How calculate a true negatives in my case (to make a ROC analisys)?

Hello together,

I have a motor that rotating in a light gate and producing a ground truth "G"

A microphone that take an audio capture of this motor.

An algorithm, analyze this audio capture and detect a ground truth (F0/F1) in spectrum "R"

I calculate a TP/FN/FP with (pseudo code):

if R is element from G-array ​% right motorspeed detected
    than TP = TP + 1;​
if R is not element from G-array​ % wrong motorspeed detected
    than FP = FP + 1;​
if G not element from R-array​ %motorspeed is not detected
    than FN = FN + 1;​
end

with a code (in a loop):

motor_actual = nonzeros(unique(motor_actual)); %No zeros no repeats 
motorspeed_detected = nonzeros(unique(motorspeed_detected)); %No zeros no repeats 
Analyse1 = ismembertol(motorspeed_detected, motor_actual*harm, tube_cnt, 'DataScale' , 1); %Elements of R in G +-tolerance 
Analyse2 = ismembertol(motor_actual*harm, motorspeed_detected, tube_cnt, 'DataScale' , 1); %Elements of G in R +-tolerance 
TP_help = nnz(Analyse1); %right frequency detected  
FP_help = nnz(~Analyse1); %wrong frequency detected  
FN_help = nnz(~Analyse2); %no frequency detected 
TP = TP + TP_help; 
FP = FP + FP_help; 
FN = FN + FN_help;

Now, I have to create a receiver operating characteristic curve (ROC curve).

To do this I need a true positive rate: TP_rate = TP/(TP+FN) and false positive rate: FP_rate = FP/(FP+TN)

So, I need also to calculate TN!

The condition for TM is:

if R is element from G-array ​== 0  %right motor stop detecting
 TN = TN + 1;
end

But how is this possible, when:

1. my motor is always on, so ground truth G is > 0

2. algorithm can detect just positive values R > 0

So, TN = 0?

So I have always FP_rate = FP/(FP+0) = 1?

Or I can use another method to find a FP_Rate?

Thank you in advice!

[Nik Rocky]

Maybe there are another existing analysis systems, where I can use just TP/FN/FP?

[Nik Rocky]

I decided to make a ROC with:

TPR, Recall, Sensitivity = TP / (TP + FN) + False discovery rate (FDR) = FP/(TP+FP)

[KALYAN ACHARJYA]

Sorry not getting the exact logic. Is this "producing a ground truth "G"? Ground truth for the comparison, whether the code classify the right or wrong.

[Nik Rocky]

Hi Kalyan,

ground truth G have a values of a real speed of motors

G =

0    60,1
0,1  60
0,2  60,5
0,3  60,15
0,4  60
.......
29,9 61,1
30   60,54

first column is time, second a real rotating speed (ground truth)

R have a detected speed via algorithm:

R =

0    60
0,1  59
0,3  60,28
0,4  61
0,8  74,28
1    60
1,1  60
.......
29,9 61,1
30   60

first column is time, second a detected speed from audio spectrum