From 8b2622781c7cd3f291c6705daa35de1f06338479 Mon Sep 17 00:00:00 2001 From: Manos Date: Sun, 10 Oct 2021 22:27:29 +0200 Subject: [PATCH 01/13] evaluation: Moved some general info to details --- text/evaluation/details.tex | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/text/evaluation/details.tex b/text/evaluation/details.tex index f8096b7..4c5a4c1 100644 --- a/text/evaluation/details.tex +++ b/text/evaluation/details.tex @@ -65,6 +65,10 @@ In order to get {\thethings} with the above distribution features, we generate p 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. +Notice that in our experiments, in the cases when we have $0\%$ and $100\%$ of the events being {\thethings}, we get the same behavior as in event- and user-level privacy respectively. +This happens due the fact that at each timestamp we take into account only the data items at the current timestamp and ignore the rest of the time series (event-level) when there are no {\thethings}. +Whereas, when each timestamp corresponds to a {\thething} we consider and protect all the events throughout the entire series (user-level). + \subsubsection{Privacy parameters} From 2e08f9d0b43d2c95ec93796ecba3d07ac644c3ea Mon Sep 17 00:00:00 2001 From: Manos Date: Sun, 10 Oct 2021 22:27:53 +0200 Subject: [PATCH 02/13] problem: OCD --- text/problem/main.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/text/problem/main.tex b/text/problem/main.tex index 2b90772..585f426 100644 --- a/text/problem/main.tex +++ b/text/problem/main.tex @@ -1,4 +1,4 @@ -\chapter{Landmark Privacy} +\chapter{{\Thething} privacy} \label{ch:lmdk-prv} % Crowdsensing applications From f84cfb205dd50d0686199dd907e98fbd5bbc9053 Mon Sep 17 00:00:00 2001 From: Manos Date: Sun, 10 Oct 2021 22:28:18 +0200 Subject: [PATCH 03/13] evaluation: Minor corrections in thething --- text/evaluation/thething.tex | 33 +++++++++++++++------------------ 1 file changed, 15 insertions(+), 18 deletions(-) diff --git a/text/evaluation/thething.tex b/text/evaluation/thething.tex index 39122ab..6528f88 100644 --- a/text/evaluation/thething.tex +++ b/text/evaluation/thething.tex @@ -3,14 +3,9 @@ % \kat{After discussing with Dimitris, I thought you are keeping one chapter for the proposals of the thesis. In this case, it would be more clean to keep the theoretical contributions in one chapter and the evaluation in a separate chapter. } % \mk{OK.} -In this section we present the experiments that we performed on real and synthetic data sets. +In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sol}, on real and synthetic data sets. With the experiments on the real data sets (Section~\ref{subsec:lmdk-expt-bgt}), we show the performance in terms of utility of our three {\thething} mechanisms. -With the experiments on the synthetic data sets (Section~\ref{subsec:lmdk-expt-cor}) we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. - - -Notice that in our experiments, in the cases when we have $0\%$ and $100\%$ of the events being {\thethings}, we get the same behavior as in event- and user-level privacy respectively. -This happens due the fact that at each timestamp we take into account only the data items at the current timestamp and ignore the rest of the time series (event-level) when there are no {\thethings}. -Whereas, when each timestamp corresponds to a {\thething} we consider and protect all the events throughout the entire series (user-level). +With the experiments on the synthetic data sets (Section~\ref{subsec:lmdk-expt-cor}) we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. \subsection{Budget allocation schemes} @@ -42,7 +37,7 @@ The Skip model excels, compared to the others, at cases where it needs to approx The combination of the low range in HUE ($[0.28$, $4.45]$ with an average of $0.88$kWh) and the large scale in the Laplace mechanism results in a low mean absolute error for Skip(Figure~\ref{fig:hue}). In general, a scheme that favors approximation over noise injection would achieve a better performance in this case. However, the Adaptive model performs by far better than Uniform and strikes a nice balance between event- and user-level protection for all {\thethings} percentages. -In the T-drive data set (Figure~\ref{fig:t-drive}), the Adaptive mechanism outperforms the Uniform one by $10$\%--$20$\% for all {\thethings} percentages greater than $40$ and by more than $20$\% the Skip one. +In the T-drive data set (Figure~\ref{fig:t-drive}), the Adaptive mechanism outperforms Uniform by $10$\%--$20$\% for all {\thethings} percentages greater than $40$ and Skip by more than $20$\%. The lower density (average distance of $623$ meters) of the T-drive data set has a negative impact on the performance of Skip. In general, we can claim that the Adaptive is the most reliable and best performing mechanism with minimal tuning, if we take into consideration the drawbacks of the Skip mechanism mentioned in Section~\ref{subsec:lmdk-mechs}. @@ -54,10 +49,6 @@ Moreover, designing a data-dependent sampling scheme would possibly result in be Figure~\ref{fig:avg-dist} shows a comparison of the average temporal distance of the events from the previous/next {\thething} or the start/end of the time series for various distributions in