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Low power sparse polynomial equalizer (SPEQ) for nonlinear digital compensation of an active anti-alias filter

Published in:
Proc. 2012 IEEE Workshop on Signal Processing Systems, 17-19 October 2012, pp. 249-253.

Summary

We present an efficient architecture to perform on-chip nonlinear equalization of an anti-alias RF filter. The sparse polynomial equalizer (SPEq) achieves substantial power savings through co-design of the equalizer and the filter, which allows including the right number of processing elements, filter taps, and bits to maximize performance and minimize power consumption. The architecture was implemented in VHDL and fabricated in CMOS 65 nm technology. Testing results show that undesired spurs are suppressed to near the noise floor, improving the system's spur-free dynamic range by 25 dB in the median case, and consuming less than 12 mW of core power when operating at 200 MHz.
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Summary

We present an efficient architecture to perform on-chip nonlinear equalization of an anti-alias RF filter. The sparse polynomial equalizer (SPEq) achieves substantial power savings through co-design of the equalizer and the filter, which allows including the right number of processing elements, filter taps, and bits to maximize performance and minimize...

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Benchmarking parallel eigen decomposition for residuals analysis of very large graphs

Published in:
HPEC 2012: IEEE Conf. on High Performance Extreme Computing, 10-12 September 2012.

Summary

Graph analysis is used in many domains, from the social sciences to physics and engineering. The computational driver for one important class of graph analysis algorithms is the computation of leading eigenvectors of matrix representations of a graph. This paper explores the computational implications of performing an eigen decomposition of a directed graph's symmetrized modularity matrix using commodity cluster hardware and freely available eigensolver software, for graphs with 1 million to 1 billion vertices, and 8 million to 8 billion edges. Working with graphs of these sizes, parallel eigensolvers are of particular interest. Our results suggest that graph analysis approaches based on eigen space analysis of graph residuals are feasible even for graphs of these sizes.
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Summary

Graph analysis is used in many domains, from the social sciences to physics and engineering. The computational driver for one important class of graph analysis algorithms is the computation of leading eigenvectors of matrix representations of a graph. This paper explores the computational implications of performing an eigen decomposition of...

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Toward matched filter optimization for subgraph detection in dynamic networks

Published in:
2012 SSP: 2012 IEEE Statistical Signal Processing Workshop, 5-8 August 2012, pp. 113-116.

Summary

This paper outlines techniques for optimization of filter coefficients in a spectral framework for anomalous subgraph detection. Restricting the scope to the detection of a known signal in i.i.d. noise, the optimal coefficients for maximizing the signal's power are shown to be found via a rank-1 tensor approximation of the subgraph's dynamic topology. While this technique optimizes our power metric, a filter based on average degree is shown in simulation to work nearly as well in terms of power maximization and detection performance, and better separates the signal from the noise in the eigenspace.
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Summary

This paper outlines techniques for optimization of filter coefficients in a spectral framework for anomalous subgraph detection. Restricting the scope to the detection of a known signal in i.i.d. noise, the optimal coefficients for maximizing the signal's power are shown to be found via a rank-1 tensor approximation of the...

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A stochastic system for large network growth

Published in:
IEEE Signal Process. Lett., Vol. 19, No. 6, June 2012, pp. 356-359.

Summary

This letter proposes a new model for preferential attachment in dynamic directed networks. This model consists of a linear time-invariant system that uses past observations to predict future attachment rates, and an innovation noise process that induces growth on vertices that previously had no attachments. Analyzing a large citation network in this context, we show that the proposed model fits the data better than existing preferential attachment models. An analysis of the noise in the dataset reveals power-law degree distributions often seen in large networks, and polynomial decay with respect to age in the probability of citing yet-uncited documents.
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Summary

This letter proposes a new model for preferential attachment in dynamic directed networks. This model consists of a linear time-invariant system that uses past observations to predict future attachment rates, and an innovation noise process that induces growth on vertices that previously had no attachments. Analyzing a large citation network...

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A scalable signal processing architecture for massive graph analysis

Published in:
ICASSP 2012, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 25-30 March 2012, pp. 5329-32.

Summary

In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the entire processing chain, from data storage to graph construction to graph analysis and subgraph detection. The data are stored in a new format that allows easy extraction of graphs representing any relationship existing in the data. The principal analysis algorithm is the partial eigendecomposition of the modularity matrix, whose running time is discussed. A large document dataset is analyzed, and we present subgraphs that stand out in the principal eigenspace of the time varying graphs, including behavior we regard as clutter as well as small, tightly-connected clusters that emerge over time.
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Summary

In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the...

