Today avalanche research primarily focuses on the reliable prediction of avalanche descents by using meteorological data and snowpack properties. This thesis complements these approaches by providing means to automatically categorize snow proles into ten predened templates, which may be used as an indicator whether potential avalanches might carry o deeper layers of snow to form avalanches of higher magnitude. For this purpose, the snow hardness prole is taken and transformed into a symbolic internal data format based on weighted strings. This representation allows for the application of well-known methods such as string alignments, which provide the foundation for the classication system. Furthermore, as a secondary strategy, the class-templates themselves are modied in a neat way that does not distort their overall shape, thereby providing matching candidates for a larger portion of input proles. Altogether, the proposed system converts the input prole into the internal representation, takes each of the modied template versions and determines a proper alignment of hardness layers as the basis for a nal error score computation that enables an ordering among the contemplable template types. The work in this thesis may be generalized to approach a wider range of problems and is closely related to the eld of time series data mining.

1. Leopold-Franzens-University Innsbruck
Institute of Computer Science
Categorization of Snow
Profile Data into
Predefined Class
Templates
MASTER THESIS
Christian Schaiter
Academic advisors: Univ.-Prof. Dr. Günther Specht
DI Robert Binna

2. Content
What you may expect in the next 15 minutes...
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
2

3. Overview
Current chapter: Introduction
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
2

4. Introduction and motivation
Aim of the thesis
 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
Categorization of Snow Profile Data into Predefined Class Templates
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5. Introduction and motivation
Snow profiles, hardness profiles, template types
 TAWS frequently takes snow profiles from different areas
 Most relevant property of a snow profile for this thesis:
Hardness profile
Hardness
profile
Snow height [cm]

Snow hardness
Categorization of Snow Profile Data into Predefined Class Templates
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6. Introduction and motivation
Snow profiles, hardness profiles, template types
 Some example hardness profiles (collected from the TAWS):
Categorization of Snow Profile Data into Predefined Class Templates
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7. Introduction and motivation
Snow profiles, hardness profiles, template types
 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
Profile types (class templates)
estimate the magnitude
of avalanches
 10 types defined so far
Categorization of Snow Profile Data into Predefined Class Templates
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8. Introduction and motivation
Snow profiles, hardness profiles, template types
 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 height [cm]
Hardness profile
Determine type
Snow hardness
Categorization of Snow Profile Data into Predefined Class Templates
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9. Overview
Current chapter: Overview of the developed system
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
8

10. Overview of the developed system
Schematic view of the proposed classification system
Categorization of Snow Profile Data into Predefined Class Templates
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11. Overview
Current chapter: Alignment of hardness profiles
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
10

12. Alignment of hardness profiles
Representation format 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

90°
Local height warping
Categorization of Snow Profile Data into Predefined Class Templates
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13. Alignment of hardness profiles
Representation format 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
Categorization of Snow Profile Data into Predefined Class Templates
matching
11

14. Alignment of hardness profiles
Hardness profiles as weighted strings
 Idea: Use symbolic representation (weighted strings)
 A weighted string is composed of weighted characters

Direction character:
D (down), U (up)

Height (as a percentage)
6
5
4
3
2
1

Hardness difference
(among adjacent layers)
Compact form uses only
direction characters
D
D, 0.15,  1.5
U, 0.05, 3.5
D
U
D, 0.35,  0.5
D
D, 0.1,  1
D, 0.05,  3
U, 0.1, 6

D, 0.05,  1.5
D, 0.15,  1
D
D
U
Categorization of Snow Profile Data into Predefined Class Templates
D
12

15. Alignment of hardness profiles
Principle of hardness profile alignment
 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
String alignment examples
 The compact string UUDUD and DUDUU may be aligned as
– U U D – U D
D – U D U U –
I D M M I M D
or
U U D U D – –
– – D U D U U , etc
D D M M M I I
Categorization of Snow Profile Data into Predefined Class Templates
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16. Alignment of hardness profiles
Principle of hardness profile alignment
Well-matching profile
U D D – U U D D D
U D D D – U D D D
M M M I D M M M M
Categorization of Snow Profile Data into Predefined Class Templates
Badly-matching profile
U D D U U D D D
U – D – – – – –
M D M D D D D D
14

17. Alignment of hardness profiles
Calculation of optimal alignments
 Algorithms for calculating optimal string alignments:
Categorization of Snow Profile Data into Predefined Class Templates
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18. Alignment of hardness profiles
Calculation of optimal alignments
Categorization of Snow Profile Data into Predefined Class Templates
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19. Alignment of hardness profiles
Computation of penalty scores
 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
Categorization of Snow Profile Data into Predefined Class Templates
match-penalty
17

20. Overview
Current chapter: Conclusion
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Intrusion Detection Systems for SOA
18

21. Conclusion
What you have heard in the last 15 minutes
 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
Categorization of Snow Profile Data into Predefined Class Templates
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22. Thank you for your
attention!
Any Question?

23. 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
Categorization of Snow Profile Data into Predefined Class Templates
Cosine of angle:
Take the smallest angle
between vectors
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24. 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
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25. 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
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26. 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
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27. Backup slides
Template type duplication
 Template type versioning:

Create different versions with multiple gradation steps
Categorization of Snow Profile Data into Predefined Class Templates
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28. 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
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29. 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
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30. 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
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31. 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
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32. 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
Categorization of Snow Profile Data into Predefined Class Templates
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