Our results show that using the benchmark set size of 7 and 08 PCA components size of 20 in WifiU are effective.Figure 0.6 10(b)gives the performance of WifiU under different bench- 8 0.4 mark set sizes.We observe that using more benchmark sub- -FAR jects gives lower EER,but the results for having 7,9,and 02 …FRR 11 benchmark subjects are almost the same.Therefore,we 0.05 吧mor ra 0.2 choose to use 7~9 benchmark subjects in WifiU.Figure 10(c) gives the performance of WifiU under different number of Figure 9.CDF of FAR and FRR PCA components used in spectrogram generation.Using 20 PCA components is enough,since adding more components do not further improve the performance of WifiU. rest 50-7-1 =42 subjects are treated as strangers in the evaluation.Note that none of the walking instances of these Robustness strangers are seen by the SVM during training.The FAR and Our results show that evolution of human gait does not sig- FRR are calculated using 10 fold cross validation,where one nificantly affect the accuracy of WifiU.To study the robust- tenth of the walking instances are used for testing and the ness of WifU against gait evolution,we collected more than remaining are used for training.After getting the individual 200 walking samples from the same subject over a period FAR and FRR for all subjects not in the benchmark set,we of four months and performed 10 fold cross validation on repeat the whole process using a new set of benchmark sub- these samples.Figure 11(a)plots FAR vs.FRR of WifiU jects.The final results are averaged over 100 randomly selec- for this scenario obtained from the 10 fold cross validation ted benchmark sets. We observe from this figure that WifiU achieves an EER of Our results show that WifiU achieves average FAR and FRR just 11.3%on these testing samples.WifiU is also robust to of 8.05%and 9.54%,respectively,when setting the probab- small changes in environments,such as moving chairs/tables ility threshold for identification to 0.5.In other words,our around the room or slightly changing the location of the system determines that the gait sample belongs to the true Router/Laptop,which actually happened frequently during user when the fitness probability is higher than the threshold the four month period of data collection. of 0.5.Figure 9 shows the distribution of FAR and FRR Our results show that the accuracy of WifiU deteriorates only on different subjects.For more than 80%subjects,WifiU when the apparel and accessories of the target subject change achieves FAR smaller than 10%and FRR smaller than 15%. significantly.To study the impact of change in apparel and By changing the probability threshold in the gait model,we accessories on the accuracy of WifiU,we first train WifiU us- can achieve different tradeoffs between FAR and FRR.Fig- ing training samples of a subject wearing winter clothes and ure 10(a)shows the tradeoff curve for FAR and FRR.At the wearing spring clothes,and then evaluate its FRR on testing point where FAR and FRR is equal,we get an EER of 8.6% samples obtained when the same subject was wearing differ- when we use all the available training data. ent types of clothes i.e.,suits or carrying a briefcase.Figure To evaluate top-k accuracy,in each experiment,we randomly 11(b)plots the FRR for different apparel and accessories op- tions when FAR is set at 11.1%.The FRR increases from pickup ten human subjects from our walking database.The top-k accuracy for the given candidate set is obtained via 10 10%in the training set(winter/spring clothes)to at least 25 fold cross validation over the samples of the ten subjects.We when the subject is wearing different apparel and accessor- perform this experiment for 100 times and calculate the av- ies.This happens due to the well studied fact that human erage top-k accuracies.WifiU achieves top-1,top-2,and top- gait changes when wearing different types of apparel and ac- 3 accuracies of 92.31%,97.58%,and 98.86%,respectively. cessories [8].Despite the fact that we never trained WifU on Note that the recognition task is considerably harder than samples with these apparel and accessories,it still provides the identification task in the previous experiment because in decent FRR while keeping FAR as low as 11.1%. the recognition task,WifiU does not just have to determine whether the test subject is the true user or not,rather has to Efficiency recognize exactly which user it is.When we increase the size Our results show that WifiU can run in realtime on laptops of subject set to 50 subjects,the top-1,top-2,and top-3 ac- and desktop computers.We evaluated the efficiency of WifU curacies are 79.28%,89.52%,and 93.05%,respectively. on a laptop equipped with an Intel Core i5 CPU running at 2.8 GHz.Table 2 gives the CPU processing time and the standard Our results show that 40 training instances are practically deviation for processing one second of CSI measurement in large enough to build the classifier as shown by Figure 10(a). our implementation on Matlab.We observe that the total CPU We plot the FAR and FRR for training schemes that use time required to process one second of data is 0.275 second all available instances for training and compare them to the so that the laptop can easily handle realtime processing for schemes that limit the training set size to 20.30 and 40 in- WifiU.The major computational cost (about 71.3%)is in the stances.We see a diminishing improvement in EER with in- PCA denoising step because PCA needs to process the raw creasing number of training instances.Furthermore,the train- CSI measurements that have 180 x 2500 =450k samples per ing set size of 40 gives nearly the same identification accuracy second.As our PCA process reduces the data size to one as the scheme that uses all available training instances,which ninth of the raw CSI measurements,the spectrogram gener- is normally more than 50 instances in our database. ation step only takes 26.2%of the total computational time.0 0.05 0.1 0.15 0.2 0.25 0 0.2 0.4 0.6 0.8 1 Error