diff --git a/sklearn/cluster/_hdbscan/_tree.pyx b/sklearn/cluster/_hdbscan/_tree.pyx
index 0e493f28379eb..6e4df6cf12592 100644
--- a/sklearn/cluster/_hdbscan/_tree.pyx
+++ b/sklearn/cluster/_hdbscan/_tree.pyx
@@ -282,40 +282,37 @@ cdef max_lambdas(cnp.ndarray hierarchy):
     return deaths
 
 
-cdef class TreeUnionFind (object):
+@cython.final
+cdef class TreeUnionFind:
 
-    cdef cnp.ndarray _data_arr
-    cdef cnp.intp_t[:, ::1] _data
-    cdef cnp.ndarray is_component
+    cdef cnp.intp_t[:, ::1] data
+    cdef cnp.uint8_t[::1] is_component
 
     def __init__(self, size):
-        self._data_arr = np.zeros((size, 2), dtype=np.intp)
-        self._data_arr.T[0] = np.arange(size)
-        self._data = self._data_arr
-        self.is_component = np.ones(size, dtype=bool)
+        cdef cnp.intp_t idx
+        self.data = np.zeros((size, 2), dtype=np.intp)
+        for idx in range(size):
+            self.data[idx, 0] = idx
+        self.is_component = np.ones(size, dtype=np.uint8)
 
-    cdef union_(self, cnp.intp_t x, cnp.intp_t y):
+    cdef void union(self, cnp.intp_t x, cnp.intp_t y):
         cdef cnp.intp_t x_root = self.find(x)
         cdef cnp.intp_t y_root = self.find(y)
 
-        if self._data[x_root, 1] < self._data[y_root, 1]:
-            self._data[x_root, 0] = y_root
-        elif self._data[x_root, 1] > self._data[y_root, 1]:
-            self._data[y_root, 0] = x_root
+        if self.data[x_root, 1] < self.data[y_root, 1]:
+            self.data[x_root, 0] = y_root
+        elif self.data[x_root, 1] > self.data[y_root, 1]:
+            self.data[y_root, 0] = x_root
         else:
-            self._data[y_root, 0] = x_root
-            self._data[x_root, 1] += 1
-
+            self.data[y_root, 0] = x_root
+            self.data[x_root, 1] += 1
         return
 
-    cdef find(self, cnp.intp_t x):
-        if self._data[x, 0] != x:
-            self._data[x, 0] = self.find(self._data[x, 0])
+    cdef cnp.intp_t find(self, cnp.intp_t x):
+        if self.data[x, 0] != x:
+            self.data[x, 0] = self.find(self.data[x, 0])
             self.is_component[x] = False
-        return self._data[x, 0]
-
-    cdef cnp.ndarray[cnp.intp_t, ndim=1] components(self):
-        return self.is_component.nonzero()[0]
+        return self.data[x, 0]
 
 
 cpdef cnp.ndarray[cnp.intp_t, ndim=1] labelling_at_cut(
@@ -361,8 +358,8 @@ cpdef cnp.ndarray[cnp.intp_t, ndim=1] labelling_at_cut(
     cluster = n_samples
     for row in linkage:
         if row[2] < cut:
-            union_find.union_(<cnp.intp_t> row[0], cluster)
-            union_find.union_(<cnp.intp_t> row[1], cluster)
+            union_find.union(<cnp.intp_t> row[0], cluster)
+            union_find.union(<cnp.intp_t> row[1], cluster)
         cluster += 1
 
     cluster_size = np.zeros(cluster, dtype=np.intp)
@@ -416,7 +413,7 @@ cdef cnp.ndarray[cnp.intp_t, ndim=1] do_labelling(
         child = child_array[n]
         parent = parent_array[n]
         if child not in clusters:
-            union_find.union_(parent, child)
+            union_find.union(parent, child)
 
     for n in range(root_cluster):
         cluster = union_find.find(n)