Unsupervised Learning

Introduction: What is Statistical Learning?

Statistical learning refers to a set of tools and techniques used to understand and extract insights from data. It’s a broad field encompassing both supervised and unsupervised learning approaches. The goal is to build models that can either predict an outcome (supervised) or discover patterns (unsupervised) in data. 📊

Supervised vs. Unsupervised Learning: Overview

Let’s start by understanding the fundamental difference between supervised and unsupervised learning. Think of it like learning with a teacher versus learning on your own.

• Supervised Learning: We have a “teacher” (the response variable, Y) guiding the learning process. 👨‍🏫 The goal is to learn a function that maps inputs to outputs.
• Unsupervised Learning: We’re exploring the data “without a teacher” to discover hidden patterns. 🕵️‍♀️ There’s no explicit output variable to predict.

Supervised Learning

• Supervised Learning: We have a set of features (X1, X2, …, Xp) and a response variable (Y). The goal is to predict Y using the Xs. We “teach” the algorithm by providing examples of inputs and their corresponding outputs.
• Examples: Linear regression (predicting house prices), logistic regression (predicting customer churn), Support Vector Machine (SVM) (image classification).

graph LR
    A[Features (X)] --> B(Model);
    C[Response (Y)] --> B;
    B --> D[Predictions];
    style A fill:#ccf,stroke:#333,stroke-width:2px
    style C fill:#f9f,stroke:#333,stroke-width:2px
    style B fill:#ccf,stroke:#333,stroke-width:2px
    style D fill:#ccf,stroke:#333,stroke-width:2px

Unsupervised Learning

• Unsupervised Learning: We only have features (X1, X2, …, Xp), without any response variable Y. No “teaching” or “supervision” – the algorithm explores the data on its own.
• Goal: Discover interesting patterns and structure in the data; find relationships among the features and/or observations.
• Examples: Principal Component Analysis (PCA) (dimensionality reduction), Clustering (finding groups of similar customers).

graph LR
    A[Features (X)] --> B(Model);
    B --> C[Patterns & Structure];
style A fill:#f9f,stroke:#333,stroke-width:2px
style B fill:#ccf,stroke:#333,stroke-width:2px
style C fill:#ccf,stroke:#333,stroke-width:2px

What is Unsupervised Learning? (Detailed)

Unsupervised learning is a collection of statistical methods used when we only have input data (features) and no corresponding output (response variable). Because there’s no “correct answer” to guide the analysis, we call it “unsupervised.” We’re essentially detectives, exploring the data to uncover hidden relationships and structures. 🔍 It’s about learning the underlying structure of the data itself.

Key Goals of Unsupervised Learning

Unsupervised learning serves several important purposes:

• Data Visualization: Finding ways to represent complex, high-dimensional data in a visually intuitive manner, often by reducing its dimensionality. Think of it like creating a map of your data, making it easier to navigate. 🗺️
• Discover Subgroups: Identifying clusters or groups within the data. This could be groups of customers with similar buying habits, or groups of genes with related functions. 🧑‍🤝‍🧑 This helps us understand the heterogeneity within the data.
• Data Pre-processing: Preparing data for supervised learning techniques. For example, we might use unsupervised learning to reduce the number of features or to create new, more informative features before applying a supervised learning algorithm. ⚙️ This can improve the performance and efficiency of supervised models.

Supervised vs. Unsupervised Learning: Comparison Table

Let’s solidify our understanding with a side-by-side comparison:

Supervised vs. Unsupervised: A Note of Caution

Applications of Unsupervised Learning

Unsupervised learning has become incredibly valuable across numerous fields:

• Genomics: Researchers studying cancer might use unsupervised learning to analyze gene expression data. This can help identify different subtypes of cancer, leading to more targeted treatments. 🧬
• E-commerce: Online retailers use unsupervised learning to group customers with similar browsing and purchasing patterns. This allows for personalized product recommendations, increasing sales and customer satisfaction. 🛍️
• Search Engines: Unsupervised learning can be used to cluster users based on their click histories, leading to more relevant search results. 🔎
• Marketing: Identifying market segments (groups of customers with shared characteristics) for targeted advertising campaigns. 🎯

Applications of Unsupervised Learning (Cont.)

