Modeling Mobility. Petteri Nurmi

Transkriptio

1 Modeling Mobility Petteri Nurmi

2 Questions What mobility models are? What is a discrete Markov model? What is an order q Markov predictor? What is the LZ predictor? What are time independent and time dependent predictors? How arrival times and visit durations can be modeled? How transportation mode can be detected from GSM, WiFi or GPS measurements?

3 Mobility Model Mathematical characterization of how people move Level of detail can vary: Fine-grained: change in location, velocity and acceleration, transportation mode For example, motion model used in a particle filter for location tracking Coarse-grained: transitions between different locations For example, movements between significant places Main focus of lecture on coarse-grained mobility Important for understanding urban phenomena and for characterizing the behavior of large masses

4 Example: Lévy-Flight model Source: evyflight.svg Characterizes displacements in human mobility Most trips have a short distance within specific areas Occasionally long movements to new areas Example of a so-called spatial mobility model Addresses an aspect related to changes in locations Aggregate model: provides information about averaged mobility behavior

5 Mobility Modeling Scope Individual: models the behavior of an individual Collective: models the behavior of large set of people Temporality Time-independent: mobility depends only on the previous state Time-dependent: mobility depends on previous time and temporal features (day of week, hour of day etc.) Memory and complexity How much historical information needs to be considered to make predictions about future behavior I.e., the order of the model

6 Application Areas for Mobility Models Epidemiology: modeling spread of viruses and infections in urban environment Diffusion of ideas: modeling propagation of innovations Urban planning: understanding how and where people move Transportation behavior monitoring: Understanding how public transportation network is being utilized Sustainability: estimating carbon footprint and encouraging greener alternatives

7 Example Application - AdNext Targeted advertising for large mall complexes Deployed within the COEX mall, the largest mall in South Korea and one of the largest in Asia Mobility model used to predict the next shop that the user is likely to visit Shown advertisements selected based on the predicted location, thus, just before potential purchase decisions Taken into account category of shops and causality in visiting patterns. For example, if the user has already visited a restaurant, no predictions related to visiting other restaurants are made

8 Example Application - UbiGreen Mobile application that gives feedback to users about their personal transportation behavior Different visualizations of the phone background depending on the sustainability of detected transportation behavior Mobility modeled in terms of transportation behavior Wearable sensor used for automatically detecting pedestrian and non-motorized transportation GSM used to detect motorized transportation behavior Users also provided opportunity to input things manually

9 Location Modeling Cluster visited locations into places I.e., perform place identification on traces Create a model that captures 1. Movement between places (location) 2. Arrival times of places 3. Duration of stay in a place Early models focused on modeling movement between places Recent work considers also arrival times and duration of stay

10 Location Modeling Transitions between places Simplest approach for modeling movements between places is to use a discrete Markov model After places have been identified, replay the data to the algorithm to detect visits to places Reconstructed visit sequence can be used to estimate the probabilities in the transition matrix Another popular choice is the LZ family of algorithms Any other algorithm can be used as well: Conditional random fields Timeseries forecasting methods

11 Mobility Modeling Example All data Places extracted from data Transition Matrix (Order 1)

12 Discrete Markov Models Stochastic finite state machine Let S 1,,S n denote a discrete set of states Let x k denote the state of the system at time k I.e., x k {S 1,,S n } The state of the system is assumed to evolve over time according to a probabilistic model p(x k x 1:k-1 ) p(x k x 1:k-1 ) are called transition probabilities The probability of the current state x k is assumed to depend only on the previous q values The value of q defines the order or memory of the model Order q model: p(x k x 1:k-1 ) = p(x k x k-q-1:k-1 )

13 Discrete Markov Models - Example Assume a place identification algorithm identifies three places for an individual: home, work, shop Transitions from one place to another are governed by the following probabilities: HOME WORK SHOP HOME WORK SHOP If the person is current in the shop, what is the probability of the person going to work and then to home? P(shop, work, home model, x k = shop) = P(shop) P(work shop) P(work home) = 1 * 0.05 * 0.15 =

14 Discrete Markov Models Estimating Transition Probabilities Transition probabilities can be estimated from data P(s i s j,d) = P(D,s j s i )P(s j s i ) Follows from Bayes theorem Standard approach is to assume P(D,s j s i ) follows a Multinomial distribution P(D,s j s i ) can simply be estimated using n ij / N, i.e., the relative frequency of state transitions in the data n ij = number of transitions from s i to s j in the data N = number of measurements in the data For P(s j s i ) a prior guess is used Or simply P(s j s i ) = 1/n (n is the number of states)