synthetic data. More particularly, we count for every event the total number of events between itself and the nearest {\thething} or the series edge. -We observe that the uniform and bimodal distributions tend to limit the regular event--{\thething} distance. -This is due to the fact that the former scatters the {\thethings}, while the latter distributes them on both edges, leaving a shorter space uninterrupted by {\thethings}. -% and as a result they reduce the uninterrupted space by landmarks in the sequence. -On the contrary, distributing the {\thethings} at one part of the sequence, as in skewed or symmetric, creates a wider space without {\thethings}. \begin{figure}[htp] \centering @@ -66,14 +57,13 @@ On the contrary, distributing the {\thethings} at one part of the sequence, as i \label{fig:avg-dist} \end{figure} +We observe that the uniform and bimodal distributions tend to limit the regular event--{\thething} distance. +This is due to the fact that the former scatters the {\thethings}, while the latter distributes them on both edges, leaving a shorter space uninterrupted by {\thethings}. +% and as a result they reduce the uninterrupted space by landmarks in the sequence. +On the contrary, distributing the {\thethings} at one part of the sequence, as in skewed or symmetric, creates a wider space without {\thethings}. + Figure~\ref{fig:dist-cor} illustrates a comparison among the aforementioned distributions regarding the overall privacy loss under (a)~weak, (b)~moderate, and (c)~strong temporal correlation degrees. The line shows the overall privacy loss---for all cases of {\thethings} distribution---without temporal correlation. -In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} distance in a distribution can result into greater overall privacy loss under moderate and strong temporal correlation. -This is due to the fact that the backward/forward privacy loss accumulates more over time in wider spaces without {\thethings} (see Section~\ref{sec:correlation}). -Furthermore, the behavior of the privacy loss is as expected regarding the temporal correlation degree. -Predictably, a stronger correlation degree generates higher privacy loss while widening the gap between the different distribution cases. -On the contrary, a weaker correlation degree makes it harder to differentiate among the {\thethings} distributions. -The privacy loss under a weak correlation degree converge. \begin{figure}[htp] \centering @@ -91,3 +81,10 @@ The privacy loss under a weak correlation degree converge. The line shows the overall privacy loss without temporal correlation.} \label{fig:dist-cor} \end{figure} + +In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} distance in a distribution can result into greater overall privacy loss under moderate and strong temporal correlation. +This is due to the fact that the backward/forward privacy loss accumulates more over time in wider spaces without {\thethings} (see Section~\ref{sec:correlation}). +Furthermore, the behavior of the privacy loss is as expected regarding the temporal correlation degree. +Predictably, a stronger correlation degree generates higher privacy loss while widening the gap between the different distribution cases. +On the contrary, a weaker correlation degree makes it harder to differentiate among the {\thethings} distributions. +The privacy loss under a weak correlation degree converge. From f48dca02aa88fecf666154135d70760a3a81d083 Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 01:12:35 +0200 Subject: [PATCH 04/13] evaluation: Re-executed some experiments --- code/expt/copenhagen-sel.py | 15 ++++++++------- code/expt/copenhagen.py | 7 ++++--- code/expt/hue-sel.py | 14 +++++++------- code/expt/hue.py | 14 +++++++------- code/expt/t-drive-sel.py | 11 ++++++----- code/expt/t-drive.py | 11 ++++++----- code/lib/lmdk_bgt.py | 2 +- .../evaluation/copenhagen-sel.pdf | Bin 16145 -> 14646 bytes graphics/evaluation/hue-sel.pdf | Bin 0 -> 17126 bytes graphics/evaluation/hue.pdf | Bin 16603 -> 17130 bytes graphics/evaluation/lmdk-sel-dist-emd.pdf | Bin 0 -> 14308 bytes graphics/evaluation/lmdk-sel-dist-norm.pdf | Bin 0 -> 14804 bytes .../evaluation/t-drive-sel.pdf | Bin 16163 -> 16330 bytes graphics/evaluation/t-drive.pdf | Bin 16163 -> 16337 bytes rslt/bgt_cmp/Copenhagen-sel.pdf | Bin 14646 -> 14642 bytes rslt/bgt_cmp/Copenhagen.pdf | Bin 14645 -> 14649 bytes rslt/bgt_cmp/HUE-sel.pdf | Bin 16603 -> 17126 bytes rslt/bgt_cmp/HUE.pdf | Bin 16603 -> 17130 bytes 18 files changed, 39 insertions(+), 35 deletions(-) rename rslt/bgt_cmp/T-drive-sel.pdf => graphics/evaluation/copenhagen-sel.pdf (72%) create mode 100644 graphics/evaluation/hue-sel.pdf create mode 100644 graphics/evaluation/lmdk-sel-dist-emd.pdf create mode 100644 graphics/evaluation/lmdk-sel-dist-norm.pdf rename rslt/bgt_cmp/T-drive.pdf => graphics/evaluation/t-drive-sel.pdf (79%) diff --git a/code/expt/copenhagen-sel.py b/code/expt/copenhagen-sel.py index 99141fd..ab17d31 100644 --- a/code/expt/copenhagen-sel.py +++ b/code/expt/copenhagen-sel.py @@ -68,29 +68,30 @@ def main(args): for _ in range(args.iter): - lmdks, eps_out = lmdk_sel.find_lmdks(seq, lmdks, epsilon) + lmdks_sel, eps_out = lmdk_sel.find_lmdks(seq, lmdks, epsilon) # Skip - rls_data_s, bgts_s = lmdk_bgt.skip_cont(seq, lmdks, eps_out) + rls_data_s, bgts_s = lmdk_bgt.skip_cont(seq, lmdks_sel, eps_out) # lmdk_bgt.validate_bgts(seq, lmdks, epsilon, bgts_s) mae_s[i] += (lmdk_bgt.mae_cont(rls_data_s)/args.iter)*100 # Uniform - rls_data_u, bgts_u = lmdk_bgt.uniform_cont(seq, lmdks, eps_out) + rls_data_u, bgts_u = lmdk_bgt.uniform_cont(seq, lmdks_sel, eps_out) # lmdk_bgt.validate_bgts(seq, lmdks, epsilon, bgts_u) mae_u[i] += (lmdk_bgt.mae_cont(rls_data_u)/args.iter)*100 # Adaptive - rls_data_a, _, _ = lmdk_bgt.adaptive_cont(seq, lmdks, eps_out, .5, .5) + rls_data_a, _, _ = lmdk_bgt.adaptive_cont(seq, lmdks_sel, eps_out, .5, .5) mae_a[i] += (lmdk_bgt.mae_cont(rls_data_a)/args.iter)*100 # Calculate once - if i == 0: + if pct == lmdks_pct[0]: # Event - rls_data_evt, _ = lmdk_bgt.uniform_cont(seq, lmdk_lib.find_lmdks_cont(lmdk_data, seq, uid, 0), epsilon) + rls_data_evt, _ = lmdk_bgt.uniform_cont(seq, lmdks, epsilon) mae_evt += (lmdk_bgt.mae_cont(rls_data_evt)/args.iter)*100 + elif pct == lmdks_pct[-1]: # User - rls_data_usr, _ = lmdk_bgt.uniform_cont(seq, lmdk_lib.find_lmdks_cont(lmdk_data, seq, uid, 100), epsilon) + rls_data_usr, _ = lmdk_bgt.uniform_cont(seq, lmdks, epsilon) mae_usr += (lmdk_bgt.mae_cont(rls_data_usr)/args.iter)*100 plt.axhline( diff --git a/code/expt/copenhagen.py b/code/expt/copenhagen.py index aa9b514..acafe9a 100644 --- a/code/expt/copenhagen.py +++ b/code/expt/copenhagen.py @@ -80,12 +80,13 @@ def main(args): mae_a[i] += (lmdk_bgt.mae_cont(rls_data_a)/args.iter)*100 # Calculate once - if i == 0: + if pct == lmdks_pct[0]: # Event - rls_data_evt, _ = lmdk_bgt.uniform_cont(seq, lmdk_lib.find_lmdks_cont(lmdk_data, seq, uid, 0), epsilon) + rls_data_evt, _ = lmdk_bgt.uniform_cont(seq, lmdks, epsilon) mae_evt += (lmdk_bgt.mae_cont(rls_data_evt)/args.iter)*100 + elif pct == lmdks_pct[-1]: # User - rls_data_usr, _ = lmdk_bgt.uniform_cont(seq, lmdk_lib.find_lmdks_cont(lmdk_data, seq, uid, 100), epsilon) + rls_data_usr, _ = lmdk_bgt.uniform_cont(seq, lmdks, epsilon) mae_usr += (lmdk_bgt.mae_cont(rls_data_usr)/args.iter)*100 plt.axhline( diff --git a/code/expt/hue-sel.py b/code/expt/hue-sel.py index 22083f4..930bd54 100644 --- a/code/expt/hue-sel.py +++ b/code/expt/hue-sel.py @@ -48,7 +48,7 @@ def main(args): # The y axis plt.ylabel('Mean absolute error (kWh)') # Set y axis label. plt.yscale('log') - plt.ylim(.1, 10000) + plt.ylim(.1, 100000) # Bar offset x_offset = -(bar_width/2)*(n - 1) @@ -80,13 +80,13 @@ def main(args): mae_a[i] += lmdk_bgt.mae_cons(seq, rls_data_a)/args.iter # Calculate once - # Event - if i == 0: - rls_data_evt, _ = lmdk_bgt.uniform_cons(seq, seq[seq[:, 1] < lmdks_th[0]], epsilon) + if pct == lmdks_pct[0]: + # Event + rls_data_evt, _ = lmdk_bgt.uniform_cons(seq, lmdks, epsilon) mae_evt += lmdk_bgt.mae_cons(seq, rls_data_evt)/args.iter - # User - if i == 0: - rls_data_usr, _ = lmdk_bgt.uniform_cons(seq, seq[seq[:, 1] < lmdks_th[len(lmdks_th)-1]], epsilon) + elif pct == lmdks_pct[-1]: + # User + rls_data_usr, _ = lmdk_bgt.uniform_cons(seq, lmdks, epsilon) mae_usr += lmdk_bgt.mae_cons(seq, rls_data_usr)/args.iter plt.axhline( diff --git a/code/expt/hue.py b/code/expt/hue.py index cb4cb2e..5562b17 100644 --- a/code/expt/hue.py +++ b/code/expt/hue.py @@ -46,7 +46,7 @@ def main(args): # The y axis plt.ylabel('Mean absolute error (kWh)') # Set y axis label. plt.yscale('log') - plt.ylim(.1, 10000) + plt.ylim(.1, 100000) # Bar offset x_offset = -(bar_width/2)*(n - 1) @@ -75,13 +75,13 @@ def main(args): mae_a[i] += lmdk_bgt.mae_cons(seq, rls_data_a)/args.iter # Calculate once - # Event - if i == 0: - rls_data_evt, _ = lmdk_bgt.uniform_cons(seq, seq[seq[:, 1] < lmdks_th[0]], epsilon) + if pct == lmdks_pct[0]: + # Event + rls_data_evt, _ = lmdk_bgt.uniform_cons(seq, lmdks, epsilon) mae_evt += lmdk_bgt.mae_cons(seq, rls_data_evt)/args.iter - # User - if i == 0: - rls_data_usr, _ = lmdk_bgt.uniform_cons(seq, seq[seq[:, 1] < lmdks_th[len(lmdks_th)-1]], epsilon) + elif pct == lmdks_pct[-1]: + # User + rls_data_usr, _ = lmdk_bgt.uniform_cons(seq, lmdks, epsilon) mae_usr += lmdk_bgt.mae_cons(seq, rls_data_usr)/args.iter plt.axhline( diff --git a/code/expt/t-drive-sel.py b/code/expt/t-drive-sel.py index 1f1683c..a9ebdcf 100644 --- a/code/expt/t-drive-sel.py +++ b/code/expt/t-drive-sel.py @@ -70,7 +70,7 @@ def main(args): # The y axis plt.ylabel('Mean absolute error (m)') # Set y axis label. plt.yscale('log') - # plt.ylim(1, 100000000) + plt.ylim(1, 1000000) # Bar offset x_offset = -(bar_width/2)*(n - 1) @@ -101,12 +101,13 @@ def main(args): rls_data_a, _, _ = lmdk_bgt.adaptive(seq, lmdks, eps_out, .5, .5) mae_a[i] += lmdk_bgt.mae(seq, rls_data_a)/args.iter - # Event - if lmdk == 0: + # Calculate once + if lmdk == min(data_info[d]['lmdks']): + # Event rls_data_evt, _ = lmdk_bgt.uniform_r(seq, lmdks, bgt['epsilon']) mae_evt += lmdk_bgt.mae(seq, rls_data_evt)/args.iter - # User - if lmdk == 100: + elif lmdk == max(data_info[d]['lmdks']): + # User rls_data_usr, _ = lmdk_bgt.uniform_r(seq, lmdks, bgt['epsilon']) mae_usr += lmdk_bgt.mae(seq, rls_data_usr)/args.iter diff --git a/code/expt/t-drive.py b/code/expt/t-drive.py index 6c485a1..7c5f607 100644 --- a/code/expt/t-drive.py +++ b/code/expt/t-drive.py @@ -68,7 +68,7 @@ def main(args): # The y axis plt.ylabel('Mean absolute error (m)') # Set y axis label. plt.yscale('log') - # plt.ylim(1, 100000000) + plt.ylim(1, 1000000) # Bar offset x_offset = -(bar_width/2)*(n - 1) @@ -103,12 +103,13 @@ def main(args): # mae_d[i] += lmdk_bgt.mae(seq, rls_data_a)/args.iter # s_d += s_d_c/args.iter - # Event - if lmdk == 0: + # Calculate once + if lmdk == min(data_info[d]['lmdks']): + # Event rls_data_evt, _ = lmdk_bgt.uniform_r(seq, lmdks, bgt['epsilon']) mae_evt += lmdk_bgt.mae(seq, rls_data_evt)/args.iter - # User - if lmdk == 100: + elif lmdk == max(data_info[d]['lmdks']): + # User rls_data_usr, _ = lmdk_bgt.uniform_r(seq, lmdks, bgt['epsilon']) mae_usr += lmdk_bgt.mae(seq, rls_data_usr)/args.iter diff --git a/code/lib/lmdk_bgt.py b/code/lib/lmdk_bgt.py index f3e668f..66f575f 100644 --- a/code/lib/lmdk_bgt.py +++ b/code/lib/lmdk_bgt.py @@ -558,10 +558,10 @@ def skip_cont(seq, lmdks, epsilon): # Add noise o = lmdk_lib.randomized_response(is_landmark, bgts[i]) if is_landmark: + bgts[i] = 0 if i > 0: # Approximate with previous o = rls_data[i - 1][1] - bgts[i] = 0 rls_data[i] = [is_landmark, o] return rls_data, bgts diff --git a/rslt/bgt_cmp/T-drive-sel.pdf b/graphics/evaluation/copenhagen-sel.pdf similarity index 72% rename from rslt/bgt_cmp/T-drive-sel.pdf rename to graphics/evaluation/copenhagen-sel.pdf index 07bc38876f6ce168cddb134165f8a19f4476c666..5db4b5b839e8d333c718fb33645f0b91fdee187b 100644 GIT binary patch delta 2958 zcmZuxdpwle8g3#qkxEgnA7#u)=9_Q6xsjPts1PDuRW6g%xQ(GmCg~=jTIE(0LZZvw z(`6GIxoq-_WaOG0hg_qSPTAD?M)ujKnZ5p*cb@gG_j%rDt@pba@rZxl8mEN7rc^qG z$pV{k5yE8qAT5US>Cwq0MFIlrB%yRPljdsyd{lip2J{EY9&(%GIEz?%!ji5{JC8rP zWKtkvGd(Tze<82!cC%DCmbqrHPo95&-x-BtmYi+RUgnrDY0%WrPh6wt-)j?J*K%pL z(@M@{o;b_QEPFvb+PglBml3;E@Zfaz>)b9;O{uWQb%B5J#x=LDHv!WT4GX0{KvQZ9 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Date: Mon, 11 Oct 2021 01:13:17 +0200 Subject: [PATCH 05/13] ecaluation: Added real-sel --- text/evaluation/theotherthing.tex | 29 +++++++++++++++++++++++++++++ 1 file changed, 29 insertions(+) diff --git a/text/evaluation/theotherthing.tex b/text/evaluation/theotherthing.tex index 188f303..66dcb85 100644 --- a/text/evaluation/theotherthing.tex +++ b/text/evaluation/theotherthing.tex @@ -1,2 +1,31 @@ \section{Selection of events} \label{sec:lmdk-sel-eval} + +In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets. +% With the experiments on the real data sets (Section~\ref{subsec:lmdk-expt-bgt}), we show the performance in terms of utility of our three {\thething} mechanisms. +% With the experiments on the synthetic data sets (Section~\ref{subsec:lmdk-expt-cor}) we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. + +Figure~\ref{fig:real-sel} exhibits the performance of Skip, Uniform, and Adaptive (see Section~\ref{subsec:lmdk-mechs}) in combination with the {\thething} selection component. + +\begin{figure}[htp] + \centering + \subcaptionbox{Copenhagen\label{fig:copenhagen-sel}}{% + \includegraphics[width=.5\linewidth]{evaluation/copenhagen-sel}% + }% + \hspace{\fill} + \subcaptionbox{HUE\label{fig:hue-sel}}{% + \includegraphics[width=.5\linewidth]{evaluation/hue-sel}% + }% + \subcaptionbox{T-drive\label{fig:t-drive-sel}}{% + \includegraphics[width=.5\linewidth]{evaluation/t-drive-sel}% + }% + \caption{The mean absolute error (a)~as a percentage, (b)~in kWh, and (c)~in meters of the released data for different {\thethings} percentages.} + \label{fig:real-sel} +\end{figure} + +In comparison with the utility performance without the {\thething} selection component (Figure~\ref{fig:real}), we notice a slight deterioration for all three models. +This is natural since we allocated part of the available privacy budget to the {\thething} selection component which in turn increased the number of {\thethings}. +Therefore, there is less privacy budget available for data publishing throughout the time series for $0$\% and $100$\% {\thethings}. +Skip performs best in our experiments with HUE, due to the low range in the energy consumption and the high scale of the Laplace noise which it avoids due to its tendency to approximate. +However, for the Copenhagen data set and T-drive it attains greater mean absolute error than the user-level. +Overall, Adaptive has a consistent performance in terms of utility for all of the data sets that we experimented with. From d5c39c4e42b6838a4b66056f6952ca05d76d76c5 Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 01:13:45 +0200 Subject: [PATCH 06/13] evaluation: Minor corrections --- text/evaluation/details.tex | 10 +++++----- text/evaluation/thething.tex | 15 ++++++++------- 2 files changed, 13 insertions(+), 12 deletions(-) diff --git a/text/evaluation/details.tex b/text/evaluation/details.tex index 4c5a4c1..f707864 100644 --- a/text/evaluation/details.tex +++ b/text/evaluation/details.tex @@ -43,7 +43,7 @@ We take into account only the temporal order of the points and the position of r \subsection{Configurations} \label{subsec:eval-conf} -\subsubsection{{\Thethings}' percentage} +\subsubsection{{\Thething} percentage} For the Copenhagen data set, we achieve $0\%$ {\thethings} by considering an empty list of contact devices, @@ -53,16 +53,16 @@ $60\%$ with $[181$, $182$, $192$, $195$, $196$, $201$, $203$, $207$, $221$, $230 $80\%$ 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 HUE, we get $0$\%, $20$\% $40$\%, $60$\%, $80$\%, and $100$\% {\thethings} by setting the energy consumption threshold below $0.28$kWh, $1.12$kWh, $0.88$kWh, $0.68$kWh, $0.54$kWh, $4.45$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 T-drive, we achieved the desired {\thething} 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 achieve $0$\%, $20$\% $40$\%, $60$\%, $80$\%, and $100$\% {\thethings} 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 example, for a left-skewed {\thething} 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. Notice that in our experiments, in the cases when we have $0\%$ and $100\%$ of the events being {\thethings}, we get the same behavior as in event- and user-level privacy respectively. diff --git a/text/evaluation/thething.tex b/text/evaluation/thething.tex index 6528f88..1af0aa0 100644 --- a/text/evaluation/thething.tex +++ b/text/evaluation/thething.tex @@ -25,20 +25,21 @@ Figure~\ref{fig:real} exhibits the performance of the three mechanisms: Skip, Un \subcaptionbox{T-drive\label{fig:t-drive}}{% \includegraphics[width=.5\linewidth]{evaluation/t-drive}% }% - \caption{The mean absolute error (a)~as a percentage, (b)~in kWh, and (c)~in meters of the released data for different {\thethings} percentages.} + \caption{The mean absolute error (a)~as a percentage, (b)~in kWh, and (c)~in meters of the released data for different {\thething} percentages.} \label{fig:real} \end{figure} % For the Geolife data set (Figure~\ref{fig:geolife}), Skip has the best performance (measured in Mean Absolute Error, in meters) because it invests the most budget overall at every regular event, by approximating the {\thething} data based on previous releases. % Due to the data set's high density (every $1$--$5$ seconds or every $5$--$10$ meters per point) approximating constantly has a low impact on the data utility. % On the contrary, the lower density of the T-drive data set (Figure~\ref{fig:t-drive}) has a negative impact on the performance of Skip. -For the Copenhagen data set (Figure~\ref{fig:copenhagen}), Adaptive has a constant overall performance and performs best for $0$, $60$, and $80$\% {\thethings}. -The Skip model excels, compared to the others, at cases where it needs to approximate a lot ($100$\%). -The combination of the low range in HUE ($[0.28$, $4.45]$ with an average of $0.88$kWh) and the large scale in the Laplace mechanism results in a low mean absolute error for Skip(Figure~\ref{fig:hue}). +For the Copenhagen data set (Figure~\ref{fig:copenhagen}), Adaptive has a constant overall performance and performs best for $0$\%, $60$\%, and $80$\% {\thethings}. +We notice that for $0$\% {\thethings}, it achieves better utility than the event-level protection. +The Skip model excels, compared to the others, at cases where it needs to approximate $20$\%--$40$\% or $100$\% of the times. +The combination of the low range in HUE ($[0.28$, $4.45]$ with an average of $0.88$kWh) and the large scale in the Laplace mechanism, results in a low mean absolute error for Skip (Figure~\ref{fig:hue}). In general, a scheme that favors approximation over noise injection would achieve a better performance in this case. -However, the Adaptive model performs by far better than Uniform and strikes a nice balance between event- and user-level protection for all {\thethings} percentages. -In the T-drive data set (Figure~\ref{fig:t-drive}), the Adaptive mechanism outperforms Uniform by $10$\%--$20$\% for all {\thethings} percentages greater than $40$ and Skip by more than $20$\%. -The lower density (average distance of $623$ meters) of the T-drive data set has a negative impact on the performance of Skip. +However, the Adaptive model performs by far better than Uniform and strikes a nice balance between event- and user-level protection for all {\thething} percentages. +In the T-drive data set (Figure~\ref{fig:t-drive}), the Adaptive mechanism outperforms Uniform by $10$\%--$20$\% for all {\thething} percentages greater than $40$\% and Skip by more than $20$\%. +The lower density (average distance of $623$m) of the T-drive data set has a negative impact on the performance of Skip. In general, we can claim that the Adaptive is the most reliable and best performing mechanism with minimal tuning, if we take into consideration the drawbacks of the Skip mechanism mentioned in Section~\ref{subsec:lmdk-mechs}. Moreover, designing a data-dependent sampling scheme would possibly result in better results for Adaptive. From 6080efece9d250a44ef1d0b20e1494af44d9d2f9 Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 04:01:08 +0200 Subject: [PATCH 07/13] evaluation: Minor corrections and text --- code/expt/lmdk_sel_cmp.py | 58 +++++++++++++----- ...lmdk-sel-dist-emd.pdf => sel-dist-emd.pdf} | Bin 14308 -> 15771 bytes ...dk-sel-dist-norm.pdf => sel-dist-norm.pdf} | Bin 14804 -> 15964 bytes rslt/lmdk_sel_cmp/lmdk_sel_cmp-emd-l.pdf | Bin 0 -> 15771 bytes rslt/lmdk_sel_cmp/lmdk_sel_cmp-norm-l.pdf | Bin 0 -> 15964 bytes text/evaluation/theotherthing.tex | 35 +++++++++-- 6 files changed, 72 insertions(+), 21 deletions(-) rename