As title, I haven't found a post explain about this, i.e. In the following diagram, for a point on a "better" ROC curve and I move that point along the curve toward the top-right corner, why both TPR and FPR approach 1? And what's the meaning of moving along a given curve?
An ROC curve shows a classification model over all possible thresholds, not a single classifier. Any point on the ROC curve represents a particular model instantiation with a particular threshold, and particular outputs. You can think of your classification model as producing a score for every sample, and to get a single classifier, you need to pick a threshold for calling things positive/negative.
The ROC curve shows the model's performance at every possible threshold - you start with a very low threshold at the bottom left, calling everything negative (FPR=0, TPR=0). As you raise the threshold, you move along the curve as you start to identify true positives. In the ideal case with the perfect model, you'll find a threshold that identifies all the positives and none of the negatives, getting you FPR=0, TPR=1. If you increase the threshold too much, the model may get somewhat worse, as you'll still identify all the positives, but also some of the negatives (TPR=1, FPR>0).
When you're all the way in the top right corner, you've set your threshold higher/lower than any score in the dataset, and you simply classify everything as positive. At that point the scores are irrelevant, so it doesn't matter if you have the "perfect" classification model that produces meaningful scores, or a random classifier that produces meaningless scores. If you set your threshold higher/lower than any of the classifier scores, the scores don't actually matter.
As you can see, you don't want a classifier that falls in the top right corner - it's a naive classifier that just calls everything positive, regardless of any input features. You want your classifier to be in the top left corner, at TPR=1 and FPR=0.