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Goodness-of-fit statistics for anomaly detection in Chung-Lu random graphs

Published in:
ICASSP 2012, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 25-30 March 2012, pp. 3265-8.

Summary

Anomaly detection in graphs is a relevant problem in numerous applications. When determining whether an observation is anomalous with respect to the model of typical behavior, the notion of "goodness of fit" is important. This notion, however, is not well understood in the context of graph data. In this paper, we propose three goodness-of-fit statistics for Chung-Lu random graphs, and analyze their efficacy in discriminating graphs generated by the Chung-Lu model from those with anomalous topologies. In the results of a Monte Carlo simulation, we see that the most powerful statistic for anomaly detection depends on the type of anomaly, suggesting that a hybrid statistic would be the most powerful.
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Summary

Anomaly detection in graphs is a relevant problem in numerous applications. When determining whether an observation is anomalous with respect to the model of typical behavior, the notion of "goodness of fit" is important. This notion, however, is not well understood in the context of graph data. In this paper...

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Moments of parameter estimates for Chung-Lu random graph models

Published in:
ICASSP 2012, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 25-30 March 2012, pp. 3961-4.

Summary

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non- Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung- Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.
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Summary

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non- Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One...

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On-chip nonlinear digital compensation for RF receiver

Published in:
HPEC 2011: Conf. on High Performance Embedded Computing, 21-22 September 2011.

Summary

A system-on-chip (SOC) implementation is an attractive solution for size, weight and power (SWaP) restricted applications, such as mobile devices and UAVs. This is partly because the individual parts of the system can be designed for a specific application rather than for a broad range of them, like commercial parts usually must be. Co-design of the analog hardware and digital processing further enhances the benefits of SOC implementations by allowing, for example, nonlinear digital equalization to further enhance the dynamic range of a given front-end component. This paper presents the implementation of nonlinear digital compensation for an active anti-aliasing filter, which is part of a low-power homodyne receiver design. The RF front-end circuitry and the digital compensation will be integrated in the same chip. Co-design allows the front-end to be designed with known dynamic range limitations that will later be compensated by nonlinear equalization. It also allows nonlinear digital compensation architectures matched to specific circuits and dynamic range requirements--while still maintaining some flexibility to deal with process variation--as opposed to higher power general purpose designs.
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Summary

A system-on-chip (SOC) implementation is an attractive solution for size, weight and power (SWaP) restricted applications, such as mobile devices and UAVs. This is partly because the individual parts of the system can be designed for a specific application rather than for a broad range of them, like commercial parts...

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Eigenspace analysis for threat detection in social networks

Published in:
Int. Conf. on Information Fusion, 5 July 2011.

Summary

The problem of detecting a small, anomalous subgraph within a large background network is important and applicable to many fields. The non-Euclidean nature of graph data, however, complicates the application of classical detection theory in this context. A recent statistical framework for anomalous subgraph detection uses spectral properties of a graph's modularity matrix to determine the presence of an anomaly. In this paper, this detection framework and the related algorithms are applied to data focused on a specific application: detection of a threat subgraph embedded in a social network. The results presented use data created to simulate threat activity among noisy interactions. The detectability of the threat subgraph and its separability from the noise is analyzed under a variety of background conditions in both static and dynamic scenarios.
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Summary

The problem of detecting a small, anomalous subgraph within a large background network is important and applicable to many fields. The non-Euclidean nature of graph data, however, complicates the application of classical detection theory in this context. A recent statistical framework for anomalous subgraph detection uses spectral properties of a...

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Anomalous subgraph detection via sparse principal component analysis

Published in:
Proc. 2011 IEEE Statistical Signal Processing Workshop (SSP), 28-30 June 2011, pp. 485-488.

Summary

Network datasets have become ubiquitous in many fields of study in recent years. In this paper we investigate a problem with applicability to a wide variety of domains - detecting small, anomalous subgraphs in a background graph. We characterize the anomaly in a subgraph via the well-known notion of network modularity, and we show that the optimization problem formulation resulting from our setup is very similar to a recently introduced technique in statistics called Sparse Principal Component Analysis (Sparse PCA), which is an extension of the classical PCA algorithm. The exact version of our problem formulation is a hard combinatorial optimization problem, so we consider a recently introduced semidefinite programming relaxation of the Sparse PCA problem. We show via results on simulated data that the technique is very promising.
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Summary

Network datasets have become ubiquitous in many fields of study in recent years. In this paper we investigate a problem with applicability to a wide variety of domains - detecting small, anomalous subgraphs in a background graph. We characterize the anomaly in a subgraph via the well-known notion of network...

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