animal-human discrimination track-level discrimination

Animal-Human Discrimination

Track-level Discrimination

Organization of Presentation

• Patterns of movement among non-human animals

• Home range concept

Analysis of Movement Data• Generally intended to delineate paths through

terrain.• Generally descriptive – not usually predictive

or intended for classification.• Examples

• Random walks• Correlated random walks

• ***Problem for present work – positional data not precise enough.***

Analysis of Movement Data• Goal of Phase 1 – develop algorithms that

would be sensitive to qualitative differences in movement patterns of non-human animals, indigenous peoples, and dismounts.

• Key feature of animals’ use of their habitat – the home range.

Home Range Concept

• Territory = area that animal actively defends – by marking or actual physical combat

• Home range – area that an animal samples on a more-or-less regular basis.

• Home range may overlap with territories/home ranges of conspecifics.

• Habitat ‘quality’ is key determinant of home range size, location and utilization patterns

Home Range Concept

• Key features – animal movements restricted by (often cryptic) boundaries

that define the home range– home range size (area) is a nonlinear function of animal

size.– movement patterns within home range often show

characteristics of Lévy flights.• Somewhat controversial• Postdicted by optimal foraging theory• Uniform or Brownian motion-based search strategies result in

oversampling of an area increased cost:benefit ratio– animals on home range tend to return to specific points on

a more-or-less regular basis.

Home Range Size in Mammals

100

101

102

103

100

101

102

103

104

105

106

Mass, kg

Hom

e R

ange

Siz

e, k

m

2

Leaf-eating MammalsCarnivorous Mammals

Carnivorous Birds

Mammals pooled

Grazing MammalsOmnivorous Mammals

Lévy flights vs. Brownian Motion

Brownian Motion Lévy Flight

3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86

x 105

5.004

5.006

5.008

5.01

5.012

5.014

5.016

5.018

5.02

x 106 Deer Movement, 1993-96

UTME, m

UT

MN

, m

3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86

x 105

5.004

5.006

5.008

5.01

5.012

5.014

5.016

5.018

5.02

x 106 Elk Movement, 1993-96

UTME, m

UT

MN

, m

3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86

x 105

5.004

5.006

5.008

5.01

5.012

5.014

5.016

5.018

5.02

x 106 Cattle Movement, 1993-96

UTME, m

UT

MN

, m

5.2 5.25 5.3 5.35 5.4 5.45 5.5

x 105

4.974

4.976

4.978

4.98

4.982

4.984

4.986x 10

6 Cougar Female #125

5.22 5.24 5.26 5.28 5.3 5.32 5.34 5.36 5.38 5.4 5.42

x 105

4.974

4.976

4.978

4.98

4.982

4.984

4.986

4.988

4.99x 10

6 Cougar Male #137

Red-knobbed Hornbill

7.34 7.36 7.38 7.4 7.42 7.44 7.46

x 105

1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74x 10

5 Red-knobbed Hornbill Movement

UTME, m

UT

MN

, m

Nonbreeding

Breeding

Giant argus

0 200 400 600 800 1000 1200 1400 1600-500

0

500

1000

1500

2000

2500

Meters

Met

ers

Giant Argus Movement

Analysis of Movement Data• We’re going to argue for a combined approach

based on a number of algorithms• My work so far – and for foreseeable future – is

aimed at producing an eclectic mix of algorithms that do the best job of meeting your needs.

Analysis of Movement Data

Wavelet Analysis(Discrete) Differential Geometry

Nonlinear algorithms

Wavelets

• Signal analysis types refer to this as space-time analysis, everybody else calls it frequency-time analysis. – Actually, it can be either, or both.

• Conceptually similar to fft, but the basis set is different.• Rather than the ***sin-cos*** basis set of fft, where amplitude-

determining coefficients do the fitting, both amplitude (as with fft) and the frequency width of the basis set (i.e., the wavelet) can vary.

• To a large extent, wavelet analysis gets around the problem of signal non-stationarity (i.e., when frequency of the signal can vary with time and/or space.

