OpenRaiser/Intern-Atlas huggingface dataset:
Exact Joint Sparse Frequency Recovery via Optimization Methods
Venue: arXiv cs.IT 2016
Year: 2016

Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit signal sparsity, work directly on continuous frequencies, and completely resolve the grid mismatch problem of previous compressed sensing methods. In this work we investigate the frequency recovery problem in the presence of multiple measurement vectors (MMVs) which share the same frequency components, termed as joint sparse frequency recovery and arising naturally from array processing applications. To study the advantage of MMVs, we first propose an $\ell_{2,0}$ norm like approach by exploiting joint sparsity and show that the number of recoverable frequencies can be increased except in a trivial case. While the resulting optimization problem is shown to be rank minimization that cannot be practically solved, we then propose an MMV atomic norm approach that is a convex relaxation and can be viewed as a continuous counterpart of the $\ell_{2,1}$ norm method. We show that this MMV atomic norm approach can be solved by semidefinite programming. We also provide theoretical results showing that the frequencies can be exactly recovered under appropriate conditions. The above results either extend the MMV compressed sensing results from the discrete to the continuous setting or extend the recent super-resolution and continuous compressed sensing framework from the single to the multiple measurement vectors case. Extensive simulation results are provided to validate our theoretical findings and they also imply that the proposed MMV atomic norm approach can improve the performance in terms of reduced number of required measurements and/or relaxed frequency separation condition.
Log-Euclidean Bag of Words for Human Action Recognition
Venue: arXiv cs.CV 2016
Year: 2016

Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this paper, we tackle the problem of categorising human actions by devising Bag of Words (BoW) models based on covariance matrices of spatio-temporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of Symmetric Positive Definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, we propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison to several state-of-the-art methods.
Selecting interesting zones at Aburrá valley and St. Nicholas Valley's using the identification method of Density-based Clustering and Improved Nearest Neighbor applied on social networks
Venue: arXiv cs.CY 2016
Year: 2016

More than ever, social networks have become an important place in the interaction and behaviour of humans in the last decade. This valuable position makes it imperative to analyze different aspects of everyday life and science in general. This paper illustrates the process of capturing and storing information, the application of density-based clustering and improved nearest neighbor, and a review of the results. The study also shows the elements used in the identification of areas of interest through clusters, circumferences and coverage radii obtained for a demographic segmentation analysis of the information procured from Twitter, Flickr and the like. This results in more profound conclusions about a predefined topic or theme. Finally, the need arises to develop an application that makes all the defined process automatic, allowing final users interested in those topics to have access to it and get important results for their organizations or interest.
PlanIt: A Crowdsourcing Approach for Learning to Plan Paths from Large Scale Preference Feedback
Venue: arXiv cs.RO 2016
Year: 2016

We consider the problem of learning user preferences over robot trajectories for environments rich in objects and humans. This is challenging because the criterion defining a good trajectory varies with users, tasks and interactions in the environment. We represent trajectory preferences using a cost function that the robot learns and uses it to generate good trajectories in new environments. We design a crowdsourcing system - PlanIt, where non-expert users label segments of the robot's trajectory. PlanIt allows us to collect a large amount of user feedback, and using the weak and noisy labels from PlanIt we learn the parameters of our model. We test our approach on 122 different environments for robotic navigation and manipulation tasks. Our extensive experiments show that the learned cost function generates preferred trajectories in human environments. Our crowdsourcing system is publicly available for the visualization of the learned costs and for providing preference feedback: \url{http://planit.cs.cornell.edu}
Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems
Venue: arXiv cs.IT 2016
Year: 2016

The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: Any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a WiFi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years, as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for 5G networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency, lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence and tradeoffs between multiple objectives. In this article, we provide a review of multi-objective optimization (MOO), which is a mathematical framework to solve design problems with multiple conflicting objectives. (...) We provide a survey of the basic definitions, properties, and algorithmic tools in MOO. This reveals how signal processing algorithms are used to visualize the inherent conflicts between 5G performance objectives, thereby allowing the network designer to understand the possible operating points and how to balance the objectives in an efficient and satisfactory way. For clarity, we provide a case study on massive MIMO.
Ergodic Theory Meets Polarization. II: A Foundation of Polarization Theory
Venue: arXiv cs.IT 2016
Year: 2016

