characteristics in flight data
DESCRIPTION
Characteristics in Flight Data. Characteristics in Flight Data Estimation with Logistic Regression and Support Vector Machines. ICRAT 2004 Claus Gwiggner, LIX, Ecole Polytechnique Palaiseau Gert Lanckriet, EECS, University of California, Berkeley. Flow Management and Planning Differences. - PowerPoint PPT PresentationTRANSCRIPT
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Characteristics in Flight DataEstimation with Logistic Regression
and Support Vector Machines
ICRAT 2004Claus Gwiggner, LIX, Ecole Polytechnique Palaiseau
Gert Lanckriet, EECS, University of California, Berkeley
Characteristics in Flight Data
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Flow Management and Planning Differences
Time slots are distributed among aircraft to avoid congestion
•In reality, delays, re-reroutings, etc. lead to missed time slots
•Not the same number of aircraft than planned arrive in sectors:
•safety, lost capacity
Planning Differences
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Related Work
Factors/Causes [ATFM Study, PRR]Slot adherence, flight plan quality, in-flight change of
route, .... Simulations [Ky, Stortz]
Random noise on departure times Reactionary Delay [Toulouse Study]
microscopic model of departure times
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Unknown
Real situation at sector entries interplay of factorscompensations of delays ...
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Program
Problem Formulation Simple Characteristics Binary Classification Conclusion Future Work
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Planning Differences
Planning Differences = Regulated Demand – Real Demand
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General Problem Formulation
Find 'regularities' of planning differences, useful to improve the current planning procedureWhy? Safety, suboptimal used capacityHow?
MACRO approach: relations between flows, not single deviations from flight plans
Daily basis, not extreme situations How? Data analysis
141 days of week-day data
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Today's Question
Are planning differences of different sectors the 'same'? if yes: any model can be greatly simplified if no: what are the differences?
Difficulty24 dimensions: one variable for each hour
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Comparison of Planning Differences
No visible regularities in both sectors ...
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Mean and Standard Deviation
...but similar mean and standard deviation over the time
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H0: same underlying distribution ... reject on 1 % levelassumes that statistical properties do not vary over time
.... but what are the characteristics?e.g. 'if high peaks at noon => sector 1'? Find a rule that tells whether a sequence of values
belongs to sector 1Classification problem
Hypothesis Tests
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(Binary) Classification
Probabilistic 'what is the probability
that a new item belongs to sector 1?'
Logistic Regression
Geometric 'on which side of the
boundary lies the new item?'
Support Vector Machines
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Comparison
Linear Logistic Regression vs SVMs linear vs non-linearsimple vs mathematically sophisticated traditional vs state-of-the-artprobabilistic vs geometric
Common points [Hastie et. al 2003], [Friedman 2003]SVM estimator of class probabilities logistic regression induces linear boundaries
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Experiments on ...
Data from 4 sectors in Upper Berlin airspaceRaw Data (random permutations)Data where number of instances in both classes are
balanced In total 8 experiments conducted
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Model Selection
Report Estimated Prediction Error (EPE) Model Selection:
Cross-Validation [Stone 1974]Wilcoxon-Mann-Whitney Test
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Parameters of SVMs
Kernel functionsLinear, Gauss, Poly, Linear CN, Gauss CN, Poly CN
Kernel parameters Cost Function
1 Norm, 2 Norm In total over 800 combinations possible
best one estimated by cross validation
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Results
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Summary
characteristics in high dimensional data
comparison of a very simple and a very complicated classification method
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Conclusions
There are systematic differences between different sectors
SVMs do not promise major improvementno more than 4% better than logistic regression
Linear Prediction is possibleExpected prediction errors around 15 %
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Future Work
(black box) prediction not satisfactory Better understanding of the underlying processes
reasons for the differencesmodel of the probability distribution of planned traffic and
realized traffic
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Questions ?
• Thanks for your attention!
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Results
Is Week End?
Sector Raw Bal+Perm Variable Sel RandomUR1 UR2 UR3 UR4
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Known: Causes for Planning Differences
Departure Slot adherenceInconsistent profile
CASA implementation
In flight change of route
Regulations too late Weekday, SeasonWeather
Source: Independent Study for the Improvement of ATFM, Final Report, 2000
Slot tolerance windowMissing flight plansIncorrect flight plan information
Priorities:Very HighHighMediumUnknown
time
# over-deliveries
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Little known: Dynamics of Planning Differences
X: timeY: Number of planning differences
Sector n...
'Error'Propagation
Sector 2Sector 1
Related Work: Simulation studies, reactionary delay studies
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Summary Motivation
Are planning differences unpredictable? Or are there hidden 'regularities'?
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Possible Research Questions
Propagation over the network Dependence on traffic density, sector complexity, ... ... Characteristics Comparison of different sectors
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Notation
A sector is represented as a vector of 24 variables, one for each hour
An instance is a value for this vector An instance belongs to class 1 or -1; dependent on the
sector from which it was drawn
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Binary Classification
● Given:
Instances from sectors 1 and -1● Question:
a rule to decide for a new instance to which sector it might belong
● Example: if 'high peaks at noon' then class 1Decision trees
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Geometric and Probabilistic Approaches
example: Instances are 2 dimensional
Geometric Instances are points in
Euclidean spaceRules are class boundaries
Problem: overlapping classes
ProbabilisticClasses have underlying
probability distributionRules are class-probabilities
Problem: which distribution?