BIRCH in Data Mining

BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) is an algorithm used for clustering large datasets. It organizes data into a tree structure, making it efficient and able to handle large amounts of data quickly.

Key Features of BIRCH:

Hierarchical Clustering: Groups data step by step into a tree structure.
Works with Large Datasets: Summarizes data into smaller clusters first, then clusters these summaries, which saves memory and time.
Handles Noise: Can deal with data points that don't fit into any cluster.
Single Scan: Often needs only one pass through the data, making it fast.
Combines with Other Algorithms: The summarized clusters can be used as input for other clustering algorithms like k-means or agglomerative clustering.

Why Use BIRCH

It’s efficient for very large datasets.
Easy to implement and works well in limited memory.
Useful for tasks where clustering needs to be fast and precise.

For example, BIRCH can quickly create summaries of large data, and these summaries can then be clustered further using other algorithms for more detailed analysis.

Problem with Previous Clustering Algorithm

Earlier clustering algorithms struggled with very large datasets, especially when the data was too big to fit in memory. These algorithms treated all data points equally when making clustering decisions, without considering which points were closer or more important. This led to high processing costs and extra input/output (IO) operations, making it harder to maintain good clustering quality efficiently.

Storage of BIRCH

BIRCH is often used with other clustering algorithms by first summarizing large datasets into smaller, manageable parts. However, its main limitation is that it only works with numeric (metric) data, where values can be represented in Euclidean space, so it cannot handle categorical data.

BIRCH has two main steps:

Building the CF Tree:
- Summarizes the dataset into compact groups called Clustering Features (CF).
- Each CF has three values:
  - N: Number of data points in the group.
  - LS: The total of all data point values (linear sum).
  - SS: The sum of squares of all data point values.
- These CF groups can also combine to form larger clusters.
- Optionally, the tree can be simplified further to reduce its size.
Global Clustering:
- Uses another clustering algorithm (like k-means) on the CF tree’s leaf nodes to create the final clusters.
- Each leaf node represents a small sub-cluster.
- Optionally, clusters can be further refined for better accuracy.

Because it first summarizes the data and then applies clustering, BIRCH is called a Two-Step Clustering Algorithm.

Algorithm

The BIRCH algorithm creates a tree structure called the Clustering Feature (CF) Tree to organize and summarize large datasets for clustering. This tree compresses data into smaller groups called CF nodes, which contain CF subclusters if they have multiple smaller groups inside.

Key Points About the CF Tree:

It’s a balanced tree that stores summarized information about the data, such as the number of points (N), the sum of their values (LS), and the sum of their squared values (SS).
Instead of working with the full dataset, the tree stores the essential details needed for clustering, saving time and memory.

Steps in the BIRCH Algorithm:

Scanning Data: Loads and organizes the data into the CF tree.
Condensing Data (Optional): Simplifies and resizes the data to fit better into the CF tree.
Global Clustering: Uses another clustering algorithm (like k-means) to group the CF tree’s summaries into final clusters.
Refining Clusters (Optional): Fixes errors in the tree where similar data points might be assigned to different groups.

These steps ensure the data is processed efficiently, summarized in the CF tree, and then clustered accurately. Optional steps, like condensing and refining, improve the quality of the clustering when needed.

Cluster Features

BIRCH clustering is efficient because it uses a small set of summary numbers to represent large amounts of data. These numbers, called Clustering Features (CF), are enough for clustering without needing to keep all the original data points.

A CF consists of three key statistics that summarize a cluster:

Count: The number of data points in the cluster.
Linear Sum: The total of all data points' values. It helps find the cluster's center or location.
Squared Sum: The total of the squared values of data points. This shows how spread out the cluster is.

These three numbers are used to represent a cluster and help the algorithm group similar data points together efficiently.

CF Tree

Here’s a simplified explanation of the process for building the CF Tree in the BIRCH algorithm:

Step 1:

When a new record arrives, BIRCH compares the record's location with the Clustering Features (CFs) in the root node. It uses either the linear sum or the mean to find the CF closest to the record. The record is then sent to this closest CF in the root node.

Step 2:

The record then moves down to the non-leaf child nodes of the selected CF. BIRCH compares the record with the non-leaf CFs and sends it to the CF that’s closest.

Step 3:

The record descends further to the leaf child nodes of the selected non-leaf CF. Again, BIRCH compares the record with the leaf CFs and sends it to the leaf CF closest to it.

Step 4:

Once the record is at a leaf, one of the following happens:

If the leaf node has enough space (i.e., the radius, or spread, of the cluster does not exceed a set limit, Threshold T), the record is added to the leaf, and both the leaf and its parent CFs are updated to reflect the new record.
If the leaf node exceeds the limit (Threshold T), a new leaf node is created just for the new record. The parent CFs are also updated accordingly.
- If the maximum number of leaves (L) is reached in the leaf node, it splits into two new leaf nodes. If the parent node is also full, it gets split too. This process continues up the tree as needed.
- To split, the most distant leaf CFs are used as seeds for the new leaf nodes, and other CFs are assigned to the closest one.

This process allows BIRCH to build a compact structure to represent large amounts of data, efficiently handling clustering without needing to keep all the original data points in memory.

Clustering the Sub-Cluster

Once the CF Tree is built, you can apply any existing clustering algorithm to the sub-clusters (the leaf nodes of the CF Tree). This makes clustering easier because now you are working with fewer sub-clusters instead of dealing with the entire dataset. When new data is added, only the summary statistics (like count, sum, and squared sum) need to be updated, which makes the whole process faster and more efficient.

Parameters of BIRCH

In the BIRCH algorithm, there are three important parameters that need to be set:

Threshold: This is the maximum number of data points that a sub-cluster in the leaf node of the CF tree can hold. It helps control the size of each sub-cluster.
Branching Factor: This sets the maximum number of sub-clusters (CFs) that can be in each internal node of the tree. It determines how the tree branches out.
n_clusters: This defines how many clusters you want to get as the final result after the BIRCH algorithm finishes. If set to "none," the algorithm won’t perform final clustering and will just return intermediate clusters.

The great thing about BIRCH is that you don’t need to specify the number of clusters (like in K-means), because it figures that out for you based on the data.

Advantages of BIRCH

BIRCH is a local algorithm, meaning it makes clustering decisions without looking at all the data points or existing clusters at once. It takes advantage of the fact that data is not always spread evenly, and some data points are more important than others.

The algorithm uses the available memory to create the best possible sub-clusters while minimizing the need to read from the hard drive (which can be slow). BIRCH is also incremental, meaning it doesn’t need the entire dataset up front and can process data as it arrives.

BIRCH in Data Mining