15 Discrete Markov Models State Duration Given that the model is in a known state S q, what is the probability that it stays in that state for d periods? Corresponds to determining the probability of the state sequence O = S q,, S q, S z (z q) P(O Model) := p(s q s q ) d-1 (1 - p(s q s q )) = p q (d) The quantity p q (d) specifies a probability distribution function for the duration of a state The expected duration of a state q is given by E[d(q)] = dp q (d) = 1 / (1 - p(s q s q )) For the example, we have: E[home] = 1 / (1 0.85) =

16 Lempel-Ziv (LZ) Predictor Text compression algorithms typically are good predictors as they identify regularities in text Can thus be used to predict location transitions Lempel-Ziv predictor Based on the Lempel-Ziv text compression algorithm Let s denote a sequence of symbols, the algorithm splits the original sequence recursively into parts so that s 0 = γ here γ denotes the empty string For all s j j >= 1, the prefix of s j is equal to some s i, i < j s 0 s 1...s k = s The splitting of a string can be represented using a LZ tree

17 LZ-Tree Input: ABABABCDCBDC S0 = γ S1 = A S2 = B S3 = AB S4 = ABC S5 = D S6 = C S7 = BD S8 = C ABABABCDCBDC BABABCDCBDC ABABCDCBDC ABCDCBDC DCBDC CBDC BDC C

18 Lempel-Ziv (LZ) Predictor Given the sequence of locations L, the probability of the next location can be estimated using Number of times s m appears as prefix Example: P(C AB) = ½ P(B) = 2/8 P(B A) = 2/3 2/3 1/2 Number of times s m appears as prefix of s 3/8 2/8 2/8 1/8 1/

19 LZ Predictor Issues and Extensions ABABABCDCBDC Patterns between two detected patterns are lost BD is followed by C but DC is not in the LZ tree LeZi update: Variation of LZ algorithm where also substrings of patterns are taken into account Results in a LZU tree, probabilities can be estimated using prediction- by-partial matching (PPM) Patters within patterns are lost Pattern abc is in the LZ tree but the pattern bc not Active LeZi: Uses LZ to determine window length and considers all suffixes when creating a tree (ALZ tree)

20 Temporal Modeling Temporal mobility models attempt to capture arrival times and duration of stay (residence) Basic idea Identify places Use arrival and departure to a place to construct pairs of (arrival time, duration) measurements Range typically restricted, e.g., to 5 minute intervals Arrival time and duration can be predicted by examining the history of measurements Once actual arrival time known, estimate of duration can be refined by restricting the history

21 Arrival Time Modeling For each location, create a time series of previous arrival times / daily visit start times Example: Monday 1:10pm, Tuesday 2:30pm, Denote the visit daily start times using C = (c 1,,c n ) Arrival time prediction: At time k, consider the previous m arrival times, C = (c k- (m+1),,c k-1 ) Search the history for sequences C = (c i-(m+1),,c i-1 ) that are similar to C Estimate arrival time by averaging the values that follow these subsequences

22 Example Current arrival time sequence 18:35, 22:10, 8:00,?? Similar arrival time sequences in historical data 18:30, 22:00, 8:15, 13:10 18:10, 21:50, 8:35, 12:40 Predicted arrival time 13:10 12:40 12:

23 Predicting Visit Duration Visit duration can be predicted in similar fashion Instead of considering arrival times of previous visits that match with the sequence of current measurements, calculate average over previous durations Example: 18:35, 22:10, 8:00,?? 13:10 Duration 40 12:40 Duration 50 Arrival time 12:55, Duration 45 minutes

24 Temporal Modeling The search for similar sequences requires a suitable measure of similarity Simple solution is to bin the arrival times using, e.g., 5 minute intervals, and compute distance between bins More elaborate techniques for the task are discussed during Lecture IX Alternative is to model time spent in a location using a probabilistic distribution E.g., using a truncated exponential distribution

25 Predictability Tuple (L,A,D) is called a visit pattern L = Location of the user A = Time when the user arrived at the location D = Duration that the user stayed at the location The pattern (L, A, D) is predictable given observation history H if and only if (L,A,D) H Predictability can be quantified using entropy H(X) = - p(x i ) log p(x i ) Measure of disorder è high entropy corresponds to poor predictability and vice versa

26 Predictability Entropy as a measure of predictability depends on the complexity of the model Consider the sequence S = H H T H H T H H T Time-independent predictor: H(S) = 0.64 Order-1 Markov predictor: H(S) = 0.35 Order-2 Markov predictor: H(S) = 0 The higher the complexity of the model, the more data is needed to construct the model Too little data easily leads to overfitting

27 Mobility Modeling Transportation Mode Detection Transportation mode is a special aspect of mobility Transportation mode detection applications include: Carbon footprint monitoring Travel route recommendations Urban planning Two subtasks 1. Distinguishing between stationary and non-stationary activities 2. Recognizing mode of locomotion (e.g., motorized, pedestrian etc.)

