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    private void initialize_cutting_inds_thresholds(){
        cutting_inds = new int[feature_dim][][];
        cutting_thresholds = new float[feature_dim][];

        for(int i=0;i<feature_dim;i++){
            //for this feature, get its cutting index
            ArrayList<Integer> list = new ArrayList<>();
            int last_index = 0;
            for(int j=0;j<attribute_list[i].length;j++){
                if(attribute_list[i][j][0]==attribute_list[i][last_index][0]){
                    last_index = j;
                }else {
                    list.add(last_index);
                    last_index = j;
                }
            }
            //for this feature,store its cutting threshold
            cutting_thresholds[i] = new float[list.size()+1];
            for(int t=0;t<cutting_thresholds[i].length-1;t++){
                cutting_thresholds[i][t] = attribute_list[i][list.get(t)][0];
            }
            cutting_thresholds[i][list.size()] = attribute_list[i][list.get(list.size()-1)+1][0];

            //for this feature,store inds of each interval
            cutting_inds[i] = new int[list.size()+1][]; //list.size()+1 interval

            list.add(0,-1);
            list.add(attribute_list[i].length-1);
            for(int k=0;k<cutting_inds[i].length;k++){
                int start_ind = list.get(k)+1;
                int end_ind = list.get(k+1);
                cutting_inds[i][k] = new int[end_ind-start_ind+1];
                for(int m=0;m<cutting_inds[i][k].length;m++){
                    cutting_inds[i][k][m] = (int) attribute_list[i][start_ind+m][1];
                }
            }

        }
    }

      private void initialize_cutting_idx_thresholds() {
		cutting_idx = new int[feature_dim][][];
		cutting_thresholds = new double[feature_dim][];
		
		for (int i = 0; i < feature_dim; ++i) {
			List<Integer> list = new ArrayList<>();
			int last_index = -1;
			for (int j = 0; j < attribute_list[i].length; ++j) {
				if (last_index == -1 || attribute_list[i][j][0] == attribute_list[i][last_index][0]) {
					last_index = j;
				}
				else {
					list.add(last_index);
					last_index = j;
				}
			}
			
			cutting_thresholds[i] = new double[list.size()];
			for (int t = 0; t < cutting_thresholds[i].length; ++t) {
				cutting_thresholds[i][t] = attribute_list[i][list.get(t)][0];
			}
			
			cutting_idx[i] = new int[list.size()][];
			list.add(attribute_list[i].length);
			
			for (int k = 0; k < cutting_idx[i].length; ++k) {
				int s_idx = list.get(k);
				int e_idx = list.get(k + 1);
				cutting_idx[i][k] = new int[e_idx - s_idx];
				for (int m = 0; m < cutting_idx[i][k].length; ++m) {
					cutting_idx[i][k][m] = (int)attribute_list[i][s_idx + m][1];
				}
			}
		}
      }