– FFT not appropriate in this case

• Additional benefit – can develop new wavelets that are more specific/appropriate for our purposes

Example Wavelet – the Daubechies 4

• Wavelet • Scaling Function

x-axis 4.9 km

y-ax

is

6.7

km

Elk Movement Pattern

0 200 400 600 8000

1000

2000

3000

4000

5000

1 x-axis unit 1.0 hours

Met

ers

Euclidean Distance from Start Point

Wavelet transform, db4 wavelet


Sca

le F

acto

r, a

200 400 600 800 1 8

15 22 29 36 43 50 57 64 71 78 85 92 99

106113120127

10

20

30

40

50

60

x-axis 24.3 km

y-ax

is

10.

8 km

Cougar Movement Pattern

0 500 1000 15000

5000

10000

15000


Met

ers




Sca

le F

acto

r, a

200 400 600 800 1000 1200 1400 1600 1 8

15 22 29 36 43 50 57 64 71 78 85 92 99

106113120127

10

20

30

40

50

60

x-axis 6.3 km

y-ax

is

4.1

km

Male Tiger Movement Pattern

0 500 1000 15000

1000

2000

3000

4000

5000


Met

ers




Sca

le F

acto

r, a

200 400 600 800 1000 1200 1400 1 8

15 22 29 36 43 50 57 64 71 78 85 92 99

106113120127

10

20

30

40

50

60

Female Tiger Movement Pattern

x-axis 10.6 km

y-ax

is

22.

3 km

0 100 200 300 400 500 6000

0.5

1

1.5

2

x 104


Met

ers




Sca

le F

acto

r, a

100 200 300 400 500 600 1 5 9

13172125293337414549535761

10

20

30

40

50

60

x-axis 2.8 km

y-ax

is

5.5

km

Hornbill Movement Pattern

0 200 400 600 8000

1000

2000

3000

4000


Met

ers




Sca

le F

acto

r, a

100 200 300 400 500 600 700 800 1 8

15 22 29 36 43 50 57 64 71 78 85 92 99

106113120127

10

20

30

40

50

60

x-axis 7.3 km

y-ax

is

7.0

km

Malay Sun Bear Movement Pattern

0 50 100 1500

1000

2000

3000

4000

5000


Met

ers




Sca

le F

acto

r, a

20 40 60 80 100 120 140 160 1 8

15 22 29 36 43 50 57 64 71 78 85 92 99

106113120127

10

20

30

40

50

60

Distance, Arbitrary Units

Dis

tanc

e, A

rbitr

ary

Uni

ts

Dismount Through Path

0 10 20 30 400

5

10

15

20

25

Time in Arbitrary Units

Dis

tanc

e, A

rbitr

ary

Uni

ts Euclidean Distance from Start Point


Time in Arbitrary Units

Sca

le F

acto

r, a

5 10 15 20 25 30 35 40 1 8

15 22 29 36 43 50 57 64 71 78 85 92 99

106113120127

10

20

30

40

50

60

Differential Geometry of Plane Curves

• Theorems from differential geometry address the question of how normal vectors to an animal’s path should ‘behave’.

• Specifically, the behavior of normal vectors differs for open paths (the most likely path taken by dismounts passing through an area) and closed paths, whether simple or complex and.

• Useful for producing null models against which data can be compared.• Osculating circles and curvature are one approach.

0 5 10 15 205

10

15

20

25

Gauss-Bonnet Theorem

• The integral of the signed curvature around a simple closed smooth curve on a flat, planar surface is equal to 2:

C G(s)ds = 2

• Leads to prediction that most normals to a simple closed smooth curve point towards the center.

-10 -5 0 5 10

-8

-6

-4

-2

0

2

4

6

8

10

3.73 3.74 3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83

x 105

5.006

5.007

5.008

5.009

5.01

5.011

5.012

5.013

5.014

5.015

x 106 Starkey Elk

7.41 7.415 7.42 7.425 7.43 7.435 7.44 7.445 7.45 7.455

x 105

1.68

1.685

1.69

1.695

1.7

1.705

1.71

1.715

1.72

1.725x 10

5 Breeding Red-knobbed Hornbill

Conclusions

• Behavioral ecology of animals and indigenous humans leads to home ranges w/ dimensional scale of < 10 to 30 kilometers

• Movements within a home range result in:» Periodic or quasiperiodic movement patterns that are

revealed by wavelet analysis .» Closed curves (tracks) for which large proportion of normal

vectors point towards points that lie close to or within home range boundaries.