graphics/evaluation/{lmdk-sel-dist-emd.pdf => sel-dist-emd.pdf} (70%) rename graphics/evaluation/{lmdk-sel-dist-norm.pdf => sel-dist-norm.pdf} (71%) create mode 100644 rslt/lmdk_sel_cmp/lmdk_sel_cmp-emd-l.pdf create mode 100644 rslt/lmdk_sel_cmp/lmdk_sel_cmp-norm-l.pdf diff --git a/code/expt/lmdk_sel_cmp.py b/code/expt/lmdk_sel_cmp.py index a7d9d71..ce466bc 100644 --- a/code/expt/lmdk_sel_cmp.py +++ b/code/expt/lmdk_sel_cmp.py @@ -20,7 +20,15 @@ def main(args): # Distribution type dist_type = np.array(range(0, 4)) # Number of landmarks - lmdk_n = np.array(range(int(.2*args.time), args.time, int(args.time/5))) + lmdk_n = np.array(range(0, args.time + 1, int(args.time/5))) + + markers = [ + '^', # Symmetric + 'v', # Skewed + 'D', # Bimodal + 's' # Uniform + ] + # Initialize plot lmdk_lib.plot_init() # Width of bars @@ -30,11 +38,13 @@ def main(args): x_margin = bar_width*(len(dist_type)/2 + 1) plt.xticks(x_i, ((lmdk_n/len(seq))*100).astype(int)) plt.xlabel('Landmarks (%)') # Set x axis label. - plt.xlim(x_i.min() - x_margin, x_i.max() + x_margin) + # plt.xlim(x_i.min() - x_margin, x_i.max() + x_margin) + plt.xlim(x_i.min(), x_i.max()) # The y axis # plt.yscale('log') - plt.ylabel('Euclidean distance') # Set y axis label. - # plt.ylabel('Wasserstein distance') # Set y axis label. + plt.ylim(0, 1) + plt.ylabel('Normalized Euclidean distance') # Set y axis label. + # plt.ylabel('Normalized Wasserstein distance') # Set y axis label. # Bar offset x_offset = -(bar_width/2)*(len(dist_type) - 1) for d_i, d in enumerate(dist_type): @@ -47,27 +57,41 @@ def main(args): print('(%d/%d) %s... ' %(d_i + 1, len(dist_type), title), end='', flush=True) mae = np.zeros(len(lmdk_n)) for n_i, n in enumerate(lmdk_n): - for r in range(args.reps): + if n == lmdk_n[-1]: + break + for r in range(args.iter): lmdks = lmdk_lib.get_lmdks(seq, n, d) hist, h = lmdk_lib.get_hist(seq, lmdks) opts = lmdk_sel.get_opts_from_top_h(seq, lmdks) delta = 1.0 res, _ = exp_mech.exponential(hist, opts, exp_mech.score, delta, epsilon) - mae[n_i] += lmdk_lib.get_norm(hist, res)/args.reps # Euclidean - # mae[n_i] += lmdk_lib.get_emd(hist, res)/args.reps # Wasserstein + mae[n_i] += lmdk_lib.get_norm(hist, res)/args.iter # Euclidean + # mae[n_i] += lmdk_lib.get_emd(hist, res)/args.iter # Wasserstein + mae = mae/21 # Euclidean + # mae = mae/11.75 # Wasserstein print('[OK]', flush=True) - # Plot bar for current distribution - plt.bar( - x_i + x_offset, + # # Plot bar for current distribution + # plt.bar( + # x_i + x_offset, + # mae, + # bar_width, + # label=label, + # linewidth=lmdk_lib.line_width + # ) + # # Change offset for next bar + # x_offset += bar_width + # Plot line + plt.plot( + x_i, mae, - bar_width, label=label, + marker=markers[d_i], + markersize=lmdk_lib.marker_size, + markeredgewidth=0, linewidth=lmdk_lib.line_width ) - # Change offset for next bar - x_offset += bar_width - path = str('../../rslt/lmdk_sel_cmp/' + 'lmdk_sel_cmp-norm') - # path = str('../../rslt/lmdk_sel_cmp/' + 'lmdk_sel_cmp-emd') + path = str('../../rslt/lmdk_sel_cmp/' + 'lmdk_sel_cmp-norm-l') + # path = str('../../rslt/lmdk_sel_cmp/' + 'lmdk_sel_cmp-emd-l') # Plot legend lmdk_lib.plot_legend() # Show plot @@ -81,7 +105,7 @@ def main(args): Parse arguments. Optional: - reps - The number of repetitions. + iter - The number of iterations. time - The time limit of the sequence. 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deletions(-) diff --git a/text/evaluation/theotherthing.tex b/text/evaluation/theotherthing.tex index a44f756..4bd09d6 100644 --- a/text/evaluation/theotherthing.tex +++ b/text/evaluation/theotherthing.tex @@ -2,8 +2,10 @@ \label{sec:lmdk-sel-eval} In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets. -With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utiliy}) we show the normaziled distances for various {\thething} percentages. -privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. +With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distances on items for various distributions and {\thething} percentages. +This allows us to justify our design decisions during the process. + +Privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. With the experiments on the real data sets (Section~\ref{subsec:sel-prv}), we show the performance in terms of utility of our three {\thething} mechanisms in combination with privacy preserving {\thething} that can be possibly applied to humans. From a549fe290f16bf8426b58f1d53242c7f776a8bfd Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 09:52:06 +0200 Subject: [PATCH 09/13] evaluation: Reviewed theotherthing --- text/evaluation/theotherthing.tex | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/text/evaluation/theotherthing.tex b/text/evaluation/theotherthing.tex index 4bd09d6..a5288c6 100644 --- a/text/evaluation/theotherthing.tex +++ b/text/evaluation/theotherthing.tex @@ -2,11 +2,9 @@ \label{sec:lmdk-sel-eval} In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets. -With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distances on items for various distributions and {\thething} percentages. -This allows us to justify our design decisions during the process. - -Privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. -With