1 Introduction
In today’s technologyadvanced and dataexplosion world, cell phone usage is woven into nearly every aspect of human life. As we enjoy the major benefits provided by cell phones, the rapid growing use of the information network brings with it a rise in malicious cyber activities, and hence proves strong reasons for cybersecurity. Evidences have shown that approaches based on cell phones data that contains both accelerometer and gyroscope signals usually provides good performance [neverova2016learning]. However, there are a fair number of cell phones have no gyroscope data recorded, especially for some lowpriced cell phones. This paper proposes new techniques for gait extraction on accelerometer signal only; identification performance can be improved by adding gyroscope data when it is available. Moreover, our gait analysis is applied on human motion identification for strong user authentication on smart phones. The current authentication process for smart phones is largely based on weak static credentials, such as passwords or swipe patterns on touchscreens. Such credentials usually has many vulnerabilities that the attacker can easily gain access to the cell phone. Therefore, this paper researches on authentication methods aim to constantly protect the cell phone and simultaneously detecting the adversary. In addition to advanced knowledge on improving cell phone security, the methods provided in this paper will have several broader impacts; the gait segmentation approach works for other human motion analysis and the new time series distance, a new way of measuring similarity between signals, can be applied in other signal analysis. The principal arguments underlying this paper including: (a) a wellperformed data preprocessing by the gait segmentation method that wipes off the nonwalking activities and accurately segments the walking series into gait cycles is discussed in Section 2; (b) a new measurement for signal distance that transforms human vision into machine language is proposed in Section 3; (c) experimental studies of segmentation as well as a fast, stable and accurate useradversary identification are demonstrated in Section 4; (d) a summary and conclusion of the impact of this research is shown in Section 5.
Gait cycle segmentation or classification is broadly preprocessing step in studying human walking. In particular, high accuracy of gait cycle segmentation is extremely important in increasing the performance of human authentication. Another crucial usage of gait segmentation is to monitor or diagnose specific diseases such as Parkinson’s disease or peripheral neuropathy. There are many systems can be used to collect gait signals, such as visionbased systems, goniometers, Inertial Measurement Units (IMUs) and foot pressure sensors, among which IMUs is mostly studied in this paper. Many gait cycle segmentation methods have been studied based on different types of signal recorded from different types of sensors. Some gait segmentation methods are applied in identification of contact events, such as heel strike and toeoff which could be particularly useful in providing online assistance during walking; different type of signals have been used, such as only kinematics data from the knee and hip joints [kalinowska2019data] or angular velocity of lower limb [grimmer2019stance]
. Some Hidden Markov Model based machinelearning methods are investigated in gait segmentation by pressure sensors, see
[crea2012development, de2012gait]. Footswitch signal gait segmentation is researched in [agostini2013segmentation]. Comparison of four gait segmentation methods, including peak detection from eventbased methods, two variations of dynamic time warping from template matching methods, and hierarchical hidden Markov models from machine learning methods, are made to exam the Parkinsonian gait in [haji2018segmentation]. Researches on pathological gait abnormality detection and segmentation are made in [khan2019pathological]. In the literature, zerocrossing and LombScargle periodogram for cycle extraction are widely used; the former is based on wave form [khan2019pathological, sugandhi2019overlap] and the latter is for detecting and characterizing periodic signals in unevenlysampled data [vanderplas2018understanding]. A robust algorithm for gait cycle segmentation is provided based on a peak detection approach in [jiang2017robust]. Many accelerometerbased gait analysis has been summarized in [D2010].Existing gait segmentation algorithms have achieved outstanding performance, but showed its deficiency when dealing with very noisy data and activity mixed gait signals. Therefore, the accelerometerbased segmentation method proposed in this paper aims to address the above problems and improves the performance of useradversary identification or, in particular, the accuracy of smart phone authentication. The gait cycle obtained by our algorithm began when one foot touched the ground and ended when the same foot touched the ground again, shown in Figure 1 with xaxis of the accelerometer data. Several geometry features of the accelerometerbased gait cycle are summarized in the following:

Both of the starting and ending points of the gait cycle are minimal peaks with bigger angles defined in Equation (3).
The robust algorithm for gait cycle
segmentation provided in [jiang2017robust], however, can not deal with the cases when in , the values of the edge points are not the lowest within a cycle, see for example the right plot in Figure 1. Our proposed gait segmentation approach is more reliable when dealing with real walking signal that involves all but not limited to the above problems and results in more accurate segmentation.
Apparently, it becomes confused when we mention the accuracy of the segmentation. We can definitely visually judge if the segmentation satisfies our criteria. However, teaching computer to determine if a cutting is good or not under the same criteria is a difficult task; many misjudgement are really out there and better approaches are urgently needed. We propose a simple and fast signal distance measurement that plays the role of translating human vision to computer language. This method provides the score of tuning the three hyperparameters involved in the segmentation and as a result decides the accuracy of the segmentation. The segmentation technology as well as the signal distance investigated in this paper should not be limited to be applied in the useradversary identification problem. Many applications in the area of human motion analysis and other type of signal analysis requires high accuracy method described here to address real world problems.
The visionbased human motion analysis in [zeng2019vision]
automatically identify the behaviour of human from a given image or a sequence of images. A human motion recognition method based on Kalman random forest algorithm model is studied in
[yi2019human] for improving the accuracy and efficiency of tracking algorithm. Many neuralnetwork based methods to recognize human motion intention are widely investigated in literature, see e.g. [wu2019neural, lang2019joint, neverova2016learning, oukrich2019daily, furuya2019personal]. A method for positive identification of smartphone user’s identity is presented in [damavsevivcius2016smartphone], using user’s gait characteristics based on the application of the Random Projections method for feature dimensionality reduction.Relying on the segmentation approach as well as the signal distance proposed, the accuracy of our useradversary identification are rapidly improved even with simple and native classification methods. Against the current existing methods, we develop a new distance function for our classification method based on novel techniques of extracting certain archetypes to identify user and adversary behaviors from the training data set. Specifically, we extract the archetypes that represent individual walking behavior by simple clustering methods based on our signal distance. Then comparison are made between new signal data to the known archetypes of candidates containing user and adversary. The overall accuracy obtained shows that our methods are wellperformed in cell phone authentication and detecting theft.
2 Accelerometerbased segmentation algorithm
In this section, a detailed gait segmentation algorithm is introduced based on the geometry features discussed in Section 1. The flow chart in Figure 2 briefly introduces the process of segmentation as well as the organization of this section.
In Subsection 2.1, several precutting detection approaches are applied to obtain a rough segmentation, which follows Subsection 2.2, where finer segmentation is processed. Next, a best cycle is determined from the finer segmentation in Subsection 2.3. Finally, Subsection 2.4 talks about approaches to obtain the final segmentation. For an example of segmentation processes, see Figure 3. In the following, let denotes the raw signal series, which has data points in total and be the value of the th data on the signal. Our goal is to find the segmentation of a given signal, where segmentation is represented by all the cycles on the signal, or in other words, all points that divide the signal into cycles. We call these dividing points "cuts". Here cycle is the partial signal between two nearby cuts.
2.1 Preprocessing
Features and provided an idea of identify cutting positions. Apparently, we are more interested in the points on critical lines (dominated lines) and at the same time has relatively smaller yvalues than others. We will use peak detection method provided by Scipy to roughly find all minimal peaks of the raw signal, before which, normalization is required to standardize different signals so that the peak detection method can be applied under same criteria. The minimal peaks obtained are the precuts of the signal.

