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Project Lachesis: Parsing and Modeling Location Histories

Project Lachesis: Parsing and Modeling Location Histories. Daniel Keeney CS 4440. Introduction. Location History is a record of an entity’s location in geographical space over time Archaeologists and historians look at migrations and census data to reconstruct location histories

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Project Lachesis: Parsing and Modeling Location Histories

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  1. Project Lachesis:Parsing and Modeling Location Histories Daniel Keeney CS 4440

  2. Introduction • Location History is a record of an entity’s location in geographical space over time • Archaeologists and historians look at migrations and census data to reconstruct location histories • New technologies such as GPS allow us to enhance the accuracy and resolution greatly

  3. Resolution • Old temporal resolutions ranged from a decade to a century • Old spatial resolutions ranged from tens to hundreds of kilometers • GPS accuracy opens up a completely different type of analysis

  4. Goal • By tracking locations in real time, new types of analysis can be performed • Goal: condense, understand, and predict the movements of an object over a period of time

  5. Stays and Destinations • Stay is a single instance of an object spending some time in one place • Destination is any place where one or more objects have experienced a stay • Trip occurs between two adjacent stays made by the same object • Path is a representation of the description of a set of trips between destinations

  6. Calculating Stays • The roaming distance, is how far an object can stray while being counted as a stay • The stay duration, is how long an object must remain within the roaming distance to count as a stay • Medoid is the data point nearest to the “center” of the set

  7. Calculating Stays

  8. Calculating Stays • Worst case: O(n2) for n data points, due to medoid and diameter working on all pairs • In practice, clusters which require computation are far smaller than n, effectively yielding O(n)

  9. Calculating Destinations • Geographic scale, determines how close two stays can be and still be considered the same destination • Destinations are represented by a location as well as the scale used:

  10. Calculating Destinations

  11. Example

  12. Creating Probabilistic Models Assumptions: • At the beginning of a given time interval, an object is at exactly one destination • During any given time interval, an object makes exactly one transition between destinations • Self-transitions are allowed

  13. Creating Probabilistic Models • Models are similar to Hidden Markov Models • Critical difference from HMM is the incorporation of time-dependence, where transition probabilities are conditioned on recurring time intervals

  14. Creating Probabilistic Models • Model consists of three probability matrices • Probability of the object starting time interval at destination is • Probability of transition from to during interval is • Observation probability: observing object at when actually at

  15. Calculating π

  16. Calculating A

  17. Calculating B

  18. Calculating Probabilistic Models • Together as these tables represent a probabilistic model • This model can be used to solve problems such as finding the most likely destination occupied at a particular time, determining the relative likelihood of a location history sequence, or generating a location history sequence

  19. Calculating Probabilistic Models • Using λ we estimate the relative likelihood of a new location history • This is done using a Non-Markovian Solution and a Markovian Solution

  20. Non-Markovian Solution

  21. Markovian Solution

  22. Experiment Results

  23. Experiment Results

  24. Experiment Results

  25. Experiment Results “I always felt more productive on Tuesdays.” - Subject A

  26. Experiment Results

  27. Experiment Results A typical (left) and an atypical (right) week from Subject A.

  28. Experimental Results Plots of synthesized weeks, using Non-Markov (left) and Markov (right) models

  29. Markov vs. Non-Markov • Markovian model showed an atypical week to have an unexpectedly high probability • This could be mitigated by “training” on larger data sets, but generally the Non-Markovian model is sufficient

  30. Conclusions • Proposed rigorous definitions for location histories, stays, and destinations, as well as accompanying algorithms • Non-Markovian is better suited for evaluating likelihoods of a location history • Markovian is better for stochastically generating a history • Future papers will examine trips and paths

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