OpenRaiser/Intern-Atlas huggingface dataset:
Solving Graph Coloring Problems with Abstraction and Symmetry
Venue: arXiv cs.AI 2015
Year: 2015

This paper introduces a general methodology, based on abstraction and symmetry, that applies to solve hard graph edge-coloring problems and demonstrates its use to provide further evidence that the Ramsey number $R(4,3,3)=30$. The number $R(4,3,3)$ is often presented as the unknown Ramsey number with the best chances of being found "soon". Yet, its precise value has remained unknown for more than 50 years. We illustrate our approach by showing that: (1) there are precisely 78{,}892 $(3,3,3;13)$ Ramsey colorings; and (2) if there exists a $(4,3,3;30)$ Ramsey coloring then it is (13,8,8) regular. Specifically each node has 13 edges in the first color, 8 in the second, and 8 in the third. We conjecture that these two results will help provide a proof that no $(4,3,3;30)$ Ramsey coloring exists implying that $R(4,3,3)=30$.
User-Base Station Association in HetSNets: Complexity and Efficient Algorithms
Venue: arXiv cs.NI 2015
Year: 2015

This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under signal-to-interference-plus-noise ratio (SINR) constraints. Both problems are formulated as linear integer programs. The weighted problem is known to be NP-hard and, in this paper, the unweighted problem is proved to be NP-hard as well. Therefore, this paper develops two heuristic polynomial-time algorithms to solve both problems. The computational complexity of the proposed algorithms is evaluated and is shown to be far more efficient than the complexity of the optimal brute-force (BF) algorithm. Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B\&B) algorithm and standard algorithms, through numerical simulations. The results demonstrate the close-to-optimal performance of the proposed algorithms. They also show that the weighted problem can be solved to provide solutions that are fair between users or to balance the load among SBSs.
Evidence for a creative dilemma posed by repeated collaborations
Venue: arXiv cs.SI 2015
Year: 2015

We focused on how repeat collaborations in projects for inventions affect performance. Repeat collaborations have two contradictory aspects. A positive aspect is team development or experience, and a negative aspect is team degeneration or decline. Since both contradicting phenomena are observed, inventors have a dilemma as to whether they should keep collaborating in a team or not. The dilemma has not previously been quantitatively analyzed. We provide quantitative and extensive analyses of the dilemma in creative projects by using patent data from Japan and the United States. We confirm three predictions to quantitatively validate the existence of the dilemma. The first prediction is that the greater the patent a team achieves, the longer the team will work together. The second prediction is that the impact of consecutive patents decreases after a team makes a remarkable invention, which is measured by the impact of patents. The third prediction is that the expectation of impact with new teams is greater than that with the same teams successful in the past. We find these predictions are validated in patents published in Japan and the United States. On the basis of these three predictions, we can quantitatively validate the dilemma in creative projects. We also propose preventive strategies for degeneration. One is developing technological diversity, and another is developing inventor diversity in teams.We find the two strategies are both effective by validating with the data.
Document Counting in Practice
Venue: arXiv cs.DS 2015
Year: 2015

We address the problem of counting the number of strings in a collection where a given pattern appears, which has applications in information retrieval and data mining. Existing solutions are in a theoretical stage. We implement these solutions and develop some new variants, comparing them experimentally on various datasets. Our results not only show which are the best options for each situation and help discard practically unappealing solutions, but also uncover some unexpected compressibility properties of the best data structures. By taking advantage of these properties, we can reduce the size of the structures by a factor of 5--400, depending on the dataset.
Histogram of Oriented Principal Components for Cross-View Action Recognition
Venue: arXiv cs.CV 2015
Year: 2015

