K-means Clustering
K-means clustering is a popular unsupervised learning algorithm used for data clustering and pattern discovery. It is a partition-based clustering algorithm that aims to divide a dataset into k distinct clusters, where each data point belongs to the cluster with the nearest mean value. The algorithm iteratively assigns data points to the closest cluster centroid and updates the centroids until convergence.
The steps involved in the K-means clustering algorithm are as follows:
- Randomly initialize k cluster centroids.
- Assign each data point to the nearest centroid.
- Update the centroids by computing the mean of the data points assigned to each cluster.
- Repeat steps 2 and 3 until convergence or a maximum number of iterations is reached.
Hierarchical Clustering
Hierarchical clustering is another unsupervised learning algorithm used to group similar data points into clusters. It builds a hierarchy of clusters in the form of a tree-like structure known as a dendrogram. The algorithm can be either agglomerative or divisive. In agglomerative hierarchical clustering, each data point initially represents a separate cluster, which are then successively merged based on similarity measures. In divisive hierarchical clustering, all data points start in one cluster, which is recursively split into smaller clusters.
The hierarchical clustering process involves the following steps:
- Compute the similarity or dissimilarity matrix between data points.
- Create initial clusters, where each data point is assigned to a separate cluster.
- Iteratively merge or split clusters based on similarity or dissimilarity measures.
- Continue merging or splitting until a desired number of clusters or a stopping criterion is reached.
Principal Component Analysis (PCA)
Principal Component Analysis (PCA) is a dimensionality reduction technique commonly used in unsupervised learning. It aims to transform high-dimensional data into a lower-dimensional representation while preserving the variance in the data. PCA identifies the principal components, which are linear combinations of the original features, capturing the most significant information in the data. The principal components are ordered based on their associated eigenvalues, and the lower-dimensional representation can be obtained by selecting a subset of the principal components.
The steps involved in performing PCA are as follows:
- Standardize the data by subtracting the mean and scaling the features.
- Compute the covariance matrix or correlation matrix of the standardized data.
- Calculate the eigenvectors and eigenvalues of the covariance or correlation matrix.
- Select the desired number of principal components based on the explained variance or other criteria.
- Transform the data into the lower-dimensional space using the selected principal components.
Association Rule Learning
Association rule learning is a technique used to discover interesting relationships or associations among items in large datasets. It is commonly applied in market basket analysis to identify patterns and dependencies between products. Association rule learning algorithms generate rules in the form of “if-then” statements, where certain items or itemsets imply the presence of other items. The widely used algorithm for association rule learning is the Apriori algorithm.
The process of association rule learning typically involves the following steps:
- Identify frequent itemsets by scanning the dataset and determining the support of each itemset.
- Generate candidate itemsets by combining frequent itemsets.
- Calculate the support and confidence of each candidate itemset.
- Prune the candidate itemsets based on minimum support and minimum confidence thresholds.
- Generate association rules from the remaining candidate itemsets.
