diff --git a/text/bibliography.bib b/text/bibliography.bib index c9a567b..896bf6d 100644 --- a/text/bibliography.bib +++ b/text/bibliography.bib @@ -1251,6 +1251,12 @@ publisher = {ACM} } +@techreport{makonin2018hue, + title = {HUE: The hourly usage of energy dataset for buildings in British Columbia}, + author = {Makonin, Stephen}, + year = {2018} +} + @article{matyas1990visual, title = {Visual analysis of single-case time series: Effects of variability, serial dependence, and magnitude of intervention effects}, author = {Matyas, Thomas A and Greenwood, Kenneth M}, @@ -1478,6 +1484,17 @@ organization = {IEEE} } +@article{sapiezynski2019interaction, + title = {Interaction data from the copenhagen networks study}, + author = {Sapiezynski, Piotr and Stopczynski, Arkadiusz and Lassen, David Dreyer and Lehmann, Sune}, + journal = {Scientific Data}, + volume = {6}, + number = {1}, + pages = {1--10}, + year = {2019}, + publisher = {Nature Publishing Group} +} + @article{satyanarayanan2017emergence, title = {The emergence of edge computing}, author = {Satyanarayanan, Mahadev}, @@ -1736,6 +1753,14 @@ publisher = {Elsevier} } +@inproceedings{wang2017locally, + title = {Locally differentially private protocols for frequency estimation}, + author = {Wang, Tianhao and Blocki, Jeremiah and Li, Ninghui and Jha, Somesh}, + booktitle = {26th $\{$USENIX$\}$ Security Symposium ($\{$USENIX$\}$ Security 17)}, + pages = {729--745}, + year = {2017} +} + @inproceedings{wang2017privacy, title = {Privacy Preserving Anonymity for Periodical SRS Data Publishing}, author = {Wang, Jie-Teng and Lin, Wen-Yang}, diff --git a/text/evaluation/details.tex b/text/evaluation/details.tex new file mode 100644 index 0000000..ce04e30 --- /dev/null +++ b/text/evaluation/details.tex @@ -0,0 +1,96 @@ +\section{Details} +\label{sec:eval-dtl} + +In this section we list all the relevant details regarding the setting of the evaluation (Section~\ref{subsec:eval-setup}), and the real and synthetic data sets that we used(Section~\ref{subsec:eval-dat}), along with the corresponding configurations (Section~\ref{subsec:eval-conf}). + + +\subsection{Setting} +\label{subsec:eval-setup} + +We implemented our experiments\footnote{Code available at \url{https://git.delkappa.com/manos/the-last-thing}} in Python $3$.$9$.$7$ and executed them on a machine with an Intel i$7$-$6700$HQ at $3$.$5$GHz CPU and $16$GB RAM, running Manjaro Linux $21$.$1$.$5$. +We repeated each experiment $100$ times and we report the mean over these iterations. + + +\subsection{Data sets} +\label{subsec:eval-dat} + +\subsubsection{Real} + +\paragraph{Copenhagen}~\cite{sapiezynski2019interaction} +data set that was collected via the smartphone devices of $851$ university students over a period of $4$ week as part of the Copenhagen Networks Study. +Each device was configured to be discoverable by and to discover nearby Bluetooth devices every $5$ minutes. +Upon discovery each device registers, (i)~the timestamp in seconds, (ii)~the device's unique identifier, (iii)~the unique identifier of the device that it discovered ($- 1$ when no device was found or $- 2$ for any non-participating device), and (iv)~the Received Signal Strength Indicator (RSSI) in dBm. +Half of the devices have registered data at at least $81\%$ of the possible timestamps. +From this data set, we utilized the $1,000$ first contacts out of $12,167$ valid unique contacts of the device with identifier `$449$'. + +\paragraph{HUE}~\cite{makonin2018hue} +contains the hourly energy consumption data of $22$ residential customers of BCHydro, a provincial power utility, in British Columbia. +The measurements for each residence are saved individually and each measurement contains (i)~the date (YYYY-MM-DD), (ii)~the hour, and (iii)~the energy consumption in kWh. +In our experiments, we used the first $1,000$ out of $29,231$ measurements of the residence with identifier `$1$', average energy consumption equal to $0.88$kWh, and value range $[0.28$, $4.45]$. + +\paragraph{T-drive}~\cite{yuan2010t} +consists of $15$ million GPS data points of the trajectories of $10,357$ taxis in Beijing, spanning a period of $1$ week and a total distance of $9$ million kilometers. +The taxis reported their location data on average every $177$ seconds and $623$ meters approximately. +Each vehicle registers (i)~the taxi unique identifier, (ii)~the timestamp (YYYY-MM-DD HH:MM:SS), (iii)~longitude, and (iv)~latitude. +These measurements are stored individually per vehicle. +We sampled the first $1000$ data items of the taxi with identifier `$2$'. + +\subsubsection{Synthetic} +We generated synthetic time series of length equal to $100$ timestamps, for which we varied the number and distribution of {\thethings}. +We take into account only the temporal order of the points and the position of regular and {\thething} events within the series. +% Note, that for the experiments performed on the synthetic data sets, the original values to be released do not influence the outcome of our conclusions, thus we ignore them. + + +\subsection{Configurations} +\label{subsec:eval-conf} + +\subsubsection{{\Thethings}' percentage} + +For Copenhagen, we achieve +$0\%$ {\thethings} by considering an empty list of contact devices, +$20\%$ by extending the list with $[3$, $6$, $11$, $12$, $25$, $29$, $36$, $39$, $41$, $46$, $47$, $50$, $52$, $56$, $57$, $61$, $63$, $78$, $80]$, +$40\%$ with $[81$, $88$, $90$, $97$, $101$, $128$, $130$, $131$, $137$, $145$, $146$, $148$, $151$, $158$, $166$, $175$, $176]$, +$60\%$ with $[181$, $182$, $192$, $195$, $196$, $201$, $203$, $207$, $221$, $230$, $235$, $237$, $239$, $241$, $254]$, +$80\%$ with $[260$, $282$, $287$, $289$, $290$, $291$, $308$, $311$, $318$, $323$, $324$, $330$, $334$, $335$, $344$, $350$, $353$, $355$, $357$, $358$, $361$, $363]$, and +$100\%$ by including all of the possible contacts. + +In HUE, we get $0$, $20$ $40$, $60$, $80$, and $100$ {\thethings} percentages by setting the energy consumption threshold below $0.28$, $1.12$, $0.88$, $0.68$, $0.54$, $4.45$kWh respectively. + +In T-drive, we achieved the desired {\thethings} percentages by utilizing the method of Li et al.~\cite{li2008mining} for detecting stay points in trajectory data. +In more detail, the algorithm checks for each data item if each subsequent item is within a given distance threshold $\Delta l$ and measures the time period $\Delta t$ between the present point and the last subsequent point. +We achieve $0$, $20$ $40$, $60$, $80$, and $100$ {\thethings} percentages by setting the ($\Delta l$ in meters, $\Delta t$ in minutes) pairs input to the stay point discovery method as [($0$, $1000$), ($2095$, $30$), ($2790$, $30$), ($3590$, $30$), ($4825$, $30$), ($10350$, $30$)]. + +We generated synthetic data with \emph{skewed} (the {\thethings} are distributed towards the beginning/end of the series), \emph{symmetric} (in the middle), \emph{bimodal} (both end and beginning), and \emph{uniform} (all over the time series) {\thething} distributions. +In order to get {\thethings} with the above distribution features, we generate probability distributions with appropriate characteristics and sample from them, without replacement, the desired number of points. +%The generated distributions are representative of the cases that we wish to examine during the experiments. +For example, for a left-skewed {\thethings} distribution we would utilize a truncated distribution resulting from the restriction of the domain of a distribution to the beginning and end of the time series with its location shifted to the center of the right half of the series. +For consistency, we calculate the scale parameter depending on the length of the series by setting it equal to the series' length over a constant. + +\subsubsection{Temporal correlation} + +We model the temporal correlation in the synthetic data as a \emph{stochastic matrix} $P$, using a \emph{Markov Chain}~\cite{gagniuc2017markov}. +$P$ is a $n \times n$ matrix, where the element $P_{ij}$ +%at the $i$th row of the $j$th column that +represents the transition probability from a state $i$ to another state $j$. +%, $\forall i, j \leq n$. +It holds that the elements of every row $j$ of $P$ sum up to $1$. +We follow the \emph{Laplacian smoothing} technique~\cite{sorkine2004laplacian} as utilized in~\cite{cao2018quantifying} to generate the matrix $P$ with a degree of temporal correlation $s > 0$ equal to +% and generate a stochastic matrix $P$ with a degree of temporal correlation $s$ by calculating each element $P_{ij}$ as follows +$$\frac{(I_{n})_{ij} + s}{\sum_{k = 1}^{n}((I_{n})_{jk} + s)}$$ +where $I_{n}$ is an \emph{identity matrix} of size $n$. +%, i.e.,~an $n \times n$ matrix with $1$s on its main diagonal and $0$s elsewhere. +% $s$ takes only positive values which are comparable only for stochastic matrices of the same size. +The value of $s$ is comparable only for stochastic matrices of the same size and dictates the strength of the correlation; the lower its value, +% the lower the degree of uniformity of each row, and therefore +the stronger the correlation degree. +%In general, larger transition matrices tend to be uniform, resulting in weaker correlation. +In our experiments, for simplicity, we set $n = 2$ and we investigate the effect of \emph{weak} ($s = 1$), \emph{moderate} ($s = 0.1$), and \emph{strong} ($s = 0.01$) temporal correlation degree on the overall privacy loss. + +\subsubsection{Privacy parameters} + +To perturb the contact tracing data of Copenhagen, we utilize the \emph{random response} technique to report with probability $p = \frac{e^\varepsilon}{e^\varepsilon + 1}$ weather the current contact is a {\thething} or not. +We randomize them the energy consumption in HUE with the Laplace mechanism. +To perturb the spatial values in T-drive, we inject noise that we sample from the Planar Laplace mechanism~\cite{andres2013geo}. + +We set the privacy budget $\varepsilon = 1$, and, for simplicity, we assume that for every query sensitivity it holds that $\Delta f = 1$. +% Finally, notice that, depending on the results' variation, most diagrams are in logarithmic scale. diff --git a/text/evaluation/main.tex b/text/evaluation/main.tex index fc72d91..f491a80 100644 --- a/text/evaluation/main.tex +++ b/text/evaluation/main.tex @@ -1,5 +1,6 @@ \chapter{Evaluation} \label{ch:eval} +\input{evaluation/details} \input{evaluation/thething} \input{evaluation/theotherthing} diff --git a/text/evaluation/thething.tex b/text/evaluation/thething.tex index 3b43a17..487434c 100644 --- a/text/evaluation/thething.tex +++ b/text/evaluation/thething.tex @@ -13,56 +13,6 @@ This happens due the fact that at each timestamp we take into account only the d Whereas, when each timestamp corresponds to a {\thething} we consider and protect all the events throughout the entire series (user-level). -\subsection{Setting, configurations, and data sets} -\paragraph{Setting} -We implemented our experiments\footnote{Code available at \url{https://gitlab.com/adhesivegoldfinch/cikm}} in Python $3$.$9$.$5$ and executed them on a machine with Intel i$7$-$6700$HQ $3$.$5$GHz CPU and $16$GB RAM, running Manjaro $21$.$0$.$5$. -We repeated each experiment $100$ times and we report the mean over these iterations. - - -\paragraph{Data sets} -For the \emph{real} data sets, we used the Geolife~\cite{zheng2010geolife} and T-drive~\cite{yuan2010t} from which we sampled the first $1000$ data items. -We achieved the desired {\thethings} percentages by utilizing the method of Li et al.