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A related interesting problem is that of perturbation (i.e., noise) en-
ergy allocation. Given a perturbation signal of a particular energy bud-
get (dictated perhaps by reconstruction accuracy requirements), how to
allocate this energy budget across the frequency spectrum to optimally
conceal an original data signal? A recent technique defines privacy as
the amount of mutual information between the original and perturbed
signals. Optimality is defined as perturbation that minimizes the upper
bound on such (leaked) mutual information. The technique describes
how optimal perturbation is computed, and demonstrates the funda-
mental trade-off between the bound on information leak (privacy) and
the bound on reconstruction accuracy [132]. We note that the privacy
protection issues for social sensing data arise both during trajectory data
collection, and trajectory data management [38]. Since this section is
focussed only on the data collection and system design issues, we will
discuss this issue in a more holistic and algorithmic way in a later section
of this chapter.
3.2 Generalized Model Construction
Many initial participatory sensing applications, such as those giving
rise to the above privacy concerns, were concerned with computing com-
munity statistics out of individual private measurements. The approach
inherently assumes richly-sampled, low-dimensional data, where many
low-dimensional measurements (e.g., measurements of velocity) are re-
dundantly obtained by individuals measuring the same variable (e.g.,
speed of trac on the same street). Only then can good statistics be
computed. Many systems, however, do not adhere to the above model.
Instead, data are often high-dimensional, and hence sampling of the
high-dimensional space is often sparse. The more interesting question
becomes how to generalize from high-dimensional, sparsely-sampled data
to cover the entire input data space? For instance, consider a fuel-
ecient navigation example, where it is desired to compute the most
fuel-ecient route between arbitrary source and destination points, for
an arbitrary vehicle and driver. What are the most important gen-
eralizable predictors of fuel eciency of current car models driven on
modern streets? A large number of predictors may exist that pertain to
parameters of the cars, the streets and the drivers. These inputs may
be static (e.g., car weight and frontal area) or dynamic (e.g., traveled
road speed and degree of congestion). In many cases, the space is only
sparsely sampled, especially in conditions of sparse deployment of the
participatory sensing service. It is very dicult to predict
apriori
which
parameters will be more telling. More importantly, the key predictors
