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