This book investigates compressive sensing techniques to provide a
robust and general framework for network data analytics. The goal
is to introduce a compressive sensing framework for missing data
interpolation, anomaly detection, data segmentation and activity
recognition, and to demonstrate its benefits. Chapter 1 introduces
compressive sensing, including its definition, limitation, and how
it supports different network analysis applications. Chapter 2
demonstrates the feasibility of compressive sensing in network
analytics, the authors we apply it to detect anomalies in the
customer care call dataset from a Tier 1 ISP in the United States.
A regression-based model is applied to find the relationship
between calls and events. The authors illustrate that compressive
sensing is effective in identifying important factors and can
leverage the low-rank structure and temporal stability to improve
the detection accuracy. Chapter 3 discusses that there are several
challenges in applying compressive sensing to real-world data.
Understanding the reasons behind the challenges is important for
designing methods and mitigating their impact. The authors analyze
a wide range of real-world traces. The analysis demonstrates that
there are different factors that contribute to the violation of the
low-rank property in real data. In particular, the authors find
that (1) noise, errors, and anomalies, and (2) asynchrony in the
time and frequency domains lead to network-induced ambiguity and
can easily cause low-rank matrices to become higher-ranked. To
address the problem of noise, errors and anomalies in Chap. 4, the
authors propose a robust compressive sensing technique. It
explicitly accounts for anomalies by decomposing real-world data
represented in matrix form into a low-rank matrix, a sparse anomaly
matrix, an error term and a small noise matrix. Chapter 5 addresses
the problem of lack of synchronization, and the authors propose a
data-driven synchronization algorithm. It can eliminate
misalignment while taking into account the heterogeneity of
real-world data in both time and frequency domains. The data-driven
synchronization can be applied to any compressive sensing technique
and is general to any real-world data. The authors illustrates that
the combination of the two techniques can reduce the ranks of
real-world data, improve the effectiveness of compressive sensing
and have a wide range of applications. The networks are constantly
generating a wealth of rich and diverse information. This
information creates exciting opportunities for network analysis and
provides insight into the complex interactions between network
entities. However, network analysis often faces the problems of (1)
under-constrained, where there is too little data due to
feasibility and cost issues in collecting data, or (2)
over-constrained, where there is too much data, so the analysis
becomes unscalable. Compressive sensing is an effective technique
to solve both problems. It utilizes the underlying data structure
for analysis. Specifically, to solve the under-constrained problem,
compressive sensing technologies can be applied to reconstruct the
missing elements or predict the future data. Also, to solve the
over-constraint problem, compressive sensing technologies can be
applied to identify significant elements To support compressive
sensing in network data analysis, a robust and general framework is
needed to support diverse applications. Yet this can be challenging
for real-world data where noise, anomalies and lack of
synchronization are common. First, the number of unknowns for
network analysis can be much larger than the number of
measurements. For example, traffic engineering requires knowing the
complete traffic matrix between all source and destination pairs,
in order to properly configure traffic and avoid congestion.
However, measuring the flow between all source and destination
pairs is very expensive or even infeasible. Reconstructing data
from a small number of measurements is an underconstrained problem.
In addition, real-world data is complex and heterogeneous, and
often violate the low-level assumptions required by existing
compressive sensing techniques. These violations significantly
reduce the applicability and effectiveness of existing compressive
sensing methods. Third, synchronization of network data reduces the
data ranks and increases spatial locality. However, periodic time
series exhibit not only misalignment but also different
frequencies, which makes it difficult to synchronize data in the
time and frequency domains. The primary audience for this book is
data engineers, analysts and researchers, who need to deal with big
data with missing anomalous and synchronization problems. Advanced
level students focused on compressive sensing techniques will also
benefit from this book as a reference.
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