During the past decade, finite mixture modeling has become a well-established technique in data analysis and clustering. This paper focus on developing a variational inference framework to learn finite Beta-Liouville mixture models that have been proposed recently as an efficient way for proportional data clustering. In contrast to the conventional expectation maximization (EM) algorithm, commonly used for learning finite mixture models, the proposed algorithm has the advantages that it is more efficient from a computational point of view and by preventing over- and under-fitting problems. Moreover, the complexity of the mixture model (i.e. the number of components) can be determined automatically and simultaneously with the parameters estimation in a closed form as part of the Bayesian inference procedure. The merits of the proposed approach are shown using both artificial data sets and two interesting and challenging real applications namely dynamic textures clustering and facial expression recognition.

In past decade, more and more data are collected from multiple sources or represented by multiple views, where different views describe distinct perspectives of the data. Although each view could be individually used for finding patterns by clustering, the clustering performance could be more accurate by exploring the rich information among multiple views. Several multi-view clustering methods have been proposed to unsupervised integrate different views of data. However, they are graph based approaches, e.g. based on spectral clustering, such that they cannot handle the large-scale data. How to combine these heterogeneous features for unsupervised large-scale data clustering has become a challenging problem. In this paper, we propose a new robust large-scale multi-view clustering method to integrate heterogeneous representations of large-scale data. We evaluate the proposed new methods by six benchmark data sets and compared the performance with several commonly used clustering approaches as well as the baseline multi-view clustering methods. In all experimental results, our proposed methods consistently achieve superiors clustering performances.

We study robust high-dimensional estimation of generalized linear models (GLMs); where a small number k of the n observations can be arbitrarily corrupted, and where the true parameter is high dimensional in the “p >> n” regime, but only has a small number s of non-zero entries. There has been some recent work connecting robustness and sparsity, in the context of linear regression with corrupted observations, by using an explicitly modeled outlier response vector that is assumed to be sparse. Interestingly, we show, in the GLM setting, such explicit outlier response modeling can be performed in two distinct ways. For each of these two approaches, we give l 2 error bounds for parameter estimation for general values of the tuple (n,p,s,k).

Parsing human poses in images is fundamental in extracting critical visual information for artificial intelligent agents. Our goal is to learn self-contained body part representations from images, which we call visual symbols, and their symbol-wise geometric contexts in this parsing process. Each symbol is individually learned by categorizing visual features leveraged by geometric information. In the categorization, we use Latent Support Vector Machine followed by an efficient cross validation procedure. Then, these symbols naturally define geometric contexts of body parts in a fine granularity for effective inference. When the structure of the compositional parts is a tree, we derive an efficient approach to estimating human poses in images. Experiments on two large datasets suggest our approach outperforms state of the art methods.

When doing learning from demonstration, it is often the case that the demonstrator provides corrective examples to fix errant behavior by the agent or robot. We present a set of algorithms which use this corrective data to identify and remove noisy examples in datasets which caused errant classifications, and ultimately errant behavior. The objective is to actually modify the source datasets rather than solely rely on the noise-insensitivity of the classification algorithm. This is particularly useful in the sparse datasets often found in learning from demonstration experiments. Our approach tries to distinguish between noisy misclassification and mere undersampling of the learning space. If errors are a result of misclassification, we potentially remove the responsible points and update the classifier. We demonstrate our method on UCI Machine Learning datasets at different levels of sparsity and noise, using decision trees, K-Nearest-Neighbor, and support vector machines.

Graph clustering has received growing attention in recent years as an important analytical technique, both due to the prevalence of graph data, and the usefulness of graph structures for exploiting intrinsic data characteristics.However, as graph data grows in scale, it becomes increasingly more challenging to identify clusters. In this paper we propose an efficient clustering algorithm for large-scale graph data using spectral methods. The key idea is to repeatedly generate a small number of "supernodes" connected to the regular nodes, in order to compress the original graph into a sparse bipartite graph. By clustering the bipartite graph using spectral methods, we are able to greatly improve efficiency without losing considerable clustering power. Extensive experiments show the effectiveness and efficiency of our approach.

We study an interesting phenomenon of social influence locality in a large microblogging network, which suggests that users' behaviors are mainly influenced by close friends in their ego networks. We provide a formal definition for the notion of social influence locality and develop two instantiation functions based on pairwise influence and structural diversity. The defined influence locality functions have strong predictive power. Without any additional features, we can obtain a F1-score of 71.65% for predicting users' retweet behaviors by training a logistic regression classifier based on the defined functions. Our analysis also reveals several intriguing discoveries. For example, though the probability of a user retweeting a microblog is positively correlated with the number of friends who have retweeted the microblog, it is surprisingly negatively correlated with the number of connected circles that are formed by those friends.

Hartigan's method for k-means clustering holds several potential advantages compared to the classical and prevalent optimization heuristic known as Lloyd's algorithm. E.g., it was recently shown that the set of local minima of Hartigan's algorithm is a subset of those of Lloyd's method. We develop a closed-form expression that allows to establish Hartigan's method for k-means clustering with any Bregman divergence, and further strengthen the case of preferring Hartigan's algorithm over Lloyd's algorithm. Specifically, we characterize a range of problems with various noise levels of the inputs, for which any random partition represents a local minimum for Lloyd's algorithm, while Hartigan's algorithm easily converges to the correct solution. Extensive experiments on synthetic and real-world data further support our theoretical analysis.

In this work, we present a new framework for large scale online kernel classification, making kernel methods efficient and scalable for large-scale online learning tasks. Unlike the regular budget kernel online learning scheme that usually uses different strategies to bound the number of support vectors, our framework explores a functional approximation approach to approximating a kernel function/matrix in order to make the subsequent online learning task efficient and scalable. Specifically, we present two different online kernel machine learning algorithms: (i) the Fourier Online Gradient Descent (FOGD) algorithm that applies the random Fourier features for approximating kernel functions; and (ii) the Nystrom Online Gradient Descent (NOGD) algorithm that applies the Nystrom method to approximate large kernel matrices. We offer theoretical analysis of the proposed algorithms, and conduct experiments for large-scale online classification tasks with some data set of over 1 million instances. Our encouraging results validate the effectiveness and efficiency of the proposed algorithms, making them potentially more practical than the family of existing budget kernel online learning approaches.

Different solution approaches for combinatorial problems often exhibit incomparable performance that depends on the concrete problem instanceto be solved. Algorithm portfolios aim to combine the strengths of multiple algorithmic approaches by training a classifier that selects or schedules solvers dependent on the given instance. We devise a new classifier that selects solvers based on a cost-sensitive hierarchical clustering model. Experimental results on SAT and MaxSAT show that the new method outperforms the most effective portfolio builders to date.