The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario where the regularization parameter $\tau$ is large we show that the minimum degree assumption can potentially be removed. As a special case, for an SBM with two blocks, the results require the maximum degree to be large (grow faster than $\log n$) as opposed to the minimum degree. More importantly, we show the usefulness of regularization in situations where not all nodes belong to well-defined clusters. Our results rely on a `bias-variance'-like trade-off that arises from understanding the concentration of the sample Laplacian and the eigen gap as a function of the regularization parameter. As a byproduct of our bounds, we propose a data-driven technique \textit{DKest} (standing for estimated Davis-Kahan bounds) for choosing the regularization parameter. This technique is shown to work well through simulations and on a real data set.

Crowdsourcing has been proven to be an effective and efficient tool to annotate large datasets. User annotations are often noisy, so methods to combine the annotations to produce reliable estimates of the ground truth are necessary. We claim that considering the existence of clusters of users in this combination step can improve the performance. This is especially important in early stages of crowdsourcing implementations, where the number of annotations is low. At this stage there is not enough information to accurately estimate the bias introduced by each annotator separately, so we have to resort to models that consider the statistical links among them. In addition, finding these clusters is interesting in itself as knowing the behavior of the pool of annotators allows implementing efficient active learning strategies. Based on this, we propose in this paper two new fully unsupervised models based on a Chinese Restaurant Process (CRP) prior and a hierarchical structure that allows inferring these groups jointly with the ground truth and the properties of the users. Efficient inference algorithms based on Gibbs sampling with auxiliary variables are proposed. Finally, we perform experiments, both on synthetic and real databases, to show the advantages of our models over state-of-the-art algorithms.

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional reduction. However, traditional Singular Value Decomposition (SVD) based PCA fails to model data which largely deviates from Gaussian distribution. The Bregman Divergence was recently introduced to achieve a generalized PCA framework. If the random variable under dimensional reduction follows Bernoulli distribution, which occurs in many emerging fields, the generalized PCA is called Logistic PCA (LPCA). In this paper, we extend the batch LPCA to a sequential version (i.e. SLPCA), based on the sequential convex optimization theory. The convergence property of this algorithm is discussed compared to the batch version of LPCA (i.e. BLPCA), as well as its performance in reducing the dimension for multivariate binary-state systems. Its application in building energy end-use profile modeling is also investigated.

Neural connectomics has begun producing massive amounts of data, necessitating new analysis methods to discover the biological and computational structure. It has long been assumed that discovering neuron types and their relation to microcircuitry is crucial to understanding neural function. Here we developed a nonparametric Bayesian technique that identifies neuron types and microcircuitry patterns in connectomics data. It combines the information traditionally used by biologists, including connectivity, cell body location and the spatial distribution of synapses, in a principled and probabilistically-coherent manner. We show that the approach recovers known neuron types in the retina and enables predictions of connectivity, better than simpler algorithms. It also can reveal interesting structure in the nervous system of C. elegans, and automatically discovers the structure of a microprocessor. Our approach extracts structural meaning from connectomics, enabling new approaches of automatically deriving anatomical insights from these emerging datasets.

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for complex-valued data and considers two cases: a) the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and b) a pure complex kernel is used to directly map the data to the induced complex feature space. The recently developed Wirtinger's calculus on complex reproducing kernel Hilbert spaces (RKHS) is employed in order to compute the Lagrangian and derive the dual optimization problem. As one of our major results, we prove that any complex SVM/SVR task is equivalent with solving two real SVM/SVR tasks exploiting a specific real kernel which is generated by the chosen complex kernel. In particular, the case of pure complex kernels leads to the generation of new kernels, which have not been considered before. In the classification case, the proposed framework inherently splits the complex space into four parts. This leads naturally in solving the four class-task (quaternary classification), instead of the typical two classes of the real SVM. In turn, this rationale can be used in a multiclass problem as a split-class scenario based on four classes, as opposed to the one-versus-all method; this can lead to significant computational savings. Experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.

Low-rank coding (LRC), originated from matrix decomposition, is recently introduced into image classification. Following the standard bag-of-words (BOW) pipeline, when coding the data matrix in the sense of low-rankness incorporates contextual information into the traditional BOW model, this can capture the dependency relationship among neighbor patches. It differs from the traditional sparse coding paradigms which encode patches independently. Current LRC-based methods use l_1 norm to increase the discrimination and sparseness of the learned codes. However, such methods fail to consider the local manifold structure between dataspace and dictionary space. To solve this problem, we propose a locality-constrained low-rank coding (LCLR) algorithm for image representations. By using the geometric structure information as a regularization term,we can obtain more discriminative representations. In addition, we present a fast and stable online algorithmto solve the optimization problem. In the experiments,we evaluate LCLR with four benchmarks, including one face recognition dataset (extended Yale B), one handwrittendigit recognition dataset (USPS), and two image datasets (Scene13 for scene recognition and Caltech101 for object recognition). Experimental results show thatour approach outperforms many state-of-the-art algorithmseven with a linear classifier.

Multiple Instance Learning (MIL) is a popular learning technique in various vision tasks including image classification. However, most existing MIL methods do not consider the problem of insufficient examples in the given target category. In this case, it is difficult for traditional MIL methods to build an accurate classifier due to the lack of training examples. Motivated by the empirical success of transfer learning, this paper proposes a novel approach of Adaptive Knowledge Transfer for Multiple Instance Learning (AKT-MIL) in image classification. The new method transfers cross-category knowledge from source categories under multiple instance setting for boosting the learning process. A unified learning framework with a data-dependent mixture model is designed to adaptively combine the transferred knowledge from sources with a weak classifier built in the target domain. Based on this framework, an iterative coordinate descent method with Constraint Concave-Convex Programming (CCCP) is proposed as the optimization procedure. An extensive set of experimental results demonstrate that the proposed AKT-MIL approach substantially outperforms several state-of-the-art algorithms on two benchmark datasets, especially in the scenario when very few training examples are available in the target domain.

Tweets ranking is important for information acquisition in Microblog. Due to the content sparsity and lackof labeled data, it is better to employ semi-supervisedlearning methods to utilize the unlabeled data. However,most of previous semi-supervised learning methods donot consider the pair conflict problem, which means thatthe new selected unlabeled data may conflict with the labeled and previously selected data. It will hurt the learning performance a lot, if the training data contains manyconflict pairs. In this paper, we propose a new collaborative semi-supervised SVM ranking model (CSR-TC)with consideration of the order conflict. The unlabeleddata is selected based on a dynamically maintained transitive closure graph to avoid pair conflict. We also investigate the two views of features, intrinsic and contentrelevant features, for the proposed model. Extensive experiments are conducted on TREC Microblogging corpus. The results demonstrate that our proposed methodachieves significant improvement, compared to severalstate-of-the-art models.

Mutual information (MI) based approaches are a popular feature selection paradigm. Although the stated goal of MI-based feature selection is to identify a subset of features that share the highest mutual information with the class variable, most current MI-based techniques are greedy methods that make use of low dimensional MI quantities. The reason for using low dimensional approximation has been mostly attributed to the difficulty associated with estimating the high dimensional MI from limited samples. In this paper, we argue a different viewpoint that, given a very large amount of data, the high dimensional MI objective is still problematic to be employed as a meaningful optimization criterion, due to its overfitting nature: the MI almost always increases as more features are added, thus leading to a trivial solution which includes all features. We propose a novel approach to the MI-based feature selection problem, in which the overfitting phenomenon is controlled rigourously by means of a statistical test. We develop local and global optimization algorithms for this new feature selection model, and demonstrate its effectiveness in the applications of explaining variables and objects.