The document discusses functional data analysis (FDA) tools for livestock scientists, focusing on how FDA can enhance GPS tracking data analysis by transforming and analyzing functional data. It highlights the principles of Fourier and wavelet transforms for periodic and non-periodic data, respectively, and lists potential applications such as parasite burden assessment in livestock. The future of FDA in livestock tracking includes semi-automated analysis and behavior monitoring.

1. Functional Data Analysis Tools
for the Livestock Scientist

2. Overview
What is functional data analysis (fda)?
How can fda be useful to you?
Application example.

3. The Nature of GPS Tracking
Data
Ordered
Spatio-Temporal Correlation
Information-Dense
Quasi-Periodic
Incomplete
Errors
Constrained Support

4. Principles of FDA Pt. I.
Each datum is a functional,
[]
v (t )I ={v (t 1 ) , v (t 2 ) ,… , v (t n )}. v (t )1
The key is to transform the data, D= v (t )2
v (t)I → 〈Φ(t) , v (t )〉 Φ(t ) ⋮
v (t )n

5. Principles of FDA Pt. II.
Fourier Transform
1 kt
F (ω)=( ) ∑ v (t )exp[−i2 π( )]
N N
Suited for periodic trends such as diurnal activity patterns.
Correlates sinusoidal functions sin (ω t ) with the signal v (t )
Creates a set of coefficients α whose magnitude
indicate the “strength” of the frequency ω

6. Principles of FDA Pt. III.
Wavelet Transform
v (t)=∑ c j , k ϕ j , k (t )+∑ ∑ d j , k ψ j , k (t)
0 0
Suited to non-periodic data with lots of
“jumps”.
Enables a multi-resolution analysis.
Coefficients c j , k encode the “smooth” and d j , k
0
the “detail”.

7. Potential Uses of FDA for SELM
Trajectory Clustering
Outlier Detection
State Classification
Interpolation
Smoothing
Multi-resolution Analysis

8. Application: Parasite Burden
Can Livestock Tracking Collars tell us if sheep
have parasite burden?

9. Application: Parasite Burden
Support-Vector Interpolation and Smoothing
̂
v (t )={x (t ) , y (t )}→ v (t )

10. Application: Parasite Burden
Adaptive Basis Using Singular Value Decomposition
T
D=U Λ V

11. The Future
FDA Livestock Tracking Software
Semi-automated analysis within Software
Aberrant Behaviour Warnings
Social Networks – very high-dimensional fda

12. Thank you!