Project Lachesis: Parsing and Modeling Location Histories

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Project LachesisParsing and Modeling Location
Histories

• Daniel Keeney
• CS 4440

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Introduction

• Location History is a record of an entitys
  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

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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

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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

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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

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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

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Calculating Stays
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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)

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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

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Calculating Destinations
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Example
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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

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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

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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

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Calculating p
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Calculating A
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Calculating B
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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

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Calculating Probabilistic Models

• Using ? we estimate the relative likelihood of a
  new location history
• This is done using a Non-Markovian Solution and a
  Markovian Solution

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Non-Markovian Solution
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Markovian Solution
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Experiment Results
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Experiment Results
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Experiment Results
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Experiment Results
I always felt more productive on Tuesdays. -
Subject A
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Experiment Results
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Experiment Results
A typical (left) and an atypical (right) week
from Subject A.
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Experimental Results
Plots of synthesized weeks, using Non-Markov
(left) and Markov (right) models
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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

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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