These are just a few examples. The power of unsupervised learning lies in its ability to extract insights from data without needing a predefined outcome, making it a versatile tool for discovery in various domains. The ability to uncover hidden patterns is what makes it so powerful.

Diving into Principal Component Analysis (PCA)

Now, let’s explore our first unsupervised learning technique: Principal Component Analysis (PCA). PCA is like taking a high-dimensional dataset (many features) and finding the best way to “flatten” it while preserving as much of its original information as possible. It’s a dimensionality reduction technique that finds the most important “directions” in your data.

What does PCA do?

• Dimensionality Reduction: PCA simplifies data by finding a smaller set of representative variables, called principal components. These components capture most of the variability in the original data.
• Data Visualization: It allows us to visualize high-dimensional data in lower dimensions (e.g., 2D or 3D plots), making it easier to spot patterns and relationships that would be hidden in higher dimensions.
• Unsupervised: PCA only uses the features (X) and doesn’t rely on any response variable (Y). It focuses solely on the relationships between the features.
• Feature Space Directions: Identifies the directions in the feature space along which the original data varies most. These are the “principal components”.
• Data Pre-processing: PCA can create new, uncorrelated features that can be used in subsequent supervised learning models. This can improve model performance and reduce overfitting.

What are Principal Components? (Explained)

Imagine you have a dataset with many variables (features). PCA helps you find new variables, called principal components, which are linear combinations of the original features. It’s like creating new “summary” variables from the original ones, but in a way that maximizes the captured variance.

Understanding the First Principal Component (Z1)

• First Principal Component (Z1): This is the most important principal component. It’s the normalized linear combination of the original features that captures the largest variance in the data. It represents the direction of greatest variability in the data cloud.

  • Normalized: The sum of the squared coefficients (loadings) equals 1. This ensures that the variance isn’t artificially inflated by using large coefficients. It’s a mathematical constraint for uniqueness.
  • Loadings: The coefficients (φ) in the linear combination are called loadings. They tell us how much each original feature contributes to the principal component. A large loading (in absolute value) means the feature has a strong influence on that component.

Subsequent Principal Components

• Subsequent Principal Components: These are also linear combinations of the original features, but they capture the most remaining variance, with the constraint that they are uncorrelated (orthogonal) to the previous components. Each component captures a different “direction” of variability in the data, and they are all perpendicular to each other.

Geometric Interpretation of PCA

The principal component loading vectors define directions in the feature space.

• First Principal Component: Represents the direction along which the data points vary the most. It’s the line of best fit through the data, minimizing the squared distances from the points to the line.
• Second Principal Component: The direction, orthogonal (perpendicular) to the first, that captures the next most variance. And so on for subsequent components.

Geometric Interpretation of PCA (Visual)

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Example: USArrests Data

Let’s apply PCA to a real-world dataset: the USArrests dataset. This dataset contains crime statistics for each of the 50 US states.

• Features: Murder, Assault, UrbanPop, Rape (all measured per 100,000 residents).
• Goal: Visualize the data and identify patterns using PCA. We want to see if we can reduce these four crime variables down to a smaller number of “summary” variables.

USArrests Data: PCA Biplot - Image

First two principal components for the USArrests data.

USArrests Data: PCA Biplot - Explanation 1

This plot is called a biplot. It shows both the principal component scores (blue state names) and the principal component loadings (orange arrows). The scores represent the projection of each state onto the plane defined by the first two principal components.

USArrests Data: PCA Biplot - Explanation 2

The loadings (orange arrows) show the contribution of each original variable to the principal components. For example, the loading for Rape on the first component is 0.54, and on the second component is 0.17. The word Rape is centered at the point (0.54, 0.17). The length and direction of the arrows indicate the strength and direction of the relationship.