First, we scale the signal to have the range of . The th scaled data is:
(1) 
Second, we shift the scaled signal to have mean. The th mean data is:
(2) 
Last, we apply the peak detection in scipy on the normalized signals with the same criteria, to obtain the precuts. Guaranteed by (1) and (2), height feature involved in the peak detection method in Scipy can be set to be for all signals. Moreover, the width feature is set to be for simplicity, since eventually the cycle cutting points are expected to be not very concentrated.
The result of the precutting process is a vector of points for with Here denotes the position of the th data in and denotes the value of the th data in . The mappings involved in (1) and (2) are invertible and have no change on the time axis of the signal, so the positions of the th precut is , which is the same on , and .
2.2 Finer processing
The cuts suppose to be the points where a gait cycle starts or ends, so the angles of the peaks in the accelerometer plots suppose to be relatively bigger, which is due to of gait cycle discussed in Section 1. Therefore, we pick peaks with larger angles to be possible candidates of the segmentation cuts. Recall that the th precut point is , the closest points left and right to on are and respectively. The angle of data point is defined as the angle between vectors and :
(3) 
Then we pick cuts from precuts with angles above the median of the precut angles. Now the finer processed cuts are denoted as for with Here denotes the position of the th point on and denotes the value of the th precut point on .
2.3 Find best cycle
Based on the finer cuts picked in last subsection 2.2, cycles involved in are denoted by
where is the th cycle of the finer cuts with and . Moreover, the th cycle cuts are and . And the lengths of cycles are
where is the the cycle’s length with . The best cycle is the cycle best represents the signal’s gait features in the sense of statistical distribution; it will be used as a reference to find the rest of cycles on the signal. Let and be the values of histogram and the bin edges of respectively. Let be the length of the best cycle .
We are going to find the best cycle on the signal in at most three steps. See Algorithm 1 for details.

Attempt to search for the best cycle that satisfies

A cycle has length that is among the nonzero frequency cycle lengths of the finer cuts.

The length of the cycle needs to be close to the hypothesized gait length , where hypothesized gait is a hyperparameter to be tuned or given. Normally is the average gait length, but it can be modified to obtain different goals such as half cycle segmentation.
If the two requirements of a best cycle can be satisfied by any cycle of the finer cuts, we will use that cycle as the best cycle and skip the next step. Otherwise, go to the next step.


In this step, we are going to modify the finer cuts based on two situations below to achieve the requirements in Step 1.

If is much smaller than the gait length , we are going to combine each nearby pair of the finer cuts to make the average cycle length of finer cuts larger than before.

If is much larger than the gait length , we are going back to Session 2.2 and pick up more finer cuts.
Either of the two modifications will renew the finer cuts. Then search for the best cycle on the new finer cuts based on the following conditions:

A cycle has length that is closest to the largest frequency of cycle lengths of the finer cuts.

The length of the cycle needs to be close to the hypothesized gait length .
If no best cycle obtained, repeat Step 2 until one is found.

Up to this point, we have found the best cycle on the signal. Next, we will discuss how to find the rest of cycles on the signal based on the features of .
2.4 Find all cycles
It remains to cut the rest of the signal into cycles to obtain full cycle segmentation, which is denoted by
where and the cutting positions are
for . In this section, we mainly introduce the approach of finding other cycles to the left of the best cycle , and the righthand side cycles can be found easily by a similar approach, so it is omitted. Two steps are included in searching to the left:

Find cycles based on the lefthand side finerpicked peaks. Since the finer cuts are highly possible the right cutting positions, it deserves to scan one by one of these cuts to utilize the previously calculated results. For instance, the lefthand side peak right next to is . Let the potential cut position on the finer cuts be and is now at the th cut of finer cuts, or . So the potential cycle length is and the left over signal length is . There are three conditions listed in the following:

If is close to , the two finer cuts are kept as a cycle, i,e, . Then update and for next iteration.

If is much smaller than , is disregarded and update and for next iteration.

If is much larger than , then find the possible cycle in between the two finer cuts and update to . Then update and record the left over signal length .


Since the finer cuts may not reach the very left end of the signal, we are going to keep searching for cycles left to the finer cuts if there is any.
The above steps are iteratively repeated until the end of the signal is reached. There are two hyperparameters and involved to be given or tuned where controls how similar the two cycles are and controls the range of searching for local minimum. Details will be shown in Algorithm 2.
3 New signal distance
We propose a new way of calculating distance between two signals. Let and be two signals and and are points on and respectively. Let be a permutation of such that
The basic idea is to find the interpolations of
on and , denoted by and with . Then the distance between and is defined asNote that here we use Euclidean distance to formalize ; in fact any distance can be fitted here depends on different situations. The details are shown in Algorithm 3. This signal distance plays a crucial role in all signal analysis. In particularly, we are going to show how it will be applied in segmentation and human motion identification.
4 Experimental study
All the experimental results in this section are based on HAPT data ^{1}^{1}1http://archive.ics.uci.edu/ml/datasets/SmartphoneBased+Recognition+of+Human+Activities+and+Postural+Transitions#. There are 30 volunteers in total within an age bracket of 1948 years engaged in the data recording and all were wearing a smartphone (Samsung Galaxy S II) on the waist and performed a protocol of activities during the experiment execution. Among all the activities, walking, walking downstairs and walking upstairs are mainly studied in this paper. More specifically, 3axial accelerometer and gyroscope data for each of the activity are studied.
The segmentation in Section 4.1 shows the results of cutting on the data set by using algorithm proposed in Section 2. The useradversary identification in Section 4.2 will continue use the segmented data. Training data are clustered to extract individual archetypes or features, while each testing cycle is compared with all volunteer’s archetypes extracted in training process to do classification. Each volunteer may have several separated periods of data recorded for each activity; several periods are studied to capture full picture of the archetypes for an individual.
4.1 Segmentation
The segmentation algorithm discussed in Section 2 is applied in this section on the HAPT data set. Recall that there are three hyperparameters involved in the segmentation algorithm: hypothesized gait length , cycle similarity threshold and local minimum searching range . The segmentation structure tunes the positions of the cuts on the signal by the three hyperparameters on a score defined as
where is a shifting parameter that can bring the two signal and as close as possible, and in our case, should be in the range of . Eventually, the segmentation we obtained is . Based on our basic statistical analysis, here for a full gait cycle, is normally around 50, which follows the value of less than . We are going to set to cut all possible cycles in the signal.
We apply the segmentation on the xaxis accelerometer of walking, walking up, walking down and mixed walking activities for each volunteer. Some results are included in Figure 4 and Figure 5. Figure 4 indicates that the segmentation algorithm works for different activities: walking, walking up and walking down. All the periods of walking, walking up and walking down in the HAPT data set can be perfectly cut by our proposed approach, except for the case shown in Figure 5.
Like what is shown in top and middle figures in Figure 5, depending on which leg step forward first in the experiments, the segmentation might not be consistent. Even though we can say both of them are perfectly segmentation individually, it might become a problem in applications like useradversary identification in next section. Our way of addressing this problem in the useradversary identification process is to include each of the different cutting as a archetype for the individual. Besides, this problem can also be easily resolved by half segmentation of the gait cycle. More precisely, we can easily set smaller that that of full cycle and go through the same process. See Figure 6 first and second plots.
Another problem is shown in bottom figure in Figure 5. Although certain period of certain activity is recorded at the same time with same volunteer, it sometimes not that stable. In this example, the first signal looks very different from the last of it, resulting in some errors in segmentation. Again, half segmentation can also resolve this problem, see Figure 6 third plot. Another alternative is using bigger which guarantee the similarity between cycles are maintained , see Figure 6 last plot. This alternative is more feasible for applications that detect the walking behaviors by cutting off the nonwalking signals. The way we deal with this problem in next section is to repeat the latter alternative to extract different patterns of the gait cycle as more archetypes for the individual user.
Our segmentation algorithm also works for a more complicated situation when all types of walking cycles are mixed. By iteratively running our segmentation algorithm, we can separately segment the different types of walking signals and cut off the nonwalking or noise signal. For example, we manually combined Xaxis accelerometer walking, walking up and walking down signal of volunteer 1 in HAPT data set and then we apply our proposed algorithm to the new mixed data set; the segmentation results is shown in Figure 7.
4.2 Useradversary identification
In this section, multiclass classification is processed to identify user and adversary based on the wellcut xaxis accelerometer based gait segmentation from Section 4.1. The cut cycles are split into training (80%) and testing (20%) set for each volunteer. Cycles in the training set are used to extract the archetypes for each individual. The approach to obtain the archetypes is shown in Algorithm 4 and that the main idea is about clustering the training cycles into classes such that cycles within each class are guaranteed to have signal distance less than a threshold . The threshold controls the speed and accuracy of the classification process; a high speeds up the process but results in lower accuracy. Archetypes are obtained by taking "average" of the cycles in each classes using the new signal distance defined. As a result, each volunteer will have several archetypes, denoted as where . See Figure 8 for an example of archetypes of volunteer 1 with . Note that all the experiments in this paper use to obtain more archetypes and then higher performance. It is important to mention that, each test sample is single cycle based in the testing process; it is labeled into the a volunteer that has the archetype closed to the test cycle by using the signal distance. Our single cycle test method is in demand in cybersecurity field since user authentication has to be done within a few seconds.
4.2.1 Results
We discuss the results from several experiments under different scenarios in this subsection. Testing samples are single cycle based. Note that all the following experiments are conducted based on fullgait xaxis accelerometer segmentation, see Section 4.1 for details.
Experiment 1: 6, 10, and 30 classes useradversary identification (classification) using xaxis accelerometer and xaxis gyroscope respectively for walking signal only.
Results are shown in Table 1
. We run 6, 10, and 30 classes classification on xaxis accelerometer and xaxis gyroscope walking signals respectively to identify the user and the adversary simultaneously. The xaxis accelerometer or xaxis gyroscope walking signals is segmented by xaxis accelerometer based segmentation. As the number of classes or the number of volunteers involved in the experiments increases, more potential adversaries are considered and therefore, adding more complicity to the classification system. This can be verified by the decreased accuracy from around 0.97 to 0.9 as the number of class rises from 6 to 30. All the performance results in the table are the mean values and standard errors of the results from 20 times randomly pick 6, 10, or 30 out of 30 volunteers in HAPT data set. In Figure
9, several confusion matrices of the classification results for each of the 4 groups contains randomly picked 6 volunteers are demonstrated. Although, multilevel classification seems to be more complicated than the binary one, our technology still reserves very high accuracy.Besides the multilevel classification to identify user and adversary, we can also demonstrate a binary classification for user only identification; while we keep the training process the same, testing set includes the test cycles of the true user and randomly pick 2 test cycles of each of the 29 potential adversaries. The results are of 0.9744 and 0.9789 on average of test results for accelerometer and gyroscope signals respectively; the results perform better than that in [neverova2016learning, damavsevivcius2016smartphone] which have accuracy of 0.9302 and 0.943 respectively.
Number  Accelerometer  Gyroscope  