28 Detecting Stationary Periods When user is moving, sensor measurements contain more variation than when user is stationary Variation can be measured from different sensors: accelerometer, GPS, WiFi etc. Basic technique is to calculate the mean intensity or variance of a sensor value over a predefined window Intensity: i=1n x i where N is the size of the window Variance: 1/(N-1) i=1 N (x i -μ i ) 2 where μ i is the mean of the measurements within the data window

29 Stationary Detection Example - LOCADIO WiFi positioning system that uses stationary inference as part of position estimation Motion detected using a two-phase approach Given a window size w, identify the strongest access point within the window and calculate its variance Classify the person as stationary or moving based on the calculated variance Use a HMM to smooth classification results over time

30 Stationary Detection Example - LOCADIO Stationary Strongest access point σ = 20 P(σ still) = P(σ moving) = Moving

31 Locomotion Detection Detecting the means of transportation Motorized (car, tram, bus, ) Pedestrian (walking, running, ) Non-motorized transportation (bicycling, ) Most common approach is to use wearable accelerometers (or accelerometers on the phone) WiFi and GSM signatures can be used for coarse-grained detection over time windows with long duration GPS features can be used to separate between transportation modes Accelerometer-based solutions out-of-scope for the course, in the following we briefly examine the others

32 GSM Based Mobility Detection Monitor changes in signal environment over time and classify mobility based on the nature of changes Fingerprinting works due to spatial variability of signal environment è changes correlate with mobility Magnitude of changes related with distance and velocity and thus can be used to detect transportation modes Temporal characteristics The faster the user moves, the more cells (s)he observes è number of unique cells linked with mobility Spatial characteristics The faster the user moves, the more likely a cell handover is taking place è residence time in cell linked with mobility

33 GSM Based Mobility Detection - Example Number of unique cells: 3 Dwell times: = 50s = 1min 40s = 10s Assume constant sampling rate of 10s

34 WiFi Based Mobility Detection Similarly to GSM, changes in WiFi signal environment give cues about mobility Temporal characteristics Variation in signal strength measurements, e.g., average variance of the k strongest access points For LOCADIO, k = 1 Spatial characteristics The amount of access points seen varies over time, similarly the time access points visible varies The dominant access point typically remains visible for the longest amount of time è can be used as a cue of dwell time

35 WiFi Based Mobility Detection Example Identify dominant access point Calculate variance of dominant access point σ = Calculate dwell time Access point visible all the time è dwell time = dwell time + number_of_measurements * sampling_rate In this example 10 seconds

36 Other Possible Features Additional features can be extracted when the measurements are multidimensional I.e., requires measurements from several cell towers and/or several WiFi access points Examples Statistical features: Euclidean Distance, mean variance, mean distance between measurements etc. Set-based features: Tanimoto coefficient, Spearman rank correlation See previous lecture

37 GPS-Based Locomotion Detection Basic idea: Partition GPS trajectories into segments Segmenting discussed during Lecture IX For each segment, extract a set of features Distance of the segment Maximum velocity and acceleration along the segment Average velocity, variance of velocity along the segment Classify transportation mode given the features Decision trees shown good performance in the literature Smooth classification results over time HMM or Conditional Random Field can be used for this

38 GPS Heading Change Rate (HCR) Intuition: transportation mode affects the degree of freedom for variations in trajectories Cars constrained to roads and lanes Pedestrian movement contains more variation Defined as the frequency that people change heading direction within a unit distance HCR = P c / d P c = number of points where headings changes more than a threshold d = distance of the segment

39 GPS Stop Rate (SR) Intuition: traveling by public transportation should contain more stops than driving In addition to traffic lights, contains picking up passengers and waiting for them to aboard etc. Defined as the frequency that people move with a slow velocity within a unit distance SR = P s / d P s = number of points where velocity below a threshold d = distance of the segment

40 GPS Velocity Change Rate (VCR) Intuition: mode of transportation affects how the velocity of movement changes Pedestrians generally have small changes in velocity Motorized transportation has larger changes, public transport should have more changes than driving Measures the frequency of significant changes in velocity over a unit distance VCR = P v / d P v = no. points where velocity rate exceeds a threshold Velocity rate = V 2 V 1 / V 1 d = distance of the segment