USArrests Data: PCA Biplot - Explanation 3

The axes are labeled as PC1 and PC2. Each point represents a state, and its position is determined by its scores on the two principal components. States closer together in this plot have similar crime profiles.

Interpreting the USArrests Biplot (Cont.)

• First Principal Component (PC1): This component places roughly equal weight on Murder, Assault, and Rape, with much less weight on UrbanPop. This suggests that PC1 primarily captures the overall level of violent crime. States with high scores on PC1 have high crime rates across these three categories.
• Second Principal Component (PC2): This component places most of its weight on UrbanPop, suggesting that it represents the degree of urbanization. States with high scores on PC2 are more urbanized.
• Correlation: The proximity of Murder, Assault, and Rape in the biplot indicates that these variables are positively correlated. UrbanPop is farther away, indicating it’s less correlated with the other three.

Interpreting the USArrests Biplot: Loading Table - Image

Interpreting the USArrests Biplot: Loading Table - Explanation 1

This table shows the numerical values of the loading vectors for each principal component. These numbers correspond to the lengths and directions of the arrows in the biplot.

Interpreting the USArrests Biplot: Loading Table - Explanation 2

States with large positive scores on PC1 (e.g., California, Nevada, Florida) have high crime rates, as indicated by the biplot and the large positive loadings for Murder, Assault, and Rape on PC1.

Interpreting the USArrests Biplot: Loading Table - Explanation 3

States with large positive scores on PC2 (e.g., California) have high urbanization, as indicated by the biplot and the large positive loading for UrbanPop on PC2.

Another Interpretation of PCA: Closest Linear Surfaces

PCA can also be understood as finding linear surfaces that are closest to the data points.

• First Principal Component: The line in p-dimensional space that is closest to the n observations (in terms of average squared Euclidean distance). It’s the best-fitting line in the sense of minimizing the sum of squared distances from the points to the line.
• First Two Principal Components: The plane that is closest to the observations. It’s the best-fitting plane in the same least-squares sense.
• And so on… For higher dimensions, PCA finds the best-fitting hyperplanes (generalizations of planes to higher dimensions).

Another Interpretation of PCA: Visual - Image

Ninety observations simulated in three dimensions.

Another Interpretation of PCA: Visual - Explanation (Left)

Left: The first two principal component directions (shown in green) span the plane that best fits the data. It’s like finding the “flattest” plane that passes through the cloud of points, minimizing the distances from the points to the plane.

Another Interpretation of PCA: Visual - Explanation (Right)

Right: The first two principal component score vectors give the coordinates of the projection of the 90 observations onto this plane. Projecting the data onto this plane gives us a lower-dimensional representation, capturing the most important aspects of the data’s variability.

Proportion of Variance Explained (PVE)

How much information do we lose when we project our data onto the first few principal components? The Proportion of Variance Explained (PVE) helps us answer this question. It quantifies the amount of information retained by each principal component.

Understanding PVE

• Total Variance: The sum of the variances of all the original features (assuming the features have been centered). This represents the total variability in the original dataset.
• Variance Explained by the m-th PC: The variance of the m-th principal component. This is the amount of variability captured by that single component.
• PVE of the m-th PC: The proportion of the total variance that is explained by the m-th principal component. It tells us how much information is retained by that component, expressed as a percentage of the total.

PVE Formula

PVE: USArrests Example (Visual) - Image

Scree plot and cumulative PVE plot for the USArrests data.

PVE: USArrests Example (Visual) - Explanation (Left)

Left: A scree plot, showing the PVE of each principal component. Each bar represents a principal component, and the height of the bar indicates the proportion of variance explained by that component.

PVE: USArrests Example (Visual) - Explanation (Right)

Right: The cumulative PVE. This plot shows the cumulative proportion of variance explained as we add more principal components. It helps us see how much variance is explained by the first few components together.

