Categorization of Snow Profile Data into Predefined Class Templates
-
Upload
christian-schaiter -
Category
Technology
-
view
255 -
download
2
description
Transcript of Categorization of Snow Profile Data into Predefined Class Templates
Christian Schaiter
Categorization of Snow
Profile Data into
Predefined Class
Templates
Academic advisors: Univ.-Prof. Dr. Günther Specht
DI Robert Binna
MASTER THESIS
Leopold-Franzens-University Innsbruck
Institute of Computer Science
Categorization of Snow Profile Data into Predefined Class Templates 2
Content
Introduction and motivation 1
What you may expect in the next 15 minutes...
Overview of the developed system 2
Alignment of hardness profiles 3
Conclusion 4
Categorization of Snow Profile Data into Predefined Class Templates 2
Overview
Introduction and motivation 1
Current chapter: Introduction
Alignment of hardness profiles 3
Conclusion
Overview of the developed system 2
4
Categorization of Snow Profile Data into Predefined Class Templates 3
Introduction and motivation
Master thesis was done in cooperation with the Tyrolean
avalanche warning service (TAWS)
Goal: Find a way to
determine the potential
magnitude of an
avalanche
Aim of the thesis
Categorization of Snow Profile Data into Predefined Class Templates 4
Introduction and motivation
TAWS frequently takes snow profiles from different areas
Most relevant property of a snow profile for this thesis:
Hardness profile
Snow profiles, hardness profiles, template types
Sn
ow
heig
ht
[cm
]
Snow hardness
Hardness
profile
Categorization of Snow Profile Data into Predefined Class Templates 5
Introduction and motivation
Some example hardness profiles (collected from the TAWS):
Snow profiles, hardness profiles, template types
Categorization of Snow Profile Data into Predefined Class Templates 6
Introduction and motivation
Idea: Introduce a group of predefined hardness profile types
(template types, class templates)
These template types describe the overall composition of the
snowpack
They may be used to
estimate the magnitude
of avalanches
10 types defined so far
Snow profiles, hardness profiles, template types
Profile types (class templates)
Categorization of Snow Profile Data into Predefined Class Templates 7
Introduction and motivation
Snow profiles, hardness profiles, template types
Hardness profile
Determine type
Goal: Automatically find the associated profile type for
each collected hardness profile
Reject hardness profile if no reasonable profile type is found
Profile types (class templates)
Snow hardness
Sn
ow
heig
ht
[cm
]
Categorization of Snow Profile Data into Predefined Class Templates 8
Overview
Overview of the developed system
Introduction and motivation 1
Current chapter: Overview of the developed system
2
Alignment of hardness profiles 3
Conclusion 4
Categorization of Snow Profile Data into Predefined Class Templates 9
Overview of the developed system
Schematic view of the proposed classification system
Categorization of Snow Profile Data into Predefined Class Templates 10
Overview
Introduction and motivation 1
Current chapter: Alignment of hardness profiles
Conclusion 4
Overview of the developed system 2
Alignment of hardness profiles 3
Categorization of Snow Profile Data into Predefined Class Templates 11
Alignment of hardness profiles
Hardness profiles may be viewed as
time series (clockwise rotated by 90°)
Height corresponds to time axis
Hardness values map to the amplitude
dimension
Desired properties of an internal data
format:
Height independence
Shape preservation
Local height warping
Representation format of hardness profiles
90°
Categorization of Snow Profile Data into Predefined Class Templates 11
Alignment of hardness profiles
Hardness profiles may be viewed as
time series (clockwise rotated by 90°)
Height corresponds to time axis
Hardness values map to the amplitude
dimension
Desired properties of an internal data
format:
Height independence
Shape preservation
Local height warping
Representation format of hardness profiles
matching
Categorization of Snow Profile Data into Predefined Class Templates 12
Alignment of hardness profiles
Idea: Use symbolic representation (weighted strings)
A weighted string is composed of weighted characters
Direction character:
D (down), U (up)
Height (as a percentage)
Hardness difference
(among adjacent layers)
Compact form uses only
direction characters
Hardness profiles as weighted strings
6 5 4 3 2 1
3050 ,.,D
110 ,.,D
50350 .,., D
610 ,.,U U
D
D
D
U
D
D
D
53050 .,.,U
51150 .,., D
1150 ,.,D
51050 .,., D
Categorization of Snow Profile Data into Predefined Class Templates 13
Alignment of hardness profiles
Hardness profiles are aligned based on their compact strings
Weights are required to calculate a penalty score