~\cite{li2008mining} for detecting stay points in trajectory data. -In more detail, the algorithm checks for each data item if each subsequent item is within a given distance threshold $\Delta l$ and measures the time period $\Delta t$ between the present point and the last subsequent point. -We achieve $0$, $20$ $40$, $60$, $80$, and $100$ {\thethings} percentages by setting the ($\Delta l$ in meters, $\Delta t$ in minutes) pairs input to the stay point discovery method for T-drive as [($0$, $1000$), ($2095$, $30$), ($2790$, $30$), ($3590$, $30$), ($4825$, $30$), ($10350$, $30$)] and for Geolife as [($0$, $100000$), ($205$, $30$), ($450$, $30$), ($725$, $30$), ($855$, $30$), ($50000$, $30$)]. - - -Next, we generated synthetic time series of length equal to $100$ timestamps, for which we varied the number and distribution of {\thethings}. -% to achieve the necessary {\thethings} distribution and percentage for where applicable. -% \paragraph{{\Thethings} distribution} -We created \emph{left-skewed} (the {\thethings} are distributed towards the end), \emph{symmetric} (in the middle), \emph{right-skewed} (in the beginning), \emph{bimodal} (both end and beginning), and \emph{uniform} (all over the time series) {\thething} distributions. -%, in the beginning and in the end (\emph{bimodal}), and all over the extend (\emph{uniform}) of a time series. -When pertinent, we group the left- and right-skewed cases as simply `skewed', since they share several features due to symmetry. -In order to get {\thethings} with the above distribution features, we generate probability distributions with appropriate characteristics and sample from them, without replacement, the desired number of points. -%The generated distributions are representative of the cases that we wish to examine during the experiments. -% For example, for a left-skewed {\thethings} distribution we would utilize a truncated distribution resulting from the restriction of the domain of a normal distribution to the beginning and end of the time series with its location shifted to the center of the right half of the series. -For consistency, we calculate the scale parameter depending on the length of the series by setting it equal to the series' length over a constant. -%We take into account only the temporal order of the points and the position of regular and {\thething} events within the series. -Note, that for the experiments performed on the synthetic data sets, the original values to be released do not influence the outcome of our conclusions, thus we ignore them. - - -\paragraph{Configurations} -We model the temporal correlation in the synthetic data as a \emph{stochastic matrix} $P$, using a \emph{Markov Chain}~\cite{gagniuc2017markov}. -$P$ is a $n \times n$ matrix, where the element $p_{ij}$ -%at the $i$th row of the $j$th column that -represents the transition probability from a state $i$ to another state $j$. -%, $\forall i, j \leq n$. -It holds that the elements of every row $j$ of $P$ sum up to $1$. -We follow the \emph{Laplacian smoothing} technique~\cite{sorkine2004laplacian} as utilized in~\cite{cao2018quantifying} to generate the matrix $P$ with a degree of temporal correlation $s>0$. -% and generate a stochastic matrix $P$ with a degree of temporal correlation $s$ by calculating each element $P_{ij}$ as follows -%$$\frac{(I_{n})_{ij} + s}{\sum_{k = 1}^{n}((I_{n})_{jk} + s)}$$ -%where $I_{n}$ is an \emph{identity matrix} of size $n$. -%, i.e.,~an $n \times n$ matrix with $1$s on its main diagonal and $0$s elsewhere. -% $s$ takes only positive values which are comparable only for stochastic matrices of the same size. -$s$ dictates the strength of the correlation; the lower its value, -%the lower the degree of uniformity of each row, and therefore -the stronger the correlation degree. -%In general, larger transition matrices tend to be uniform, resulting in weaker correlation. -In our experiments, for simplicity, we set $n = 2$ and we investigate the effect of \emph{weak} ($s = 1$), \emph{moderate} ($s = 0.1$), and \emph{strong} ($s = 0.01$) temporal correlation degree on the overall privacy loss. - -We set $\varepsilon = 1$. -To perturb the spatial values of the real data sets, we inject noise that we sample from the Planar Laplace mechanism~\cite{andres2013geo}. -Finally, notice that all diagrams are in logarithmic scale. - \subsection{Experiments} \paragraph{Budget allocation schemes}