Existing techniques for 3D action recognition are sensitive to viewpoint variations because they extract features from depth images which are viewpoint dependent. In contrast, we directly process pointclouds for cross-view action recognition from unknown and unseen views. We propose the Histogram of Oriented Principal Components (HOPC) descriptor that is robust to noise, viewpoint, scale and action speed variations. At a 3D point, HOPC is computed by projecting the three scaled eigenvectors of the pointcloud within its local spatio-temporal support volume onto the vertices of a regular dodecahedron. HOPC is also used for the detection of Spatio-Temporal Keypoints (STK) in 3D pointcloud sequences so that view-invariant STK descriptors (or Local HOPC descriptors) at these key locations only are used for action recognition. We also propose a global descriptor computed from the normalized spatio-temporal distribution of STKs in 4-D, which we refer to as STK-D. We have evaluated the performance of our proposed descriptors against nine existing techniques on two cross-view and three single-view human action recognition datasets. The Experimental results show that our techniques provide significant improvement over state-of-the-art methods.
Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem
Venue: arXiv cs.AI 2015
Year: 2015

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison.
Hybrid Channel Pre-Inversion and Interference Alignment Strategies
Venue: arXiv cs.IT 2015
Year: 2015

In this paper we consider strategies for MIMO interference channels which combine the notions of interference alignment and channel pre-inversion. Users collaborate to form data-sharing groups, enabling them to clear interference within a group, while interference alignment is employed to clear interference between groups. To improve the capacity of our schemes at finite SNR, we propose that the groups of users invert their subchannel using a regularized Tikhonov inverse. We provide a new sleeker derivation of the optimal Tikhonov parameter, and use random matrix theory to provide an explicit formula for the SINR as the size of the system increases, which we believe is a new result. For every possible grouping of K = 4 users each with N = 5 antennas, we completely classify the degrees of freedom available to each user when using such hybrid schemes, and construct explicit interference alignment strategies which maximize the sum DoF. Lastly, we provide simulation results which compute the ergodic capacity of such schemes.
Generalized Twin Gaussian Processes using Sharma-Mittal Divergence
Venue: arXiv cs.LG 2015
Year: 2015

There has been a growing interest in mutual information measures due to their wide range of applications in Machine Learning and Computer Vision. In this paper, we present a generalized structured regression framework based on Shama-Mittal divergence, a relative entropy measure, which is introduced to the Machine Learning community in this work. Sharma-Mittal (SM) divergence is a generalized mutual information measure for the widely used Rényi, Tsallis, Bhattacharyya, and Kullback-Leibler (KL) relative entropies. Specifically, we study Sharma-Mittal divergence as a cost function in the context of the Twin Gaussian Processes (TGP)~\citep{Bo:2010}, which generalizes over the KL-divergence without computational penalty. We show interesting properties of Sharma-Mittal TGP (SMTGP) through a theoretical analysis, which covers missing insights in the traditional TGP formulation. However, we generalize this theory based on SM-divergence instead of KL-divergence which is a special case. Experimentally, we evaluated the proposed SMTGP framework on several datasets. The results show that SMTGP reaches better predictions than KL-based TGP, since it offers a bigger class of models through its parameters that we learn from the data.
Large-scale Online Feature Selection for Ultra-high Dimensional Sparse Data
Venue: arXiv cs.LG 2015
Year: 2015

Feature selection with large-scale high-dimensional data is important yet very challenging in machine learning and data mining. Online feature selection is a promising new paradigm that is more efficient and scalable than batch feature section methods, but the existing online approaches usually fall short in their inferior efficacy as compared with batch approaches. In this paper, we present a novel second-order online feature selection scheme that is simple yet effective, very fast and extremely scalable to deal with large-scale ultra-high dimensional sparse data streams. The basic idea is to improve the existing first-order online feature selection methods by exploiting second-order information for choosing the subset of important features with high confidence weights. However, unlike many second-order learning methods that often suffer from extra high computational cost, we devise a novel smart algorithm for second-order online feature selection using a MaxHeap-based approach, which is not only more effective than the existing first-order approaches, but also significantly more efficient and scalable for large-scale feature selection with ultra-high dimensional sparse data, as validated from our extensive experiments. Impressively, on a billion-scale synthetic dataset (1-billion dimensions, 1-billion nonzero features, and 1-million samples), our new algorithm took only 8 minutes on a single PC, which is orders of magnitudes faster than traditional batch approaches. \url{http://arxiv.org/abs/1409.7794}
10-Gabriel graphs are Hamiltonian
Venue: arXiv cs.CG 2015
Year: 2015

Given a set $S$ of points in the plane, the $k$-Gabriel graph of $S$ is the geometric graph with vertex set $S$, where $p_i,p_j\in S$ are connected by an edge if and only if the closed disk having segment $\bar{p_ip_j}$ as diameter contains at most $k$ points of $S \setminus \{p_i,p_j\}$. We consider the following question: What is the minimum value of $k$ such that the $k$-Gabriel graph of every point set $S$ contains a Hamiltonian cycle? For this value, we give an upper bound of 10 and a lower bound of 2. The best previously known values were 15 and 1, respectively.
$\ell_1$-K-SVD: A Robust Dictionary Learning Algorithm With Simultaneous Update
Venue: arXiv cs.CV 2015
Year: 2015

We develop a dictionary learning algorithm by minimizing the $\ell_1$ distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization of weighted $\ell_2$ error. We refer to this algorithm as $\ell_1$-K-SVD, where the dictionary atoms and the corresponding sparse coefficients are simultaneously updated to minimize the $\ell_1$ objective, resulting in noise-robustness. We demonstrate through experiments that the $\ell_1$-K-SVD algorithm results in higher atom recovery rate compared with the K-SVD and the robust dictionary learning (RDL) algorithm proposed by Lu et al., both in Gaussian and non-Gaussian noise conditions. We also show that, for fixed values of sparsity, number of dictionary atoms, and data-dimension, the $\ell_1$-K-SVD algorithm outperforms the K-SVD and RDL algorithms when the training set available is small. We apply the proposed algorithm for denoising natural images corrupted by additive Gaussian and Laplacian noise. The images denoised using $\ell_1$-K-SVD are observed to have slightly higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise, but the improvement in structural similarity index (SSIM) is significant (approximately $0.1$) for lower values of input PSNR, indicating the efficacy of the $\ell_1$ metric.
An Algorithmic Metatheorem for Directed Treewidth
Venue: arXiv cs.DS 2015
Year: 2015

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some NP-complete properties such as Hamiltonicity can be decided in polynomial time on digraphs of constant directed treewidth. Nevertheless, despite more than one decade of intensive research, the list of hard combinatorial problems that are known to be solvable in polynomial time when restricted to digraphs of constant directed treewidth has remained scarce. In this work we enrich this list by providing for the first time an algorithmic metatheorem connecting the monadic second order logic of graphs to directed treewidth. We show that most of the known positive algorithmic results for digraphs of constant directed treewidth can be reformulated in terms of our metatheorem. Additionally, we show how to use our metatheorem to provide polynomial time algorithms for two classes of combinatorial problems that have not yet been studied in the context of directed width measures. More precisely, for each fixed $k,w \in \mathbb{N}$, we show how to count in polynomial time on digraphs of directed treewidth $w$, the number of minimum spanning strong subgraphs that are the union of $k$ directed paths, and the number of maximal subgraphs that are the union of $k$ directed paths and satisfy a given minor closed property. To prove our metatheorem we devise two technical tools which we believe to be of independent interest. First, we introduce the notion of tree-zig-zag number of a digraph, a new directed width measure that is at most a constant times directed treewidth. Second, we introduce the notion of $z$-saturated tree slice language, a new formalism for the specification and manipulation of infinite sets of digraphs.
Theoretical Analysis of Radiative Cooling for Mobile and Embedded Systems
Venue: arXiv cs.OH 2015
Year: 2015