the experiments on the real data sets (Section~\ref{subsec:sel-prv}), we show the performance in terms of utility of our three {\thething} mechanisms in combination with privacy preserving {\thething} that can be possibly applied to humans. +With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distances of the time series histogram for various distributions and {\thething} percentages. +This allows us to justify our design decisions for our concept that we showcased in Section~\ref{subsec:lmdk-sel-sol}. +With the experiments on the real data sets (Section~\ref{subsec:sel-prv}), we show the performance in terms of utility of our three {\thething} mechanisms in combination with the privacy preserving {\thething} selection component. \subsection{{\Thething} selection utility metrics} @@ -27,8 +25,11 @@ Figure~\ref{fig:sel-dist} demonstrates the normalized distance that we obtain wh \end{figure} Comparing the results of the Euclidean distance in Figure~\ref{fig:sel-dist-norm} with those of the Wasserstein in Figure~\ref{fig:sel-dist-emd} we conclude that the Euclidean distance provides more consistent results for all possible distributions. +% (0 + (0.25 + 0.25 + 0.3 + 0.3)/4 + (0.45 + 0.45 + 0.45 + 0.5)/4 + (0.5 + 0.5 + 0.7 + 0.7)/4 + (0.6 + 0.6 + 1 + 1)/4 + (0.3 + 0.3 + 0.3 + 0.3)/4)/6 +% (0 + (0.15 + 0.15 + 0.15 + 0.15)/4 + (0.2 + 0.2 + 0.3 + 0.4)/4 + (0.3 + 0.3 + 0.6 + 0.6)/4 + (0.3 + 0.3 + 1 + 1)/4 + (0.05 + 0.05 + 0.05 + 0.05)/4) The maximum difference is approximately $0.4$ for the former and $0.7$ for the latter between the bimodal and skewed {\thething} distribution. -Therefore, we choose to utilize the Euclidean distance metric for the implementation of the privacy-preserving {\thething} selection. +While both methods share the same mean normalized distance of $0.4$, the Euclidean distance demonstrates a more consistent performance among all possible {\thething} distributions. +Therefore, we choose to utilize the Euclidean distance metric for the implementation of the privacy-preserving {\thething} selection in Section~\ref{subsec:lmdk-sel-sol}. \subsection{Budget allocation and {\thething} selection} @@ -53,8 +54,8 @@ Figure~\ref{fig:real-sel} exhibits the performance of Skip, Uniform, and Adaptiv \end{figure} In comparison with the utility performance without the {\thething} selection component (Figure~\ref{fig:real}), we notice a slight deterioration for all three models. -This is natural since we allocated part of the available privacy budget to the {\thething} selection component which in turn increased the number of {\thethings}. +This is natural since we allocated part of the available privacy budget to the privacy-preserving {\thething} selection component which in turn increased the number of {\thethings}. Therefore, there is less privacy budget available for data publishing throughout the time series for $0$\% and $100$\% {\thethings}. Skip performs best in our experiments with HUE, due to the low range in the energy consumption and the high scale of the Laplace noise which it avoids due to its tendency to approximate. -However, for the Copenhagen data set and T-drive it attains greater mean absolute error than the user-level. +However, for the Copenhagen data set and T-drive it attains greater mean absolute error than the user-level protection scheme. Overall, Adaptive has a consistent performance in terms of utility for all of the data sets that we experimented with. From 875999bdf2afb96af9d70ab4059ae29244928da2 Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 11:07:29 +0200 Subject: [PATCH 10/13] evaluation: Added intro --- text/evaluation/main.tex | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/text/evaluation/main.tex b/text/evaluation/main.tex index f491a80..e3b2f12 100644 --- a/text/evaluation/main.tex +++ b/text/evaluation/main.tex @@ -1,6 +1,13 @@ \chapter{Evaluation} \label{ch:eval} +In this chapter we present the experiments that we performed, to evaluate the methodology that we introduced in chapter~\ref{ch:lmdk-prv}, on real and synthetic data sets. +Section~\ref{sec:eval-dtl} contains all the details regarding the data sets the we utilized for our experiments (Section~\ref{subsec:eval-dat}) along with the parameter configurations. +Section~\ref{sec:eval-lmdk} evaluates the data utility of the {\thething} privacy mechanisms that we designed in Section~\ref{sec:thething} and investigates the behavior of the privacy loss under temporal correlation for different distributions of {\thethings}. +Section~\ref{sec:eval-lmdk-sel} justifies our decisions while designing the privacy-preserving {\thething} selection component in Section~\ref{sec:theotherthing} and the data utility impact of the latter. +Finally, Section~\ref{sec:eval-sum} concludes this chapter by summarizing the main takeaways of the results of the experiments that we performed. + \input{evaluation/details} \input{evaluation/thething} \input{evaluation/theotherthing} +\input{evaluation/summary} From eb055b52aa4122bdb590478f6511ed5aab3feab8 Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 11:07:40 +0200 Subject: [PATCH 11/13] evaluation: Added summary --- text/evaluation/summary.tex | 8 ++++++++ 1 file changed, 8 insertions(+) create