PVE: USArrests Example (Interpretation)

• PC1: Explains 62.0% of the variance in the data.
• PC2: Explains 24.7% of the variance.
• Together: PC1 and PC2 explain almost 87% of the total variance.

This means that the biplot (from earlier slides) provides a reasonably good two-dimensional summary of the data, capturing a large portion of its variability. The scree plot helps us decide how many components to keep. We often look for an “elbow” in the plot – a point where the PVE starts to drop off significantly. This suggests that adding further components adds little additional information.

Scaling the Variables: A Crucial Step

Before performing PCA, we usually scale the variables to have a standard deviation of one (also called standardization or z-scoring). This is a very important step in most cases!

Why Scale?

• Different Units/Variances: If variables are measured in different units (e.g., meters and kilograms) or have vastly different variances (e.g., one variable ranges from 0 to 1, another from 0 to 1000), the variables with the largest variances will dominate the principal components, regardless of whether they are actually the most important or informative.
• Equal Weight: Scaling prevents this by putting all variables on a “level playing field.” It ensures that each variable contributes equally to the principal components, based on its relative variability, not its absolute scale.

When Not to Scale

• Same Units: If variables are measured in the same units (e.g., gene expression levels measured using the same technology), and the differences in variance are scientifically meaningful, we might not want to scale. In this case, the differences in variance might reflect real biological differences.

Scaling: USArrests Example (Visual) - Image

Effect of scaling on the USArrests biplot.

Scaling: USArrests Example (Visual) - Explanation (Left)

Left: PCA with scaled variables (this is the same as the biplot we saw earlier). Notice that all variables contribute reasonably to PC1.

Scaling: USArrests Example (Visual) - Explanation (Right)

Right: PCA with unscaled variables. Notice how Assault dominates the first principal component in the unscaled version simply because it has the highest variance among the four variables. Scaling gives a more balanced representation, reflecting the relative importance of the variables.

How Many Principal Components to Use?

This is a common question, and unfortunately, there’s no single “magic number” that works for all datasets. The best approach depends on the specific context, the dataset, and the goals of the analysis.

Guidelines for Choosing the Number of Components

• Scree Plot: Look for an “elbow” in the scree plot – a point where the PVE drops off significantly. This suggests that adding more components beyond that point doesn’t provide much additional information.
• Interpretation: Keep enough components to capture the interesting patterns in the data. If you can interpret the first few components in a meaningful way, that’s a good sign.
• Ad Hoc: The process is inherently somewhat subjective and requires judgment.
• Supervised Learning: If PCA is used for pre-processing in a supervised learning context (e.g., Principal Components Regression), we can use cross-validation to select the optimal number of components. This involves trying different numbers of components and seeing which number leads to the best predictive performance on unseen data.

Clustering Methods: Finding Subgroups

Now, let’s move on to the second major type of unsupervised learning: clustering. Clustering aims to find subgroups (clusters) within a dataset, grouping observations that are similar to each other.

Clustering: The Goal

• Goal: Partition observations into groups (clusters) so that observations within a group are similar, and observations in different groups are dissimilar. It’s like sorting a collection of objects into meaningful categories based on their shared characteristics.
• Similarity: What does “similar” mean? This is a crucial, and often domain-specific, consideration. We need to define how we measure the similarity or dissimilarity between observations, and this choice can significantly affect the results.
• Unsupervised: We’re looking for structure without a predefined outcome or “correct answer.” We don’t know the “true” clusters beforehand.

K-Means Clustering: A Popular Choice

K-means clustering is a simple, widely used, and efficient clustering algorithm.

• Input: A dataset and a desired number of clusters, K.
• Output: Assigns each observation to exactly one of K clusters.
• Goal: Minimize the within-cluster variation. This means we want the observations within each cluster to be as close to each other as possible, forming tight, compact groups.

