Linear Discriminant Analysis (LDA) and Clustering
Linear Discriminant Analysis (LDA) and Clustering are two important techniques in Machine Learning, but they serve different purposes.
-
LDA is a supervised dimensionality-reduction and classification technique.
-
Clustering is an unsupervised learning approach that groups similar data points.
1. Linear Discriminant Analysis (LDA)
LDA finds a projection of the data that maximizes separation between known classes while minimizing variation within each class.
The objective can be expressed as:
J(w)=\frac{w^T S_B w}{w^T S_W w}
where:
-
(S_B): between-class scatter matrix
-
(S_W): within-class scatter matrix
-
(w): projection vector
Key Characteristics
-
Requires labeled training data
-
Produces at most (C-1) discriminant components for (C) classes
-
Often improves classification accuracy and interpretability
2. Clustering
Clustering partitions data into groups without using class labels.
Common algorithms include:
-
K-means clustering
-
Hierarchical clustering
-
DBSCAN
-
Gaussian Mixture Models
Goal
Points within the same cluster are more similar to one another than to points in different clusters.
3. LDA for Clustering Support
Although LDA itself is not a clustering algorithm, it can be used before clustering when some labeled data are available.
Benefits include:
-
Reducing dimensionality
-
Removing noisy features
-
Emphasizing class-discriminative structure
In purely unlabeled problems, techniques such as PCA are more commonly used before clustering.
4. LDA vs Clustering
| Feature | Linear Discriminant Analysis | Clustering |
|---|---|---|
| Learning Type | Supervised | Unsupervised |
| Requires Labels | Yes | No |
| Primary Goal | Maximize class separation | Discover natural groups |
| Output | Discriminant components | Cluster assignments |
| Typical Use | Classification preprocessing | Exploratory analysis |
5. Applications
-
Face recognition
-
Medical diagnosis
-
Gene-expression analysis
-
Customer segmentation
-
Document grouping
Summary
Linear Discriminant Analysis is a supervised method that projects data into a lower-dimensional space with maximum class separability, while clustering is an unsupervised method that discovers groups in unlabeled data. LDA is not itself a clustering technique, but it can be a powerful preprocessing step when label information is available.