Machine Learning: Unsupervised Learning

Unsupervised learning is the branch of machine learning focused on finding structure in data that has no explicit labels. Instead of learning a direct mapping from inputs to known targets, an unsupervised system looks for patterns, groupings, and underlying factors that explain how the data is organized. It is used when labels are expensive, unavailable, or too limiting, and when the goal is discovery rather than prediction.

In practical terms, unsupervised learning helps answer questions like: Which customers behave similarly? Are there natural groupings of products? What are the main dimensions along which documents differ? Can we generate new examples that resemble the data we have? The core toolkit includes clustering, dimensionality reduction, and generative models.

Why unsupervised learning matters

Many real-world datasets arrive unlabeled: clickstreams, sensor measurements, transaction histories, network logs, images scraped from the web, or free-form text. Labels often require human annotation, domain expertise, and ongoing maintenance as definitions change. Unsupervised learning provides a way to extract value early, guide hypotheses, and even improve supervised pipelines by creating better features or identifying anomalies and mislabeled cases.

It is also central to exploratory data analysis. Before building a predictive model, it can be useful to understand whether the data naturally separates into subpopulations, whether there are redundant variables, or whether noise and outliers dominate.

Clustering: finding groups without labels

Clustering algorithms partition observations into groups so that points within a cluster are more similar to each other than to points in other clusters. “Similarity” depends on a chosen distance or affinity measure, which must match the data type and problem setting.

k-means clustering

k-means is one of the most widely used clustering methods because it is simple and fast. It aims to divide data into $k$ clusters by minimizing the within-cluster sum of squared distances to each cluster’s centroid. Informally, it alternates between two steps:

1. Assign each point to the nearest centroid.
2. Recompute each centroid as the mean of the points assigned to it.

This repeats until assignments stabilize. k-means works best when clusters are roughly spherical, similarly sized, and separable in the chosen feature space. It is sensitive to feature scaling, so standardization is typically necessary. It is also sensitive to initialization; different starting centroids can lead to different outcomes, which is why multiple restarts are common.

Choosing $k$ is a practical challenge. Analysts often use the elbow method (looking for diminishing returns in variance explained as $k$ increases) or silhouette scores (how well-separated clusters appear), but domain knowledge usually matters more than any single metric. For customer segmentation, for example, the “right” number of segments is partly determined by what a business can act on.

Hierarchical clustering

Hierarchical clustering builds a tree of nested clusters, typically visualized as a dendrogram. It can be:

• Agglomerative: start with each point as its own cluster and iteratively merge the closest clusters.
• Divisive: start with all points in one cluster and iteratively split.

A key choice is the linkage criterion, which defines the distance between clusters, such as single linkage (minimum pairwise distance), complete linkage (maximum pairwise distance), or average linkage. Different linkages produce different shapes of clusters. Hierarchical clustering can reveal multi-level structure, which is valuable when there is no single “correct” clustering granularity.

Hierarchical methods are often more interpretable than k-means because they show relationships between clusters at multiple scales. They can also work with arbitrary distance measures, which is useful for text or biological sequences. The trade-off is computational cost on large datasets.

Practical considerations for clustering

Clustering results are only as meaningful as the features and distance measures used. Common pitfalls include:

• Mixing incompatible scales (for example, income in dollars and age in years) without normalization.
• Using Euclidean distance for sparse, high-dimensional text data where cosine similarity is often more appropriate.
• Interpreting clusters as “real” categories when they may be artifacts of preprocessing or noise.

Validation often combines internal metrics with external checks: do clusters align with known behaviors, operational constraints, or outcomes not used in training? A useful sanity check is whether clusters remain stable under small data perturbations or reasonable preprocessing changes.

Dimensionality reduction: simplifying data while preserving structure

Dimensionality reduction transforms high-dimensional data into a lower-dimensional representation that preserves important information. This can improve visualization, reduce noise, compress data, and make downstream models easier to train.

Principal Component Analysis (PCA)

PCA is a linear technique that finds orthogonal directions (principal components) capturing the greatest variance in the data. Projecting data onto the first few components often retains much of the signal while discarding redundant dimensions.

Conceptually, PCA re-expresses the dataset in a new coordinate system where the first axis explains the most variance, the second explains the next most, and so on. If the original variables are correlated, PCA can reveal a smaller set of latent factors.

PCA is widely used for:

• Noise reduction in sensor data
• Visualizing datasets in 2D or 3D
• Preprocessing before clustering or regression
• Identifying multicollinearity in tabular features

Because PCA is sensitive to scale, centering and scaling are standard practice. Also, variance is not always synonymous with importance: a low-variance feature could still be critical for a specific task, so PCA should be applied with awareness of the end goal.

t-SNE for visualization

t-SNE (t-distributed Stochastic Neighbor Embedding) is a nonlinear dimensionality reduction method designed primarily for visualization. It excels at preserving local neighborhood structure, often producing compelling 2D maps where similar points form tight groupings.

t-SNE is especially popular for exploring image embeddings, document embeddings, and learned representations from neural networks. However, it is easy to over-interpret. Distances between far-apart clusters in a t-SNE plot are not necessarily meaningful, and results can change with hyperparameters such as perplexity and random seed. t-SNE should be treated as an exploratory lens rather than a definitive clustering method.

A good practice is to pair t-SNE with quantitative checks: run clustering in the original feature space or in a PCA-reduced space, and verify whether the apparent visual groups correspond to stable structure.

Generative models: learning how data is produced

Generative models aim to learn the underlying data distribution so they can generate new samples resembling the training data. In unsupervised settings, they are trained without labels, focusing on capturing the patterns that define the dataset.

Generative modeling supports tasks such as:

• Data synthesis for simulation or augmentation
• Density estimation and anomaly detection (unlikely samples can be flagged)
• Representation learning, where internal model features serve as useful embeddings

Different families of generative models exist, but the central idea is consistent: fit a model so it can produce realistic data. Evaluating generative models is nuanced, because “realistic” depends on context. For images, visual inspection and distributional metrics might be used; for tabular data, constraints, correlations, and downstream utility matter.

In practice, generative models raise important operational questions: how to prevent memorization of sensitive records, how to validate synthetic data fidelity, and how to ensure generated samples do not introduce bias or violate constraints.

Putting unsupervised learning to work

Unsupervised learning is most effective when treated as a disciplined discovery process:

1. Define the purpose: segmentation, visualization, compression, anomaly detection, or synthesis.
2. Prepare features carefully: scaling, encoding, and domain-specific transformations often matter more than algorithm choice.
3. Compare methods: run k-means and hierarchical clustering, or PCA followed by clustering, and look for consistent structure.
4. Validate with reality: connect findings to external signals, expert review, and stability checks.
5. Iterate: unsupervised learning is exploratory by nature, and the first result is rarely the final answer.

At its best, unsupervised learning turns raw, unlabeled data into structure that humans and systems can use. It uncovers groups worth targeting, representations worth modeling, and patterns worth investigating, often before a single label is ever collected.