of class  ACC  PPV  TPR  F  ACC  PPV  TPR  F 
6  0.9649  0.9730  0.9558  0.9592  0.9706  0.9759  0.9620  0.9647 
(0.008)  (0.006)  (0.009)  (0.008)  (0.007)  (0.006)  (0.009)  (0.008)  
10  0.9348  0.9490  0.9247  0.9270  0.9394  0.9528  0.9284  0.9326 
(0.008)  (0.006)  (0.009)  (0.009)  (0.008)  (0.006)  (0.009)  (0.009)  
30  0.8789  0.8986  0.8677  0.8684  0.9000  0.9190  0.8835  0.8890 
Experiment 2: 6, 10, 30 classes useradversary identification (classification) using 3axis accelerometer and 3axis gyroscope respectively for walking signal only.
Results are shown in Table 2. Similar to Experiment 1, but use three axes of accelerometer or three axes of gyroscope signal in the classification process. Each test cycle (contains 3 axes as a group) is labeled to the volunteer that has the closet archetype (from 3 axes) to at least one of the axes of the test cycle. All the results are improved compared with the results using xaxis data only. The binary classification established the same as that in Experiment 1 provides an accuracy of 0.9906 for both accelerometer and gyroscope type classification.
Number  Accelerometer  Gyroscope  

