Apparantly you are not passing an ArrayList of ArrayLists but rather an ArrayLists of Floats into this function.

Also, int i in the train function is never used (because of the int i in the for loop) so what's the point of it?

Also, you are working backwards, but is there a reason you don't include the ArrayList at zero?

Also, it is not fully clear what your data look like and what you want to retreive exactly. Values from different ArrayLists at a specific index? All the values from one specific ArrayList? Go through all the ArrayLists and let findBMU() find something? Your code at the moment seems like a mix between all three, which is not good.

You should type your array lists, it would be clearer which level you are dealing with.
For example, you have an ArrayList<ArrayList<Float>>, and at one time, you need a simple ArrayList<Float>.
One advantage: no need to cast when you get().

Indeed that would be a solution. Let me elaborate and give an example.

In the code below (without casting, that solution follows below) the ArrayListOfArrays works, while the floatArray give the familiar exception. As pointed out earlier, there are one or more floats in your main ArrayList, thus causing the error.

1. ArrayList floatArray = new ArrayList();
2. ArrayList ArrayListOfArrays = new ArrayList();
3.  
4. void setup() {
5.   size(250,250);
6.   floatArray.add(random(100));
7.   ArrayListOfArrays.add(floatArray);
8.   train(1,ArrayListOfArrays); // this works as it should
   
9. //  train(1,floatArray); // uncomment this and see the ClassCastException
10. }
11.  
12. void train(int i, ArrayList w) {
13.   for (int m = 0; m < w.size(); ++m) {     
14.     ArrayList tempList = (ArrayList) w.get(m); // problem lies here: how to cast the ArrayList
15.   }
16. }

The solution is to NOT have any floats in your main arrayList. The easiest way to make sure (and in your case find where it happens) is by setting a type, like so...

1. ArrayList <ArrayList> ArrayListOfArrays = new ArrayList <ArrayList> ();

This will turn up any floats that are trying to get into your ArrayListOfArrays, because that is no longer allowed. Like phi.lho pointed out, another advantage is you don't need to explicitly cast when you get it. So you could then just use...

1. ArrayList tempList = w.get(m);

Hope this helps.

Many thanks!