mode 100644 text/evaluation/summary.tex diff --git a/text/evaluation/summary.tex b/text/evaluation/summary.tex new file mode 100644 index 0000000..4d65264 --- /dev/null +++ b/text/evaluation/summary.tex @@ -0,0 +1,8 @@ +\section{Evaluation} +\label{sec:eval-sum} + +In this chapter we presented the experimental evaluation of the {\thething} privacy mechanisms and privacy-preserving {\thething} selection mechanism, that we developed in chapter~\ref{ch:lmdk-prv}, on real and synthetic data sets. +The Adaptive mechanism is the most reliable and best performing mechanism, in terms of overall data utility, with minimal tuning across most cases. +Skip performs optimally in data sets with a lower value range where approximation fits best. +The {\thething} selection component introduces a reasonable data utility decline to all of our mechanisms however, the Adaptive handles it well and bounds the data utility to higher levels compared to user-level protection. +In terms of temporal correlation, we observe that under moderate and strong temporal correlation, a greater average regular--{\thething} event distance in a {\thething} distribution causes greater overall privacy loss. From 3741803b063515a48d02854c71d02bf1fde7dcee Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 11:08:03 +0200 Subject: [PATCH 12/13] evaluation: Minor corrections --- text/evaluation/theotherthing.tex | 6 +++--- text/evaluation/thething.tex | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/text/evaluation/theotherthing.tex b/text/evaluation/theotherthing.tex index a5288c6..6586cb6 100644 --- a/text/evaluation/theotherthing.tex +++ b/text/evaluation/theotherthing.tex @@ -1,8 +1,8 @@ \section{Selection of events} -\label{sec:lmdk-sel-eval} +\label{sec:eval-lmdk-sel} -In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets. -With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distances of the time series histogram for various distributions and {\thething} percentages. +In this section, we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets. +With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distances of the time series histograms for various distributions and {\thething} percentages. This allows us to justify our design decisions for our concept that we showcased in Section~\ref{subsec:lmdk-sel-sol}. With the experiments on the real data sets (Section~\ref{subsec:sel-prv}), we show the performance in terms of utility of our three {\thething} mechanisms in combination with the privacy preserving {\thething} selection component. diff --git a/text/evaluation/thething.tex b/text/evaluation/thething.tex index 1af0aa0..4cae89d 100644 --- a/text/evaluation/thething.tex +++ b/text/evaluation/thething.tex @@ -1,9 +1,9 @@ \section{Significant events} -\label{sec:lmdk-eval} +\label{sec:eval-lmdk} % \kat{After discussing with Dimitris, I thought you are keeping one chapter for the proposals of the thesis. In this case, it would be more clean to keep the theoretical contributions in one chapter and the evaluation in a separate chapter. } % \mk{OK.} -In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sol}, on real and synthetic data sets. +In this section, we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sol}, on real and synthetic data sets. With the experiments on the real data sets (Section~\ref{subsec:lmdk-expt-bgt}), we show the performance in terms of utility of our three {\thething} mechanisms. With the experiments on the synthetic data sets (Section~\ref{subsec:lmdk-expt-cor}) we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. @@ -83,7 +83,7 @@ The line shows the overall privacy loss---for all cases of {\thethings} distribu \label{fig:dist-cor} \end{figure} -In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} distance in a distribution can result into greater overall privacy loss under moderate and strong temporal correlation. +In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} even distance in a distribution can result into greater overall privacy loss under moderate and strong temporal correlation. This is due to the fact that the backward/forward privacy loss accumulates more over time in wider spaces without {\thethings} (see Section~\ref{sec:correlation}). Furthermore, the behavior of the privacy loss is as expected regarding the temporal correlation degree. Predictably, a stronger correlation degree generates higher privacy loss while widening the gap between the different distribution cases. From 3fc928fc49393a42dcde6a7feb1c3b9283e13511 Mon Sep 17 00:00:00 2001 From: Manos Date: Mon, 11 Oct 2021 11:09:30 +0200 Subject: [PATCH 13/13] evaluation: Corrected the summary section title --- text/evaluation/summary.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/text/evaluation/summary.tex b/text/evaluation/summary.tex index 4d65264..9ce39df 100644 --- a/text/evaluation/summary.tex +++ b/text/evaluation/summary.tex @@ -1,4 +1,4 @@ -\section{Evaluation} +\section{Summary} \label{sec:eval-sum} In this chapter we presented the experimental evaluation of the {\thething} privacy mechanisms and privacy-preserving {\thething} selection mechanism, that we developed in chapter~\ref{ch:lmdk-prv}, on real and synthetic data sets.