• Dismounts should exhibit qualitatively different movement patterns from those of indigenous humans and non-human animals

***The following slides would be optional***

Animal-Human Discrimination

Alternative approaches•Nonlinear Time-series Analysis

• Sensitive to signal complexity

•Stochastic Resonance• Can dramatically enhance SNR

Nonlinear Algorithms

• Entropy measures – old & new» Shannon – » Kolmogorov –» Spectral Entropy – basically a Shannon entropy of the

power spectrum » Approximate Entropy (AppEn) – suffers from significant

statistical bias, supplanted by Sample Entropy» Sample Entropy (SampEn) – used in various

applications » Permutation Entropy (PermEn) –

Algorithms Based on Chaos Theory

• Largest Lyapunov exponent (1) – reflects time-dependent evolution of the initial nearest-neighbor distance. Specifically

d12(t) = d12(0)e1 – 1 > 0 implies chaotic (complex) dynamics.

• Correlation dimension (D2)

Chaotic Dynamics

0 20 40 60 80 100 120 140 160 180 200-20

-15

-10

-5

0

5

10

15

20

Time, Arbitrary Units

x

Chaotic Dynamics

-20 -10 0 10 200

5

10

15

20

25

30

35

40

45

50

x

z

-20 -10 010 20 -50

0

50

0

10

20

30

40

50

yx

z

Chaotic Dynamics

0 20 40 60 80 100 120 140 160 180 200-20

-15

-10

-5

0

5

10

15

20

Time, Arbitrary Units

x

Chaotic Dynamics – 2D

0 2 4 6 8 10 12 14 16 180

5

10

15

20

25

x

y

Chaotic Dynamics – 3D

-20-15-10-505101520

-50

0

50

0

5

10

15

20

25

30

35

40

45

xy

z

Chaotic Dynamics

Orbits of Planetary Bodies Electroencephalogram

From Hinse et al., 2008


• Significant controversy about the applicability of chaos theory-based algorithms to analysis of most time series data.

• Algorithms for computing each work well…but only if applied to mathematical models.

• Results are in doubt if signal is:» Of limited duration.» Nonstationary – statistical properties change with time.» Corrupted by noise – leads to high estimates of 1 and low

estimates of D2, both suggestive of “low-dimensional chaotic dynamics” which may not, if fact, be present.

• However, 1 and D2 appear to Pragmatic approach


• 1 and D2 are easily computed from time series data

• 1 and D2 appear to be sensitive to different features in the data than FFT, wavelets, entropy measures, etc.

• Recommend a pragmatic approach – – Apply many algorithms to our data– Assess which work best in a cost-based classification

scheme.

Multiscale measures

• Exciting relatively new conceptual approach• Lyapunov Exponents (1) – so-called Scale-dependent

Lyapunov Exponents (SDLE) may be highly sensitive to weak signals embedded in a return pulse corrupted by clutter

• Entropy measures» Multiscale Sample Entropy (MSE) – used in various

applications, including analysis of human gait » Multiscale Permutation Entropy – not yet applied to human

locomation• Detrended Fluctuation Analysis• ***

Stochastic Resonance

• Conceptually simple• Sub-threshold signal may become detectable

if augmented with appropriate amount of noise.

Stochastic Resonance

• Applications in radar detection of large aerial targets

• Not applied to the micro-Doppler problem as of yet.

Have to decide whether to use the following slides and, if so, where to put?

Animal-Human DiscriminationLimb movement scales in fractal way in mammals; don’t know about limb behavior in birds.Movement speed scales differently for small and large mammals = multifractal?•Need to account for these two facts when modeling micro-Doppler signals.

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9

10

Deer Movement Speeds, 1993-96

Speed, m/s

log(

Fre

quen

cy)

0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

Elk Movement Speeds, 1993-96

Speed, m/s

log(

Fre

quen

cy)

0 0.2 0.4 0.6 0.8 1 1.20

1

2

3

4

5

6

7

8

9

10

Cattle Movement Speeds, 1993-96

Speed, m/s

log(

Fre

quen

cy)

animal-human discrimination track-level discrimination

Documents

purposes slide

giant argus slide

wavelet scaling function

redknobbed hornbill

spacetime analysis

home range concept territory

frequencytime analysis

wavelets signal analysis