1 - MAD
There are two different definitions of MAD. In machine learning papers, you have to check which one they mean.
1- 1 Mean Absolute Deviation
Given measurements
\[x = [3,4,5,8]\]Mean:
\[\mu = 5\]Absolute deviations:
\[|x-\mu| = [2,1,0,3]\]MAD is
\[\frac{2+1+0+3}{4}=1.5\]1 - 2 Median Absolute Deviation (more common for robust statistics)
Median = 4.5
Absolute deviations:
\[[1.5,0.5,0.5,3.5]\]Median of those:
\[MAD=1.0\]2. Lag : delay between an observed data point and its preceding values
2 - 1 Definitions
Lag simply means looking one time step into the past. Suppose your boat probability is
| Frame | Probability |
|---|---|
| 1 | 0.10 |
| 2 | 0.20 |
| 3 | 0.75 |
| 4 | 0.85 |
| 5 | 0.82 |
Lag-1 is simply:
\[x_{t-1}\]1
2
3
4
5
6
7
8
9
Current frame Previous frame
0.20 ← 0.10
0.75 ← 0.20
0.85 ← 0.75
0.82 ← 0.85
Lag-2:
\[x_{t-2}\]Example
| Current | Lag-1 | Lag-2 |
|---|---|---|
| 0.75 | 0.20 | 0.10 |
| 0.85 | 0.75 | 0.20 |
| 0.82 | 0.85 | 0.75 |
2 - 2 Why are lag features useful?
Imagine the point count from the boat.
1
2
3
4
5
6
7
8
9
10
11
Frame
500
503
498
505
510
Very stable.
Now a random clutter patch
1
2
3
4
5
6
7
8
9
120
40
250
70
180
Highly unstable.
The relationship between is very different.
1
2
3
4
5
6
7
8
9
current
vs
lag-1
vs
lag-2
A classifier can learn that.
2 - 3 Another common meaning: lag correlation
Sometimes papers don’t mean the lagged value itself.
They mean the autocorrelation.
For lag-1,
\[Corr(x_t,x_{t-1})\]For lag-2,
\[Corr(x_t,x_{t-2})\]Suppose your point count is
1
2
3
4
5
500
501
502
503
504
Lag-1 correlation is almost 1 because every frame looks like the previous one. Random noise
1
2
3
4
5
20
400
90
310
15
has a lag-1 correlation near 0
3 - Coefficient of Variation (CV)
CV here means coefficient of variation, not covariance.
\[CV=\frac{\text{standard deviation}}{\text{mean}}\]It is dimensionless. For example, if sonar intensity has mean (100) and standard deviation (45),
\[CV=\frac{45}{100}=0.45\]Intensity fluctuates by roughly 45% of its mean.