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arıkan style constructions. This paper, which is presented in two parts, solves this problem by providing a necessary and sufficient condition for a binary operation to be polarizing. This (second) part provides a foundation of polarization theory based on the ergodic theory of binary operations which we developed in the first part. We show that a binary operation is polarizing if and only if it is uniformity preserving and its right-inverse is strongly ergodic. The rate of polarization of single user channels is studied. It is shown that the exponent of any polarizing operation cannot exceed $\frac{1}{2}$, which is the exponent of quasigroup operations. We also study the polarization of multiple access channels (MAC). In particular, we show that a sequence of binary operations is MAC-polarizing if and only if each binary operation in the sequence is polarizing. It is shown that the exponent of any MAC-polarizing sequence cannot exceed $\frac{1}{2}$, which is the exponent of sequences of quasigroup operations.
Three Datatype Defining Rewrite Systems for Datatypes of Integers each extending a Datatype of Naturals
Venue: arXiv cs.LO 2016
Year: 2016

Integer arithmetic is specified according to three views: unary, binary, and decimal notation. The binary and decimal view have as their characteristic that each normal form resembles common number notation, that is, either a digit, or a string of digits without leading zero, or the negated versions of the latter. The unary view comprises a specification of integer arithmetic based on 0, successor function $S$, and predecessor function, with negative normal forms $-S^i(0)$. Integer arithmetic in binary and decimal notation is based on (postfix) digit append functions. For each view we define a ground-confluent and terminating datatype defining rewrite system (DDRS), and in each case the resulting datatype is a canonical term algebra that extends a corresponding canonical term algebra for natural numbers. Then, for each view, we consider an alternative DDRS based on tree constructors that yield comparable normal forms, which for that binary and decimal view admits expressions that are algorithmically more involved. These DDRSes are incorporated because they are closer to existing literature. For these DDRSes we also provide ground-completeness results. Finally, we define a DDRS for the ring of Integers (comprising fifteen rewrite rules) and prove its ground-completeness.
Identifying roles in an IP network with temporal and structural density
Venue: arXiv cs.NI 2016
Year: 2016

Captures of IP traffic contain much information on very different kinds of activities like file transfers, users interacting with remote systems, automatic backups, or distributed computations. Identifying such activities is crucial for an appropriate analysis, modeling and monitoring of the traffic. We propose here a notion of density that captures both temporal and structural features of interactions, and generalizes the classical notion of clustering coefficient. We use it to point out important differences between distinct parts of the traffic, and to identify interesting nodes and groups of nodes in terms of roles in the network.
Blind Sensor Calibration using Approximate Message Passing
Venue: arXiv cs.IT 2016
Year: 2016

The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them on real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal ac- quisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measures. Cal-AMP shares the scalability of approximate message passing, allowing to treat big sized instances of these problems, and ex- perimentally exhibits a phase transition between domains of success and failure.
Fast, Robust and Non-convex Subspace Recovery
Venue: arXiv cs.LG 2016
Year: 2016

This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of outliers that do not lie nearby this subspace. The proposed algorithm, which we refer to as Fast Median Subspace (FMS), is designed to robustly determine the underlying subspace of such data sets, while having lower computational complexity than existing methods. We prove convergence of the FMS iterates to a stationary point. Further, under a special model of data, FMS converges to a point which is near to the global minimum with overwhelming probability. Under this model, we show that the iteration complexity is globally bounded and locally $r$-linear. The latter theorem holds for any fixed fraction of outliers (less than 1) and any fixed positive distance between the limit point and the global minimum. Numerical experiments on synthetic and real data demonstrate its competitive speed and accuracy.
Rateless Lossy Compression via the Extremes
Venue: arXiv cs.IT 2016
Year: 2016

