Triplet loss function for face recognition? In the Andrew-NG coursera course on Convnets he talked about triplet loss function for one shot face recognition.

The formula given in the video is,
$$\to \small \small \small ||f(A)-f(P)||^2 \;+\;\alpha \leq\;||f(A)-f(N)||^2$$
$$\to \small \small \small D(A, P) + \alpha \leq D(A, N)$$
$$L(A,P,N) = max(||f(A)-f(P)||^2 - ||f(A)-f(N)||^2 + \alpha,  0)$$
Here,
$$f(A) - \small \text{ Person }A$$
$$f(P) - \small \text{Different Picture of Person }A$$
$$F(N) - \small \text{Another Person}$$

I couldn't understand why did we use $\alpha$ in the formula. I understood that the ideal loss function is to decrease $\small \small D(A, P)$ and increase $\small \small D(A, N)$ but if we add $\alpha$ to $\small \small D(A,P)$ it will increase it which is not we require right?
$\alpha$ is known as the margin. 

Not only that we want to minimize $D(A,P)$ and maximize $D(A,N)$, that is we want  $D(A,P)-D(A,N)$ to be small. Not only that we want it to be non-positive, we want it to be sufficiently negative.

That is not only that we want  $$D(A,P)-D(A,N) \le 0$$ 

We want $$D(A,P)-D(A,N) \le -\alpha.$$