rate CDF FAR FRR Figure 9. CDF of FAR and FRR rest 50 − 7 − 1 = 42 subjects are treated as strangers in the evaluation. Note that none of the walking instances of these strangers are seen by the SVM during training. The FAR and FRR are calculated using 10 fold cross validation, where one tenth of the walking instances are used for testing and the remaining are used for training. After getting the individual FAR and FRR for all subjects not in the benchmark set, we repeat the whole process using a new set of benchmark sub￾jects. The final results are averaged over 100 randomly selec￾ted benchmark sets. Our results show that WifiU achieves average FAR and FRR of 8.05% and 9.54%, respectively, when setting the probab￾ility threshold for identification to 0.5. In other words, our system determines that the gait sample belongs to the true user when the fitness probability is higher than the threshold of 0.5. Figure 9 shows the distribution of FAR and FRR on different subjects. For more than 80% subjects, WifiU achieves FAR smaller than 10% and FRR smaller than 15%. By changing the probability threshold in the gait model, we can achieve different tradeoffs between FAR and FRR. Fig￾ure 10(a) shows the tradeoff curve for FAR and FRR. At the point where FAR and FRR is equal, we get an EER of 8.6% when we use all the available training data. To evaluate top-k accuracy, in each experiment, we randomly pickup ten human subjects from our walking database. The top-k accuracy for the given candidate set is obtained via 10 fold cross validation over the samples of the ten subjects. We perform this experiment for 100 times and calculate the av￾erage top-k accuracies. WifiU achieves top-1, top-2, and top- 3 accuracies of 92.31%, 97.58%, and 98.86%, respectively. Note that the recognition task is considerably harder than the identification task in the previous experiment because in the recognition task, WifiU does not just have to determine whether the test subject is the true user or not, rather has to recognize exactly which user it is. When we increase the size of subject set to 50 subjects, the top-1, top-2, and top-3 ac￾curacies are 79.28%, 89.52%, and 93.05%, respectively. Our results show that 40 training instances are practically large enough to build the classifier as shown by Figure 10(a). We plot the FAR and FRR for training schemes that use all available instances for training and compare them to the schemes that limit the training set size to 20, 30 and 40 in￾stances. We see a diminishing improvement in EER with in￾creasing number of training instances. Furthermore, the train￾ing set size of 40 gives nearly the same identification accuracy as the scheme that uses all available training instances, which is normally more than 50 instances in our database. Our results show that using the benchmark set size of 7 and PCA components size of 20 in WifiU are effective. Figure 10(b) gives the performance of WifiU under different bench￾mark set sizes. We observe that using more benchmark sub￾jects gives lower EER, but the results for having 7, 9, and 11 benchmark subjects are almost the same. Therefore, we choose to use 7∼9 benchmark subjects in WifiU. Figure 10(c) gives the performance of WifiU under different number of PCA components used in spectrogram generation. Using 20 PCA components is enough, since adding more components do not further improve the performance of WifiU. Robustness Our results show that evolution of human gait does not sig￾nificantly affect the accuracy of WifiU. To study the robust￾ness of WifiU against gait evolution, we collected more than 200 walking samples from the same subject over a period of four months and performed 10 fold cross validation on these samples. Figure 11(a) plots FAR vs. FRR of WifiU for this scenario obtained from the 10 fold cross validation. We observe from this figure that WifiU achieves an EER of just 11.3% on these testing samples. WifiU is also robust to small changes in environments, such as moving chairs/tables around the room or slightly changing the location of the Router/Laptop, which actually happened frequently during the four month period of data collection. Our results show that the accuracy of WifiU deteriorates only when the apparel and accessories of the target subject change significantly. To study the impact of change in apparel and accessories on the accuracy of WifiU, we first train WifiU us￾ing training samples of a subject wearing winter clothes and wearing spring clothes, and then evaluate its FRR on testing samples obtained when the same subject was wearing differ￾ent types of clothes i.e., suits or carrying a briefcase. Figure 11(b) plots the FRR for different apparel and accessories op￾tions when FAR is set at 11.1%. The FRR increases from 10% in the training set (winter/spring clothes) to at least 25% when the subject is wearing different apparel and accessor￾ies. This happens due to the well studied fact that human gait changes when wearing different types of apparel and ac￾cessories [8]. Despite the fact that we never trained WifiU on samples with these apparel and accessories, it still provides decent FRR while keeping FAR as low as 11.1%. Efficiency Our results show that WifiU can run in realtime on laptops and desktop computers. We evaluated the efficiency of WifiU on a laptop equipped with an Intel Core i5 CPU running at 2.8 GHz. Table 2 gives the CPU processing time and the standard deviation for processing one second of CSI measurement in our implementation on Matlab. We observe that the total CPU time required to process one second of data is 0.275 second so that the laptop can easily handle realtime processing for WifiU. The major computational cost (about 71.3%) is in the PCA denoising step because PCA needs to process the raw CSI measurements that have 180×2500 = 450k samples per second. As our PCA process reduces the data size to one ninth of the raw CSI measurements, the spectrogram gener￾ation step only takes 26.2% of the total computational time