K-Means Clustering (Visual) - Image

K-means clustering results on simulated data.

K-Means Clustering (Visual) - Explanation (K=2)

This figure shows the results of applying K-means clustering with K=2 (two clusters). The color of each observation indicates the cluster to which it was assigned. The algorithm has separated the data into two distinct groups.

K-Means Clustering (Visual) - Explanation (K=3)

Here, K=3. The algorithm has identified three clusters. Notice how the cluster assignments change as we change the value of K.

K-Means Clustering (Visual) - Explanation (K=4)

With K=4, the data is further divided. The choice of K significantly impacts the resulting clusters.

The K-Means Algorithm (Local Optima)

K-Means: An Illustrative Example

graph LR
    A[Data] --> B(Step 1: Randomly Assign Clusters);
    B --> C(Iteration 1, Step 2a: Compute Centroids);
    C --> D(Iteration 1, Step 2b: Reassign Observations);
    D --> E(Iteration 2, Step 2a: Compute Centroids);
     E --> F(Iteration 2, Step 2b: Reassign Observations);
    F --> G(Continue Iterating Until Convergence);
    G --> H(Final Cluster Assignments);
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style H fill:#ccf,stroke:#333,stroke-width:4px

This flowchart illustrates the iterative nature of the K-means algorithm. The process continues until the cluster assignments no longer change, indicating that a local optimum has been reached.

K-Means Algorithm in Action - Image

Progress of the K-means algorithm.

K-Means Algorithm in Action - Explanation (First Row)

This figure shows the progress of the K-means algorithm over several iterations. The crosses represent the cluster centroids. The first row shows the random initialization of cluster assignments and the initial centroids.

K-Means Algorithm in Action - Explanation (Second Row)

The second row shows the state after the first iteration. The centroids have moved, and some observations have been reassigned to different clusters.

K-Means Algorithm in Action - Explanation (Third and Fourth Rows)

The third and fourth rows show further iterations. The algorithm continues to update the centroids and reassign observations until convergence.

K-Means: The Problem of Local Optima

Because K-means finds a local optimum, the results can vary depending on the initial random assignment of observations to clusters. Different starting points can lead to different final cluster assignments, and some solutions may be better (lower within-cluster variation) than others.

Dealing with Local Optima

• Recommendation: Run K-means multiple times with different initializations and choose the solution with the lowest within-cluster variation. This helps to mitigate the problem of getting stuck in a poor local optimum. It increases the chances of finding a good solution, although it doesn’t guarantee finding the global optimum.

K-Means: Local Optima (Visual) - Image

K-means clustering with different initializations.

K-Means: Local Optima (Visual) - Explanation 1

This figure shows K-means clustering performed six times on the same data, each with a different random initialization.

K-Means: Local Optima (Visual) - Explanation 2

Three different local optima were obtained. This highlights the variability in the results due to the random initialization.

K-Means: Local Optima (Visual) - Explanation 3

One of these local optima (bottom right) resulted in a better separation between the clusters. This emphasizes the importance of running K-means multiple times and comparing the results.

Hierarchical Clustering: A Different Approach

Hierarchical clustering offers an alternative to K-means, building a hierarchy of clusters. It provides a more nuanced view of the relationships between observations.

Advantages of Hierarchical Clustering

• No Need to Pre-specify K: Unlike K-means, we don’t need to pre-specify the number of clusters (K). We can choose the number of clusters after the algorithm has run by examining the resulting dendrogram. This provides more flexibility.
• Dendrogram: The output of hierarchical clustering is a dendrogram, a tree-like diagram that visually represents the hierarchy of clusters and the relationships between observations. It provides a visual summary of the clustering process.

Agglomerative Clustering (Bottom-Up)

• Agglomerative (Bottom-Up): We’ll focus on agglomerative clustering, which is the most common type of hierarchical clustering. It starts with each observation as its own cluster and successively merges the most similar clusters until only one cluster remains, building the hierarchy from the bottom up.

