Is the threshold of the Anomaly score dynamic for the Streaming detection?

[shihyulee]

On the streaming data, is it necessary to design the dynamic threshold of the anomaly score to adapt over time as the input data changes?

Thank you.

[yasirroni]

In my case, static model with static threshold is prefered. Here is the code:

# Set tree parameters
NUM_TREES = 100 # around 100 trees or more is recommended
SHINGLE_SIZE = 10 # number of data treated as single data
NUM_SHINGLE = n_points - SHINGLE_SIZE + 1 # number of shingle
TREE_SIZE = NUM_SHINGLE # number of points in the tree for fifo, minutes in a day are 1440
SPROUT_PROBABILITY = 0.8 # the probability of leaf grow on single tree independently, lower means better generality

TREE_FULL_FLAG = False # flag to mark tree status

# Create a forest of empty trees
forest = [None] * NUM_TREES
for i in range(NUM_TREES):
    tree = rrcf.RCTree()
    forest[i] = tree

# Use the "shingle" generator to create rolling window
points = rrcf.shingle(X, size=SHINGLE_SIZE)

# transpose
def shingle_transpose(shingle):
    for val in shingle:
        yield val.T.flatten()

points = shingle_transpose(points)

# create a dict to store anomaly score of each point
avg_codisp = pd.Series(0.0, index=np.arange(NUM_SHINGLE))

# create a dict to store anomaly score of each point
avg_codisp = pd.Series(0.0, index=np.arange(NUM_SHINGLE))

# for each shingle...
for index, point in enumerate(points):
    # record number of tree that save the shingle
    freq = 0
    # for each tree in the forest...
    for tree in forest:
        # roll dice to determine point become a leave or not
        if np.random.random() <= SPROUT_PROBABILITY:
            # insert the new point into the tree
            tree.insert_point(point, index=index)
            
            # add 1 to freq record
            freq += 1
            
        # if tree already full
        if len(tree.leaves) == TREE_SIZE: 
            TREE_FULL_FLAG = True
            
    # if no tree save current shingle
    if freq == 0:
        # chose any tree
        tree = np.random.choice(forest)

        # insert the new point into the tree
        tree.insert_point(point, index=index)
        
        # if tree already full
        if len(tree.leaves) == TREE_SIZE: # if TREE_SIZE
            TREE_FULL_FLAG = True
    
    # if any tree is above permitted size...
    if TREE_FULL_FLAG:
        break

# Compute codisp
freq = np.zeros(index + 1)
for tree in forest:
    codisp = pd.Series({leaf : tree.codisp(leaf) for leaf in tree.leaves})
    avg_codisp[codisp.index] += codisp
    np.add.at(freq, codisp.index.values, 1)

for i in range(index + 1):
    if freq[i] >= 1:
        avg_codisp[i] = avg_codisp[i] / freq[i]
        
# After any tree is above permitted size and if points haven't empty, for each shingle...
for point in points:
    # Continue index counter
    index += 1
    
    codisp = 0
    freq = 0
    for tree in forest:
        # Roll dice to plant or not
        if np.random.random() <= SPROUT_PROBABILITY:
            # Check if leave can sprout
            if len(tree.leaves) == TREE_SIZE:
                # Drop the oldest point (FIFO)
                tree.forget_point(min(tree.leaves.keys()))

            # Insert the new point into the tree
            tree.insert_point(point, index=index)
            
            codisp += tree.codisp(index)
            freq += 1

    if freq == 0: # leaf not sprouted at any tree
        tree = np.random.choice(forest)
        # Check if leave can sprout
        if len(tree.leaves) == TREE_SIZE:
            # Drop the oldest point (FIFO)
            tree.forget_point(min(tree.leaves.keys()))

        # Insert the new point into the tree
        tree.insert_point(point, index=index)

        codisp += tree.codisp(index)
        freq += 1
        
    avg_codisp[index] = codisp / freq

plt.plot(avg_codisp)
plt.show()

Then, I will double (based on your case) the maximum value of train CoDisp as the threshold, and you can use insert and delete the new point in testing or deployment.