We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components based on this information. This scheme turns out to be near-optimal for the memoryless Gaussian source in the sense of achieving the zero-rate slope of its distortion-rate function. Motivated by this finding, we then propose a scheme comprised of iterating the above lossy compressor on an appropriately transformed version of the difference between the source and its reconstruction from the previous iteration. The proposed scheme achieves the rate distortion function of the Gaussian memoryless source (under squared error distortion) when employed on any finite-variance ergodic source. It further possesses desirable properties we respectively refer to as infinitesimal successive refinability, ratelessness, and complete separability. Its storage and computation requirements are of order no more than $\frac{n^2}{\log^β n}$ per source symbol for $β>0$ at both the encoder and decoder. Though the details of its derivation, construction, and analysis differ considerably, we discuss similarities between the proposed scheme and the recently introduced Sparse Regression Codes (SPARC) of Venkataramanan et al.
Minimax rates of entropy estimation on large alphabets via best polynomial approximation
Venue: arXiv cs.IT 2016
Year: 2016

Consider the problem of estimating the Shannon entropy of a distribution over $k$ elements from $n$ independent samples. We show that the minimax mean-square error is within universal multiplicative constant factors of $$\Big(\frac{k }{n \log k}\Big)^2 + \frac{\log^2 k}{n}$$ if $n$ exceeds a constant factor of $\frac{k}{\log k}$; otherwise there exists no consistent estimator. This refines the recent result of Valiant-Valiant \cite{VV11} that the minimal sample size for consistent entropy estimation scales according to $Θ(\frac{k}{\log k})$. The apparatus of best polynomial approximation plays a key role in both the construction of optimal estimators and, via a duality argument, the minimax lower bound.
Near-Linear Time Constant-Factor Approximation Algorithm for Branch-Decomposition of Planar Graphs
Venue: arXiv cs.DS 2016
Year: 2016

We give an algorithm which for an input planar graph $G$ of $n$ vertices and integer $k$, in $\min\{O(n\log^3n),O(nk^2)\}$ time either constructs a branch-decomposition of $G$ with width at most $(2+δ)k$, $δ>0$ is a constant, or a $(k+1)\times \lceil{\frac{k+1}{2}\rceil}$ cylinder minor of $G$ implying $bw(G)>k$, $bw(G)$ is the branchwidth of $G$. This is the first $\tilde{O}(n)$ time constant-factor approximation for branchwidth/treewidth and largest grid/cylinder minors of planar graphs and improves the previous $\min\{O(n^{1+ε}),O(nk^2)\}$ ($ε>0$ is a constant) time constant-factor approximations. For a planar graph $G$ and $k=bw(G)$, a branch-decomposition of width at most $(2+δ)k$ and a $g\times \frac{g}{2}$ cylinder/grid minor with $g=\frac{k}β$, $β>2$ is constant, can be computed by our algorithm in $\min\{O(n\log^3n\log k),O(nk^2\log k)\}$ time.
An Alternating Direction Method Approach to Cloud Traffic Management
Venue: arXiv cs.NI 2016
Year: 2016

In this paper, we introduce a unified framework for studying various cloud traffic management problems, ranging from geographical load balancing to backbone traffic engineering. We first abstract these real-world problems as a multi-facility resource allocation problem, and then present two distributed optimization algorithms by exploiting the special structure of the problem. Our algorithms are inspired by Alternating Direction Method of Multipliers (ADMM), enjoying a number of unique features. Compared to dual decomposition, they converge with non-strictly convex objective functions; compared to other ADMM-type algorithms, they not only achieve faster convergence under weaker assumptions, but also have lower computational complexity and lower message-passing overhead. The simulation results not only confirm these desirable features of our algorithms, but also highlight several additional advantages, such as scalability and fault-tolerance.
A Blind Adaptive CDMA Receiver Based on State Space Structures
Venue: arXiv cs.IT 2016
Year: 2016

Code Division Multiple Access (CDMA) is a channel access method, based on spread-spectrum technology, used by various radio technologies world-wide. In general, CDMA is used as an access method in many mobile standards such as CDMA2000 and WCDMA. We address the problem of blind multiuser equalization in the wideband CDMA system, in the noisy multipath propagation environment. Herein, we propose three new blind receiver schemes, which are based on state space structures and Independent Component Analysis (ICA). These blind state-space receivers (BSSR) do not require knowledge of the propagation parameters or spreading code sequences of the users they primarily exploit the natural assumption of statistical independence among the source signals. We also develop three semi blind adaptive detectors by incorporating the new adaptive methods into the standard RAKE receiver structure. Extensive comparative case study, based on Bit error rate (BER) performance of these methods, is carried out for different number of users, symbols per user, and signal to noise ratio (SNR) in comparison with conventional detectors, including the Blind Multiuser Detectors (BMUD) and Linear Minimum mean squared error (LMMSE). The results show that the proposed methods outperform the other detectors in estimating the symbol signals from the received mixed CDMA signals. Moreover, the new blind detectors mitigate the multi access interference (MAI) in CDMA.
Non-hierarchical Structures: How to Model and Index Overlaps?
Venue: arXiv cs.DB 2016
Year: 2016

Overlap is a common phenomenon seen when structural components of a digital object are neither disjoint nor nested inside each other. Overlapping components resist reduction to a structural hierarchy, and tree-based indexing and query processing techniques cannot be used for them. Our solution to this data modeling problem is TGSA (Tree-like Graph for Structural Annotations), a novel extension of the XML data model for non-hierarchical structures. We introduce an algorithm for constructing TGSA from annotated documents; the algorithm can efficiently process non-hierarchical structures and is associated with formal proofs, ensuring that transformation of the document to the data model is valid. To enable high performance query analysis in large data repositories, we further introduce an extension of XML pre-post indexing for non-hierarchical structures, which can process both reachability and overlapping relationships.
A Parallel Algorithm for Exact Bayesian Structure Discovery in Bayesian Networks
Venue: arXiv cs.AI 2016
Year: 2016

Exact Bayesian structure discovery in Bayesian networks requires exponential time and space. Using dynamic programming (DP), the fastest known sequential algorithm computes the exact posterior probabilities of structural features in $O(2(d+1)n2^n)$ time and space, if the number of nodes (variables) in the Bayesian network is $n$ and the in-degree (the number of parents) per node is bounded by a constant $d$. Here we present a parallel algorithm capable of computing the exact posterior probabilities for all $n(n-1)$ edges with optimal parallel space efficiency and nearly optimal parallel time efficiency. That is, if $p=2^k$ processors are used, the run-time reduces to $O(5(d+1)n2^{n-k}+k(n-k)^d)$ and the space usage becomes $O(n2^{n-k})$ per processor. Our algorithm is based the observation that the subproblems in the sequential DP algorithm constitute a $n$-$D$ hypercube. We take a delicate way to coordinate the computation of correlated DP procedures such that large amount of data exchange is suppressed. Further, we develop parallel techniques for two variants of the well-known \emph{zeta transform}, which have applications outside the context of Bayesian networks. We demonstrate the capability of our algorithm on datasets with up to 33 variables and its scalability on up to 2048 processors. We apply our algorithm to a biological data set for discovering the yeast pheromone response pathways.
Co-Localization of Audio Sources in Images Using Binaural Features and Locally-Linear Regression
Venue: arXiv cs.SD 2016
Year: 2016

This paper addresses the problem of localizing audio sources using binaural measurements. We propose a supervised formulation that simultaneously localizes multiple sources at different locations. The approach is intrinsically efficient because, contrary to prior work, it relies neither on source separation, nor on monaural segregation. The method starts with a training stage that establishes a locally-linear Gaussian regression model between the directional coordinates of all the sources and the auditory features extracted from binaural measurements. While fixed-length wide-spectrum sounds (white noise) are used for training to reliably estimate the model parameters, we show that the testing (localization) can be extended to variable-length sparse-spectrum sounds (such as speech), thus enabling a wide range of realistic applications. Indeed, we demonstrate that the method can be used for audio-visual fusion, namely to map speech signals onto images and hence to spatially align the audio and visual modalities, thus enabling to discriminate between speaking and non-speaking faces. We release a novel corpus of real-room recordings that allow quantitative evaluation of the co-localization method in the presence of one or two sound sources. Experiments demonstrate increased accuracy and speed relative to several state-of-the-art methods.