C-means clustering is a type of unsupervised machine learning algorithm that is used for data clustering. It is a soft clustering method that partitions the data into several clusters, with each point belonging to multiple clusters with a degree of membership.
The C in C-means stands for "fuzzy c-means," and the algorithm is also known as fuzzy clustering. The main idea behind C-means clustering is to minimize the fuzzy objective function that calculates the degree of membership of each point to each cluster.
Algorithm
Initialization: Choose the number of clusters K and randomly assign a degree of membership to each data point for each cluster. The degree of membership is a value between 0 and 1 that reflects the degree of association with each cluster.
Calculate Centroids: Calculate the centroid of each cluster as the weighted average of the data points, with the weights being the degree of membership of each point.
Update Memberships: Update the degree of membership of each point to each cluster based on the distance to the cluster centroid. The closer a point is to a cluster centroid, the higher its degree of membership to that cluster.
Repeat Steps 2 and 3 until convergence: Keep iterating Steps 2 and 3 until the degree of membership of each point to each cluster stabilizes.
Output: The final output of the algorithm is the partition of the data into K clusters, with each point belonging to multiple clusters with a degree of membership.
Example
To explain c-means clustering with an example, let's consider a dataset of customers of an e-commerce platform. The dataset contains information about each customer's age, gender, income, and spending habits. The goal is to group similar customers together to better understand their behavior and preferences.
Step 1: Initialize the cluster centers: The first step in the algorithm is to initialize the cluster centers. For simplicity, let's assume that we want to group the customers into two clusters. We randomly select two customers from the dataset and set their feature values as the initial cluster centers.
Step 2: Assign data points to the nearest cluster: In this step, we calculate the distance between each customer and the cluster centers. Each customer is then assigned to the nearest cluster based on the calculated distances. The distance can be calculated using the Euclidean distance formula, which measures the distance between two points in n-dimensional space.
Step 3: Calculate the new cluster centers: Once all the customers are assigned to a cluster, we calculate the new cluster centers by taking the mean of the feature values of all the customers in the cluster.
Step 4: Repeat steps 2 and 3 until convergence: We repeat steps 2 and 3 until the cluster centers no longer change, indicating that the optimal clustering has been achieved.
Step 5: Interpret the results: Once the clustering is complete, we can interpret the results to gain insights into the customer behavior and preferences. For example, we may find that customers in one cluster tend to be younger, have a lower income, and spend more on clothing, while customers in the other cluster tend to be older, have a higher income, and spend more on electronics.
Difference between C-Means and K-Means Clustering
Definition: K-means clustering is a type of centroid-based clustering, whereas C-means clustering is a type of fuzzy clustering.
Number of Clusters: In k-means clustering, the number of clusters is fixed, and the algorithm tries to group the data into k clusters, whereas in C-means clustering, the number of clusters is not predetermined, and the algorithm tries to partition the data into several fuzzy clusters.
Membership: In k-means clustering, each point belongs to one and only one cluster, whereas in C-means clustering, each point belongs to multiple clusters with a degree of membership, reflecting the degree of association with each cluster.
Centroid Calculation: In k-means clustering, the centroid of each cluster is calculated as the mean of the data points belonging to that cluster. In contrast, in C-means clustering, the centroids are calculated as the weighted average of the data points, with the weights being the degree of membership of each point.
Convergence Criteria: K-means clustering aims to minimize the sum of squared distances between each data point and its assigned cluster centroid. In contrast, C-means clustering aims to minimize the fuzzy objective function that calculates the degree of membership of each point to each cluster.
Robustness: C-means clustering is more robust to outliers than k-means clustering because each point belongs to multiple clusters with a degree of membership. In contrast, in k-means clustering, outliers can significantly affect the final clustering results.
Advantages of C-Means Clustering
Flexibility: C-means clustering is more flexible than other clustering algorithms because it allows each point to belong to multiple clusters with a degree of membership, reflecting the degree of association with each cluster. This flexibility makes it suitable for data with overlapping clusters.
Robustness: C-means clustering is more robust to outliers than other clustering algorithms because each point's degree of membership to each cluster is taken into account. Outliers have a lesser effect on the clustering results than in other methods.
No Prior Knowledge of Number of Clusters: C-means clustering does not require prior knowledge of the number of clusters in the data. The algorithm automatically determines the number of clusters based on the data and the user-defined parameters.
Efficiency: C-means clustering is computationally efficient and can handle large datasets with ease.
Convergence: C-means clustering is guaranteed to converge to a solution, although the solution may be a local minimum.
Soft Partitioning: C-means clustering provides a soft partitioning of the data into clusters, allowing each point to have a degree of membership to each cluster. This soft partitioning is more realistic than the hard partitioning provided by other clustering algorithms.