Goal: Find a global alignment with a maximum number of
matching characters (optimal alignment)
Edit transcript describes operations (match M, deletion D,
insertion I) required to transform the first string into the second
Principle of hardness profile alignment
The compact string UUDUD and DUDUU may be aligned as
– U U D – U D U U D U D – –
D – U D U U – or – – D U D U U , etc I D M M I M D D D M M M I I
String alignment examples
Categorization of Snow Profile Data into Predefined Class Templates 14
Alignment of hardness profiles
Principle of hardness profile alignment
Well-matching profile Badly-matching profile
U D D – U U D D D U D D U U D D D
U D D D – U D D D U – D – – – – –
M M M I D M M M M M D M D D D D D
Categorization of Snow Profile Data into Predefined Class Templates 15
Alignment of hardness profiles
Calculation of optimal alignments
Algorithms for calculating optimal string alignments:
Categorization of Snow Profile Data into Predefined Class Templates 16
Alignment of hardness profiles
Calculation of optimal alignments
Categorization of Snow Profile Data into Predefined Class Templates 17
Alignment of hardness profiles
After all optimal alignments have been found: Compute penalty
scores
2 types of penalties:
Match-penalty
for differences in:
- Height
- Hardness
Mismatch-penalty
for mismatching blocks
- Much more severe
Computation of penalty scores
match-penalty
Intrusion Detection Systems for SOA 18
Overview
Introduction and motivation 1
Current chapter: Conclusion
Overview of the developed system 2
Conclusion 4
Alignment of hardness profiles 3
Categorization of Snow Profile Data into Predefined Class Templates 19
Conclusion
Template types are used to
estimate magnitude of avalanches
Classification is based on string
alignment techniques
Well matching strings similar
hardness profiles
Achieved success rate of > 90% for
example set (if not rejected)
Approach may be used for any time
series data
What you have heard in the last 15 minutes
Any Question?
Thank you for your attention!
Categorization of Snow Profile Data into Predefined Class Templates 21
Backup slides
Distance measures: Cosine of angle, Euclidean Distance
Similarity measure: Cosine of angle
Dissimilarity measure: Euclidean Distance
Euclidean Distance:
Take the smallest distance
between points
in the vector space
Cosine of angle:
Take the smallest angle
between vectors
Categorization of Snow Profile Data into Predefined Class Templates 22
Backup slides
Problems with the Euclidean Distance
Consider the hardness profile
(in blue) and its dedicated
template (in green)
In principle they are
well-matching
Nevertheless, a large error
occurs (in red) when applying
the Euclidean Distance
measure
ED does not handle “height
warps”
Categorization of Snow Profile Data into Predefined Class Templates 23
Backup slides
Calculation of optimal alignments
Compute a distance table (with dynamic programming)
Example: Compact strings UUDUD and DUDUU
Categorization of Snow Profile Data into Predefined Class Templates 24
Backup slides
Calculation of optimal alignments
Based on the distance table, compute the edit graph and
perform a traceback
U U D U D – –
– – D U D U U
D D M M M I I
– U U D – U D
D – U D U U –
I D M M I M D
Categorization of Snow Profile Data into Predefined Class Templates 25
Backup slides
Template type duplication
Template type versioning:
Create different versions with multiple gradation steps
Categorization of Snow Profile Data into Predefined Class Templates 26
Backup slides
Template type duplication
Variations of template type versions:
Scale up one layer at the cost of the other layers
Categorization of Snow Profile Data into Predefined Class Templates 27
Backup slides
Profile matching
Alignment of hardness layers: Limitations
Example should be of type 4, but perfectly matches type 3
Categorization of Snow Profile Data into Predefined Class Templates 28
Backup slides
Profile matching
Alignment of hardness layers: Limitations
Problem of deceptive local extremes
Causing false negatives
badly matching
perfect match
Categorization of Snow Profile Data into Predefined Class Templates 29
Backup slides
Profile matching
Alignment of hardness layers: Limitations
Problem of abusing misalignments
Causing false positives
Apparently wrong profiles may achieve too good penalty scores
(see examples)
Categorization of Snow Profile Data into Predefined Class Templates 30
Backup slides
Genetic Algorithm principles
Mechanics of a simple Genetic Algorithm: 5 Steps
Step I: Encoding of the search domain with a small alphabet
Step II: Creation of an initial string population
Step III: Reproduction of strings
Step IV: Crossover of strings
Step V: Mutation of strings