A new global analytical model of the heat dissipation process that occurs in passively-cooled embedded systems is introduced, and we explicit under what circumstances the traditional assumption that exponential cooling laws apply in such context is valid. Since the power consumption and reliability of microprocessors are highly dependent on temperature, management units need accurate thermal models. Exponential cooling models are justified for actively-cooled systems. Here, we analyze the tractability of the cooling law for a passively cooled body, subject to radiative and convective cooling, including internal heat generation. Focusing then on embedded system-like objects, we compare the performance difference between our new passive cooling law and the conventionally-used exponential one. We show that, for quasi isothermal cooling surfaces of the order of 1\,dm$^2$ or greater, the radiative cooling effect may become comparable to the convective cooling one. In other words, radiation becomes non-negligible for systems with a cooling surface larger than about 1\,dm$^2$. Otherwise for surfaces below 1\,dm$^2$, we show that the differences between the exact solution and the exponential cooling law becomes negligible. In the absence of accurate temperature measurements, an exponential cooling model is shown to be accurate enough for systems, such as small-sized SoCs, that require low processing overhead.
Structural operational semantics for non-deterministic processes with quantitative aspects
Venue: arXiv cs.LO 2015
Year: 2015

General frameworks have been recently proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format and a corresponding notion of bisimulation for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function GSOS (WF-GSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness and completeness of the WF-GSOS specification format, and that bisimilarities induced by these specifications are always congruences.
On Transmit Beamforming for MISO-OFDM Channels With Finite-Rate Feedback
Venue: arXiv cs.IT 2015
Year: 2015

With finite-rate feedback, we propose two feedback methods for transmit beamforming in a point-to-point MISO-OFDM channel. For the first method, a receiver with perfect channel information, quantizes and feeds back the optimal transmit beamforming vectors of a few selected subcarriers, which are equally spaced. Based on those quantized vectors, the transmitter applies either constant, linear, or higher-order interpolation with the remaining beamforming vectors. With constant interpolation, we derive the approximate sum achievable rate and the optimal cluster size that maximizes the approximate rate. For linear interpolation, we derive a closed-form expression for the phase rotation by utilizing the correlation between OFDM subcarriers. We also propose a higher-order interpolation that requires more than two quantized vectors to interpolate transmit beamformers, and is based on existing channel estimation methods. Numerical results show that interpolation with the optimized cluster size can perform significantly better than that with an arbitrary cluster size. For the second proposed method, a channel impulse response is quantized with a uniform scalar quantizer. With channel quantization, we also derive the approximate sum achievable rate. We show that switching between the two methods for different feedback-rate requirements can perform better than the existing schemes.
Minimization Problems Based on Relative $α$-Entropy I: Forward Projection
Venue: arXiv cs.IT 2015
Year: 2015

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $α$-entropies (denoted $\mathscr{I}_α$), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative $α$-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative $α$-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Rényi or Tsallis entropy principle. The minimizing probability distribution (termed forward $\mathscr{I}_α$-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse $\mathscr{I}_α$-projection is studied.
Local-set-based Graph Signal Reconstruction
Venue: arXiv cs.IT 2015
Year: 2015

Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of the graph signal. In this paper, the concept of local set is introduced and two local-set-based iterative methods are proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, one of the proposed methods reweights the sampled residuals for different vertices, while the other propagates the sampled residuals in their respective local sets. These algorithms are built on frame theory and the concept of local sets, based on which several frames and contraction operators are proposed. We then prove that the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a significantly faster convergence compared with the baseline method. Furthermore, the correspondence between graph signal sampling and time-domain irregular sampling is analyzed comprehensively, which may be helpful to future works on graph signals. Computer simulations are conducted. The experimental results demonstrate the effectiveness of the reconstruction methods in various sampling geometries, imprecise priori knowledge of cutoff frequency, and noisy scenarios.
Multi-Level Anomaly Detection on Time-Varying Graph Data
Venue: arXiv cs.SI 2015
Year: 2015

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer levels, and these closely related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. To illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.