41 GPS Example HCR = P c / d = P c = 5 if we assume a change threshold of 5 degrees or more SR = P s / d = 5.1 P s = 1 if we assume a threshold of 1 km/h VCR = P v / d = P v = 3 if we assume a threshold of 0.25 for velocity rate Lat Lon Dist Dir Vel Total distance of segment meters Assume unit distance equals 1km

42 Summary Mobility model is a mathematical characterization of how people move Movement between locations Visit arrival times and durations Movement in general (stationary/non-stationary, motorized/non-motorized, ) Location Transition Models (Discrete) Markov Predictors LZ predictor Prediction model can be represented using LZ-Tree

43 Summary Arrival time and duration modeling NextPlace: history fingerprinting, estimate arrival time and duration by averaging historical values Predictability Entropy can be used to quantify how predictable a visiting pattern is Transportation mode detection Stationary detection: measure intensity of signal variations and use that to detect movement Locomotion detection: spatial and temporal characteristics used to distinguish different modes

44 Literature Froehlich, J.; Dillahunt, T.; Klasnja, P.; Mankoff, J.; Consolvo, S.; Harrison, B. & Landay, J. A., UbiGreen: investigating a mobile tool for tracking and supporting green transportation habits, Proceedings of the 27th international conference on Human factors in computing systems (CHI), ACM, 2009, Kim, B.; Ha, J.-Y.; Lee, S.-J.; Kang, S.; Lee, Y.; Rhee, Y.; Nachman, L. & Song, J. AdNext: A Visit-Pattern-Aware Mobile Advertising System for Urban Commercial Complexes, Proceedings of Workshop on Hot Topics for Mobile Computing (HotMobile), ACM, 2011 Song, L.; Kotz, D.; Jain, R. & He, X., Evaluating location predictors with extensive Wi-Fi mobility data, Proceedings of the 23rd Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), IEEE, 2004, Rodriguez-Carrion, A.; Garcia-Rubio, C. & Campo, C., Performance Evaluation of LZ-Based Location Prediction Algorithms in Cellular Networks, IEEE Communications Letters, 2010, 14,

45 Literature Ashbrook, D. & Starner, T., Using GPS to learn significant locations and predict movement across multiple users, Personal and Ubiquitous Computing, 2003, 7, Song, C.; Qu, Z.; Blumm, N. & Barabási, A.-L., Limits of Predictability in Human Mobility, Science, 2010, 19, Scellato, S.; Musolesi, M.; Mascolo, C.; Latora, V. & Campbell, A. T. NextPlace: A Spatio-temporal Prediction Framework for Pervasive Systems Proceedings of the 9th International Conference in Pervasive Computing (Pervasive), Spring, 2011, Bhattacharya, A. & Das, S. K., LeZi-update: an information-theoretic approach to track mobile users in PCS networks, Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking, ACM, 1999, 1-12 Song, L.; Kotz, D.; Jain, R. & He, X. Evaluating Next-Cell Predictors with Extensive Wi-Fi Mobility Data IEEE Transactions on Mobile Computing, 2006, 5,

46 Literature Krumm, J. & Horvitz, E., LOCADIO: Inferring Motion and Location from Wi-Fi Signal Strengths, Proceedings of the 1st International Conference on Mobile and Ubiquitous Systems (Mobiquitous), IEEE, 2004, 4-14 Zheng, Y.; Li, Q.; Chen, Y.; Xie, X. & Ma, W.-Y., Understanding Mobility Based on GPS Data, Proceedings of the 10th international conference on Ubiquitous computing, 2008, Mun, M.; Estrin, D.; Burke, J. & Hansen, M., Parsimonious Mobility Classification using GSM and WiFi Traces, Proceedings of the 5th International Conference on Embedded Networked Sensor Systems (SenSys), Proceedings of the 5th International Conference on Embedded Networked Sensor Systems (SenSys), 2008, 1-5 Sohn, T.; Varshavsky, A.; LaMarca, A.; Chen, M. Y.; Choudhury, T.; Smith, I.; Consolvo, S.; Hightower, J.; Griswold, W. G. & de Lara, E., Mobility Detection Using Everyday GSM Traces, Proceedings of the 8th International Conference on Ubiquitous Computing (Ubicomp), 2006, Reddy, S.; Mun, M.; Burke, J.; Estrin, D.; Hansen, M. & Srivastava, M. Using Mobile Phones to Determine Transportation Modes ACM Transactions on Sensor Networks, 2010, 6, 13:1-13: