We are concerned with the selection of a small subset of characteristics for which the classification of a system according to one of the states in its state set is optimal according to the Rayleigh quotient criterion. This problem is relevant in various scenarios where a few explanatory variables have to be selected from a large set, including sensor selection in sensor networks, classification in image processing, and feature selection in data mining for bioinformatics applications. We show that the optimization is equivalent to finding the submatrix of the features covariance matrix for which the sum of elements of its inverse is maximized, and we present bounds related to a similar metric based on elements of the original covariance matrix.

Sensor networks measuring correlated data are considered, where the task is to gather data from the network nodes to a sink. A specific scenario is addressed, where data at nodes are lossy coded with high-resolution, and the information measured by the nodes has to be reconstructed at the sink within both certain total and individual distortion bounds. The first problem considered is to find the optimal transmission structure and the rate-distortion allocations at the various spatially located nodes, such as to minimize the total power consumption cost of the network, by assuming fixed nodes positions. The optimal transmission structure is the shortest path tree and the problems of rate and distortion allocation separate in the high-resolution case, namely, first the distortion allocation is found as a function of the transmission structure, and second, for a given distortion allocation, the rate allocation is computed. The second problem addressed is the case when the node positions can be chosen, by finding the optimal node placement for two different targets of interest, namely total power minimization and network lifetime maximization. Finally, a node placement solution that provides a tradeoff between the two metrics is proposed.

We consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use either joint entropy coding based on explicit communication between sensor nodes, where coding is done when side information is available, or Slepian-Wolf coding where nodes have knowledge of network correlation statistics. We consider both maximum and average distortion bounds. We prove that this optimization is NP-complete since it involves an interplay between the spaces of possible transmission structures given radio reachability limitations, and feasible placements satisfying distortion bounds.We address this problem by first looking at the simplified problem of optimal placement in the one-dimensional case. An analytical solution is derived for the case when there is a simple aggregation scheme, and numerical results are provided for the cases when joint entropy encoding is used. We use the insight from our 1-D analysis to extend our results to the 2-D case and compare it to typical uniform random placement and shortest-path tree. Our algorithm for two-dimensional placement and transmission structure provides two to three fold reduction in total power consumption and between one to two orders of magnitude reduction in bottleneck power consumption. We perform an exhaustive performance analysis of our scheme under varying correlation models and model parameters and demonstrate that the performance improvement is typical over a range of data correlation models and parameters. We also study the impact of performing computationally-efficient data conditioning over a local scope rather than the entire network. Finally, we extend our explicit placement results to a randomized placement scheme and show that such a scheme can be effective when deployment does not permit exact node placement.

We consider large sensor networks where the cost of collecting data from the network nodes to the data gathering sink is critical. We propose several algorithms that use limited local communication and distributed signal processing to make communication more efficient in terms of transmission cost. We consider a model that uses distributed wavelet-based signal processing. We first propose an algorithm that performs processing at nodes as data is forwarded to the sink. Then, we analyze algorithms that perform network division into groups of adaptive size and for which signal processing is applied separately to each group. We show by numerical simulations that such multiresolution approaches result in significant improvements for data gathering in terms of total communication costs.

We consider data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information, collected by the nodes, to the sink node. This problem requires a joint optimization of the data representation at the nodes and of the transmission structure. First, we study the case when the measured data are correlated random variables, both in the lossless scenario with Slepian-Wolf coding, and in the high-resolution lossy scenario with optimal rate-distortion allocation. We show that the optimal transmission structure is the shortest path tree, and we find, in closed-form, the rate and distortion allocation. Second, we study the case when the measured data are deterministic piecewise constant signals, and data is described with adaptive level wavelet-based multiresolution representation. We show experimentally that, when computation is decentralized, there is an optimal network division into node groups of adaptive size. Finally, we also analyze the node positioning problem where, given a correlation structure and an available number of sensors, the goal is to place the nodes optimally in terms of minimizing the transmission cost; our results show that important gains can be obtained compared to a uniformly distributed sensor positioning.

We consider a sensor network measuring correlated data, where the task is to gather all data from the network nodes to a sink. We consider the case where data at nodes is lossy coded with high-resolution, and the information measured by the nodes should be available at the sink within certain total and individual distortion bounds. First, we consider the problem of finding the optimal transmission structure and the rate-distortion allocations at the various spatially located nodes, such as to minimize the total power consumption cost of the network. We prove that the optimal transmission structure is the shortest path tree and that the problems of rate and distortion allocation separate in the high-resolution case, namely, we first find the distortion allocation as a function of the transmission structure, and then the rate allocation is computed. Then, we also study the case when the node positions can be chosen, by finding the optimal node placement when two different targets of interest are considered, namely total power minimization and network lifetime extension.

We consider sensor networks that measure spatio-temporal correlated processes. An important task in such settings is the reconstruction at a certain node, called the sink, of the data at all points of the field. We consider scenarios where data is time critical, so delay results in distortion, or suboptimal estimation and control. For the reconstruction, the only data available to the sink are the values measured at the nodes of the sensor network, and knowledge of the correlation structure: this results in spatial distortion of reconstruction. Also, for the sake of power efficiency, sensor nodes need to transmit their data by relaying through the other network nodes: this results in delay, and thus temporal distortion of reconstruction if time critical data is concerned. We study data gathering for the case of Gaussian processes in one- and two-dimensional grid scenarios, where we are able to write explicit expressions for the spatial and time distortion, and combine them into a single total distortion measure. We prove that, for various standard correlation structures, there is an optimal finite density of the sensor network for which the total distortion is minimized. Thus, when power efficiency and delay are both considered in data gathering, it is useless from the point of view of accuracy of the reconstruction to increase the number of sensors above a certain threshold that depends on the correlation structure characteristics.

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed.

We consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a Slepian-Wolf model where optimal coding is complex and transmission optimization is simple, and a joint entropy coding model with explicit communication where coding is simple and transmission optimization is difficult. This problem requires a joint optimization of the rate allocation at the nodes and of the transmission structure. For the Slepian-Wolf setting, we derive a closed form solution and an efficient distributed approximation algorithm with a good performance. For the explicit communication case, we prove that building an optimal data gathering tree is NP-complete and we propose various distributed approximation algorithms.

We consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use joint entropy coding based on explicit communication between sensor nodes, and consider both maximum and average distortion bounds. The optimization is complex since it involves an interplay between the spaces of possible transmission structures given radio reachability limitations, and feasible placements satisfying distortion bounds. We address this problem by first looking at the simplified problem of optimal placement in the one-dimensional case. An analytical solution is derived for the case when there is a simple aggregation scheme, and numerical results are provided for the cases when joint entropy encoding is used. We use the insight from our 1-D analysis to extend our results to the 2-D case, and show that our algorithm for two-dimensional placement and transmission structure provides significant power benefit over a commonly used combination of uniformly random placement and shortest path trees.

Consider a set of correlated sources located at the nodes of a network, and a sink to which the data from all the sources have to arrive. We address the minimization of a separable joint communication cost function given by the product [rate] o [edge weight]. We present two possible approaches for rate allocation, namely Slepian-Wolf coding, and coding by explicit communication, and compare asymptotically (large networks) the associated total costs by finding their corresponding scaling laws and analyzing the ratio between them. We also provide the specific conditions on the correlation structure which determine the different cases of asymptotic behaviors.

Distributed ways of communicating, processing, and sensing are replacing more traditional centralized architectures. An early example of this revolution in distributed communications is appearing in the form of sensor networks, which are densely distributed networks of embedded signal sensors, controls and processors. These nodes could be simple signal sensors, but could also be cameras and microphones. In this distributed scenario, there are several interesting topics to investigate that span from traditional signal processing problems (i.e. sampling, compression, detection) to communication and information theory (i.e. transmission protocols, capacity bounds for ad-hoc networks). This paper reviews some recent results on the topic of source representations and distributed source coding and transmission.

In this paper, we propose a method for estimating the fading channel coefficients of the desired user in a code-division multiple access (CDMA) system. The essential assumption made is that the transmission channel is Gaussian. An independent component analysis approach based on complexity minimization is used for separating the signal of interest. Both the time structure of the fading channel and the independence of different transmission paths are taken into account. Simulations with downlink data, propagated through a Rayleigh fading channel, shows noticeable performance gains compared to blind MMSE channel estimation.

In this paper, we propose a method for timing acquisition in a code division multiple access (CDMA) system. The assumptions made are that the data signals corresponding to different users are independent, and that a minor pilot sequence corresponding to the desired user is available. An independent component analysis (ICA) approach based on a fast fixed-point algorithm is used for simultaneous demodulation of the symbol sequence and finding of synchronisation information of the user of interest; no additional pilot signal is used for the timing acquisition. Our method shows better performance than conventional CMOE receiver and matched filter detector.

We introduce a very fast method for estimating over-complete bases of independent components from image data. This is based on the concept of quasi-orthogonality, which means that in a very high-dimensional space, there can be a large, over-complete set of vectors that are almost orthogonal to each other. Thus we may estimate an over-complete basis by using one-unit ICA algorithms and forcing only partial decorrelation between the different independent components. The method can be implemented using a modification of the FastICA algorithm, which leads to a computationally highly efficient method.