Hierarchical Clustering: Dendrogram - Image

Dendrogram of hierarchically clustering the data.

Hierarchical Clustering: Dendrogram - Explanation

This dendrogram visually represents the hierarchy of clusters. Each leaf represents an observation, and the branches show how clusters are merged.

Interpreting a Dendrogram

• Leaves: The leaves at the bottom of the dendrogram represent individual observations.
• Fusions: As you move up the tree, leaves and branches fuse together. These fusions represent the merging of similar clusters. Earlier fusions indicate greater similarity.
• Height of Fusion: The height at which two clusters fuse indicates their dissimilarity. Lower fusions mean the merged clusters are more similar. Higher fusions mean the clusters are more dissimilar. The height provides a measure of the distance between merged clusters.
• Cutting the Dendrogram: A horizontal cut across the dendrogram gives a specific number of clusters. The height of the cut determines the number of clusters obtained. This is how we can choose the number of clusters after running the algorithm.

Interpreting a Dendrogram (Visual) - Image

Interpreting a dendrogram.

Interpreting a Dendrogram (Visual) - Explanation (Left)

Left: A dendrogram generated using Euclidean distance and complete linkage. Observations 5 and 7 are quite similar, as indicated by the low height of their fusion. Observations 1 and 6 are also quite similar.

Interpreting a Dendrogram (Visual) - Explanation (Right)

Right: The raw data that was used to generate the dendrogram. This allows us to see how the dendrogram reflects the relationships in the original data. The dendrogram accurately captures the similarity between observations 5 and 7, and between observations 1 and 6.

The Key Question: Linkage

Linkage: Defining Inter-Cluster Dissimilarity

Linkage defines how we measure the dissimilarity between two groups of observations (clusters). It’s a crucial choice in hierarchical clustering. There are several different linkage methods:

Linkage Methods: A Table

Linkage: Recommendations

Choice of Dissimilarity Measure

In addition to choosing a linkage method, we also need to choose a dissimilarity measure between individual observations. This is the foundation upon which the clustering is built.

Common Dissimilarity Measures

• Euclidean Distance: The most common choice. Measures the straight-line distance between two points in the feature space: \[\sqrt{\sum_{j=1}^{p}(x_{ij} - x_{i'j})^2}\]. Suitable when features are continuous and on similar scales (or have been scaled).
• Correlation-Based Distance: Considers two observations to be similar if their features are highly correlated, even if their absolute values are far apart in terms of Euclidean distance. Useful when we’re interested in the shape of the feature profiles, rather than their magnitude. It’s calculated as 1 - correlation.

Dissimilarity Measures: An Example - Image

Euclidean vs. correlation-based distance.

Dissimilarity Measures: An Example - Explanation (Top)

The top panel shows three observations with two features. In terms of Euclidean distance, observations 1 and 3 are most similar, and observations 2 and 3 are most dissimilar.

Dissimilarity Measures: An Example - Explanation (Bottom)

The bottom panel shows the same observations, but now we consider correlation-based distance. Observations 1 and 2 have a perfect correlation of 1, so their correlation-based distance is 0. Observation 3 is negatively correlated with observations 1 and 2.

The choice of dissimilarity measure depends on the type of data and the scientific question being addressed. Euclidean distance focuses on the magnitude of differences, while correlation-based distance focuses on the pattern of changes across features.

Practical Issues in Clustering

Clustering, while powerful, comes with some practical challenges that require careful consideration.

• Scaling: Should we scale the variables before clustering? (Usually yes, for the same reasons as in PCA: to give equal weight to each variable and prevent variables with large variances from dominating the results.)
• Small Decisions, Big Consequences: Seemingly small choices, such as the dissimilarity measure, linkage method, and scaling, can have a substantial impact on the clustering results. There’s no single “correct” set of choices, and different choices can lead to very different clusters.
• Validating Clusters: It’s difficult to definitively know if the clusters found are real and meaningful, or just an artifact of the clustering process. There’s no “ground truth” to compare against in most unsupervised learning scenarios.
• Robustness: Clustering methods are often not very robust. Small changes in the data (e.g., adding or removing a few observations) can lead to significantly different cluster assignments.