of class  ACC  PPV  TPR  F  ACC  PPV  TPR  F 
6  0.9812  0.9838  0.9833  0.9811  0.9879  0.9900  0.9889  0.9880 
(0.006)  (0.005)  (0.005)  (0.006)  (0.005)  (0.004)  (0.004)  (0.004)  
10  0.9798  0.9848  0.9783  0.9785  0.9767  0.9822  0.9775  0.9766 
(0.005)  (0.003)  (0.005)  (0.005)  (0.005)  (0.004)  (0.005)  (0.005)  
30  0.9573  0.9659  0.9556  0.9537  0.9573  0.9659  0.9556  0.9537 
Experiment 3: 6 classes useradversary identification (classification) using 3axis accelerometer and 3axis gyroscope respectively for walking up, walking down and mixed walking signals.
Results are shown in Table 3. The experiments on walking up and walking down signals are similar to Experiment 1 with 6 classes but replace the activity with walking up and walking down respectively. The mixed walking experiment using the iterative segmentation presented in Figure 7; the classification is applied on three axes of accelerometer or gyroscope signal together for mixed walking activities.
Signal  Accelerometer  Gyroscope  

Type  ACC  PPV  TPR  F  ACC  PPV  TPR  F 
Walking up  0.9423  0.9632  0.9417  0.9388  0.9385  0.9569  0.9375  0.9336 
(0.015)  (0.009)  (0.015)  (0.016)  (0.013)  (0.010)  (0.013)  (0.014)  
Walking down  0.8140  0.7715  0.7936  0.7604  0.8408  0.7768  0.7992  0.7692 
(0.032)  (0.042)  (0.032)  (0.038)  (0.020)  (0.034)  (0.025)  (0.030)  
Mixed Walking  0.7170  0.7444  0.6936  0.6928  0.7903  0.8163  0.7857  0.7834 
(0.025)  (0.025)  (0.025)  (0.024)  (0.014)  (0.013)  (0.014)  (0.013) 
5 Discussion and Conclusion
The technology developed here would have great impact on cell phone useradversary identification and cybersecurity. Comparing with existing segmentation methods such as zero crossing and LombScargle Periodogram, we cut at the critical points based on geometric features integrated with statistical and iterative methods. Our method is more robust and scalable. Moreover, the new segmentation method is applicable for different walkingtype signals such as walking, walking upstairs, walking downstairs and mixed walking. Further research involves applying our proposed technology on more flexible walking signals such as walking with cell phone in hand, in pocket or in bag. The signal distance proposed in this paper provides a new approach of measuring the difference between signals which gives a possibility of translating the way human vision in distinguishing signals to machine language. It can be broadly used in all kinds of signal processing analysis which indicates many possible directions of further researches. The useradversary identification algorithm we proposed easily detects if certain walking behaviors are from the user or not. More precisely, it is possible to determine who is this imposter if potential imposters are provided. Comparing to the fact of tuning a large number of hyperparameters in Neutral Network methods, our approaches only have four parameters with clear geometric meaning involved; the parameters can be tuned or given based on geometric analysis integrated by statistics. We obtain an accuracy of 0.9879 for 6class classification on walking signal using 3 axes of the both accelerometer and gyroscope data; the accuracy is of 0.9812 when using only 3 axes of the accelerometer data; we still keep an accuracy of 0.9649 or 0.9706 when only using xaxis of the accelerometer or xaxis of accelerometer and gyroscope data. Even if the classification is on all the possible classes (30 classes) in HAPT, we still reserve an accuracy of 0.9573 by our approaches. When the multilevel classification degenerates to binary classification, we obtain an accuracy of around 0.99 for walking signal. It is worth to point out that the walking up and walking down data sets are very small, yet our experiments still showing solid results while there is not enough data for training in Neutral Network methods. In summary, the techniques we developed here is in high accuracy in useradversary identification even with multilevel classification, which is crucial in cybersecurity.
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