Subspace clustering is an important unsupervised learning problem with wide applications in computer vision and data analysis. However, the state-of-the-art methods for this problem suffer from high time complexity---quadratic or cubic in $n$ (the number of data instances). In this paper we exploit a data selection algorithm to speedup computation and the robust principal component analysis to strengthen robustness. Accordingly, we devise a scalable and robust subspace clustering method which costs time only linear in $n$. We prove theoretically that under certain mild assumptions our method solves the subspace clustering problem exactly even for grossly corrupted data. Our algorithm is based on very simple ideas, yet it is the only linear time algorithm with noiseless or noisy recovery guarantee. Finally, empirical results verify our theoretical analysis.

Recently with the explosive growth of visual content on the Internet, large-scale image search has attracted intensive attention. It has been shown that mapping highdimensional image descriptors to compact binary codes can lead to considerable efficiency gains in both storage and similarity computation of images. However, most existing methods still suffer from expensive training devoted to large-scale binary code learning. To address this issue, we propose a sub-selection based matrix manipulation algorithm which can significantly reduce the computational cost of code learning. As case studies, we apply the sub-selection algorithm to two popular quantization techniques PCA Quantization (PCAQ) and Iterative Quantization (ITQ). Crucially, we can justify the resulting sub-selective quantization by proving its theoretic properties. Extensive experiments are carried out on three image benchmarks with up to one million samples, corroborating the efficacy of the sub-selective quantization method in terms of image retrieval.

Keepaway soccer is a challenging robot control task that has been widely used as a benchmark for evaluating multi-agent learning systems. The majority of research in this domain has been from the perspective of reinforcement learning (function approximation) and neuroevolution. One of the challenges under multi-agent tasks such as keepaway is to formulate effective mechanisms for diversity maintenance. Indeed the best results to date on this task utilize some form of neuroevolution with genotypic diversity. In this work, a symbiotic framework for evolving teams of programs is utilized with both genotypic and behavioural forms of diversity maintenance considered. Specific contributions of this work include a simple scheme for characterizing genotypic diversity under teams of programs and its comparison to behavioural formulations for diversity under the keepaway soccer task. Unlike previous research concerning diversity maintenance in genetic programming (GP), we are explicitly interested in solutions taking the form of teams of programs.

Classical approaches to visualization directly reduce a document's high-dimensional representation into visualizable two or three dimensions, using techniques such as multidimensional scaling. More recent approaches consider an intermediate representation in topic space, between word space and visualization space, which preserves the semantics by topic modeling. We call the latter semantic visualization problem, as it seeks to jointly model topic and visualization. While previous approaches aim to preserve the global consistency, they do not consider the local consistency in terms of the intrinsic geometric structure of the document manifold. We therefore propose an unsupervised probabilistic model, called Semafore, which aims to preserve the manifold in the lower-dimensional spaces. Comprehensive experiments on several real-life text datasets of news articles and web pages show that Semafore significantly outperforms the state-of-the-art baselines on objective evaluation metrics.

Color refinement is a basic algorithmic routine for graph isomorphismtesting and has recently been used for computing graph kernels as well as for lifting belief propagation and linear programming. So far, color refinement has been treated as a combinatorial problem. Instead, we treat it as a nonlinear continuous optimization problem and prove thatit implements a conditional gradient optimizer that can be turned into graph clustering approaches using hashing and truncated power iterations. This shows that color refinement is easy to understand in terms of random walks, easy to implement (matrix-matrix/vector multiplications) and readily parallelizable. We support our theoretical results with experiments on real-world graphs with millions of edges.

In machine learning, linear discriminant analysis (LDA) is a popular dimension reduction method. In this paper, we first provide a new perspective of LDA from an information theory perspective. From this new perspective, we propose a new formulation of LDA, which uses the pairwise averaged class covariance instead of theglobally averaged class covariance used in standard LDA. This pairwise (averaged) covariance describes data distribution more accurately. The new perspective also provides a natural way to properly weigh different pairwise distances, which emphasizes the pairs of class with small distances, and this leads to the proposed pairwise covariance properly weighted LDA (pcLDA). The kernel version of pcLDA is presented to handle nonlinear projections. Efficient algorithms are presented to efficiently compute the proposed models.

A Simple Temporal Network with Uncertainty (STNU) is a structure for representing and reasoning about temporal constraints in domains where some temporal durations are not controlled by the executor. The most important property of an STNU is whether it is dynamically controllable (DC) whether there exists a strategy for executing the controllable time-points that guarantees that all constraints will be satisfied no matter how the uncontrollable durations turn out. This paper provides a novel mapping from STNUs to Timed Game Automata (TGAs) that: (1) explicates the deep theoretical relationships between STNUs and TGAs; and (2) enables the memoryless strategies generated from the TGA to be transformed into equivalent STNU execution strategies that reduce the real-time computational burden for the executor. The paper formally proves that the STNU-to-TGA encoding properly captures the execution semantics of STNUs.

Image-based localization is an important problem in robotics and an integral part of visual mapping and navigation systems. An approach to robustly match images to previously recorded ones must be able to cope with seasonal changes especially when it is supposed to work reliably over long periods of time. In this paper, we present a novel approach to visual localization of mobile robots in outdoor environments, which is able to deal with substantial seasonal changes. We formulate image matching as a minimum cost flow problem in a data association graph to effectively exploit sequence information. This allows us to deal with non-matching image sequences that result from temporal occlusions or from visiting new places. We present extensive experimental evaluations under substantial seasonal changes. Our approach achieves accurate matching across seasons and outperforms existing state-of-the-art methods such as FABMAP2 and SeqSLAM.

Selection bias is caused by preferential exclusion of units from the samples and represents a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can rarely be detected in either experimental or observational studies. In this paper, we provide complete graphical and algorithmic conditions for recovering conditional probabilities from selection biased data. We also provide graphical conditions for recoverability when unbiased data is available over a subset of the variables. Finally, we provide a graphical condition that generalizes the backdoor criterion and serves to recover causal effects when the data is collected under preferential selection.

We consider the problem of personalization of online services from the viewpoint of ad targeting, where we seek to find the best ad categories to be shown to each user, resulting in improved user experience and increased advertiser's revenue. We propose to address this problem as a task of ranking the ad categories depending on a user's preference, and introduce a novel label ranking approach capable of efficiently learning non-linear, highly accurate models in large-scale settings. Experiments on real-world advertising data set with more than 3.2 million users show that the proposed algorithm outperforms the existing solutions in terms of both rank loss and top-K retrieval performance, strongly suggesting the benefit of using the proposed model on large-scale ranking problems.