Clustering: Recommendations and Cautions

Recommendations:

• Experiment: Try different choices of dissimilarity measure, linkage (for hierarchical clustering), and scaling. Don’t rely on a single clustering result.
• Consistency: Look for consistent patterns across different clustering results. If different methods produce similar clusters, this increases confidence in the findings.
• Domain Knowledge: Use domain knowledge to assess the plausibility and interpretability of the clusters. Do the clusters make sense in the context of the problem?

Caution: Clustering should be viewed as a starting point for further investigation, not as the final answer. It’s an exploratory technique that can generate hypotheses, but these hypotheses should be validated using other methods or domain knowledge. Don’t over-interpret clustering results.

Data Mining, Machine Learning and Statistical Learning

graph LR
    A[Data Mining] --> C(Common Ground)
    B[Machine Learning] --> C
    D[Statistical Learning] --> C
    C --> E[Insights & Predictions]
    style A fill:#ccf,stroke:#333,stroke-width:2px
    style B fill:#ccf,stroke:#333,stroke-width:2px
    style D fill:#ccf,stroke:#333,stroke-width:2px
     style C fill:#f9f,stroke:#333,stroke-width:4px
      style E fill:#ccf,stroke:#333,stroke-width:4px

• Data Mining: Focuses on discovering patterns, anomalies, and insights from large datasets, often using techniques from both machine learning and statistical learning.
• Machine Learning: Emphasizes the development of algorithms that can learn from data and make predictions without explicit programming.
• Statistical Learning: A subfield of statistics that focuses on developing and understanding models and methods for learning from data, with a strong emphasis on statistical inference and uncertainty quantification.

All three fields share the common goal of extracting knowledge and making predictions from data, but they differ in their emphasis and approaches.

Summary

• Unsupervised learning is about finding patterns and structure in data without a response variable (no “teacher” to guide the learning). It’s about discovering hidden relationships.
• PCA reduces dimensionality by finding linear combinations of features (principal components) that capture the most variance. It’s useful for visualization and pre-processing data for other analyses.
• Clustering aims to find subgroups (clusters) within the data, grouping similar observations together.
  • K-means requires pre-specifying the number of clusters (K). It’s an iterative algorithm that minimizes within-cluster variation. It’s sensitive to initialization.
  • Hierarchical clustering builds a hierarchy of clusters, represented by a dendrogram. It doesn’t require pre-specifying K, and it provides a visual representation of the relationships between observations.
• Choices of dissimilarity measure, linkage (for hierarchical clustering), and scaling can significantly affect clustering results. These choices should be made carefully and thoughtfully.
• Clustering is a powerful, but often subjective and non-robust, technique. It’s best used for exploration and hypothesis generation, not for definitive conclusions. Always consider the limitations.

Thoughts and Discussion

• Can you think of other real-world applications where unsupervised learning might be useful? Consider areas like image analysis (grouping similar images), anomaly detection (identifying unusual transactions), or natural language processing (clustering documents by topic).
• What are the potential limitations of relying too heavily on clustering results without further validation? How could you try to validate the clusters you find? (e.g., using external data, domain expertise, or comparing results across different methods).
• How might you combine supervised and unsupervised learning techniques in a single analysis? For example, could you use clustering to identify subgroups and then build separate supervised models for each subgroup (this is called “cluster-then-predict”)? Or could you use PCA to reduce dimensionality before applying a supervised learning algorithm?
• How do you understand the differences and connections between data mining, machine learning, and statistical learning? Can you give examples of techniques used in each field?
• What is the biggest difference do you think supervised and unsupervised learning?