS.

Variable selection problems are typically addressed under apenalized optimization framework. Nonconvex penalties such as the minimax concave plus (MCP) and smoothly clipped absolute deviation(SCAD), have been demonstrated to have the properties of sparsity practically and theoretically. In this paper we propose a new nonconvex penalty that we call exponential-type penalty. The exponential-type penalty is characterized by a positive parameter,which establishes a connection with the ell 0 and ell 1 penalties.We apply this new penalty to sparse supervised learning problems. To solve to resulting optimization problem, we resort to a reweighted ell 1 minimization method. Moreover, we devise an efficient method for the adaptive update of the tuning parameter. Our experimental results are encouraging. They show that the exponential-type penalty is competitive with MCP and SCAD.