LECTURE 10

Summary

This lecture introduces unsupervised learning and covers three related topics in earth observation: clustering, dimensionality reduction, and unsupervised change detection. It concludes the course’s introductory weeks and previews a later move to CNN-based deep learning.

1. Unsupervised Learning

Unsupervised learning seeks useful structure in data without class labels or other supervision. Its central tasks include:

• Clustering: Grouping similar samples and separating dissimilar ones.
• Dimensionality reduction: Representing data with fewer features while retaining important information.
• Density or distribution estimation: Inferring the probability distribution that may have generated the data.

These ideas remain relevant in deep learning, including through self-supervised learning and generative methods. In remote sensing, unsupervised methods can help analyze or segment imagery when annotated examples are unavailable. The lecturer mentions a 2004 example involving self-organizing maps and k-means.

2. K-Means Clustering

K-means divides unlabeled data into a chosen number, (K), of clusters. Each sample is assigned to the cluster whose center is nearest, with similarity determined by the selected features and distance measure.

Basic Procedure

1. Choose the number of clusters, (K).
2. Initialize (K) cluster centers (centroids), often randomly.
3. Assign each data point to its nearest centroid.
4. Recompute each centroid as the mean of the points assigned to that cluster.
5. Repeat the assignment and centroid-update steps until a stopping condition is met.

The process resembles repeatedly forming teams and updating who best represents each team. A centroid is a calculated mean and need not be an actual data point.

Stopping Conditions

• Cluster assignments stop changing or change very little.
• Centroids move by less than a chosen amount.
• A maximum number of iterations is reached.

Objective and Practical Considerations

• K-means seeks to reduce the within-cluster sum of squares.
• Its alternating assignment-and-update procedure does not increase the objective at each iteration, but it can converge to a local optimum.
• Results can depend strongly on initialization; poor starting centroids may produce a poor solution.
• One way to choose (K) is to plot the objective against different values of (K) and look for an elbow, where the reduction in objective begins to level off.

The lecture describes k-means++ initialization:

1. Choose one centroid at random.
2. Compute each point’s distance to its nearest selected centroid.
3. Give points farther from existing centroids a higher probability of being selected next.
4. Repeat until (K) centroids have been chosen.

A brief Python example uses scikit-learn to cluster synthetic data generated from three distributions.

3. Principal Component Analysis (PCA)

PCA reduces high-dimensional data while retaining as much of its important variation as possible. This is useful when data contain redundant or correlated features, and when high dimensionality increases computational cost. The lecturer highlights hyperspectral imagery as one relevant case.

PCA Procedure

1. Compute the data mean and subtract it from each sample to center the data.
2. Arrange the centered samples in a data matrix.
3. Compute the covariance matrix.
4. Perform eigenvalue decomposition of the covariance matrix.
5. Select the top (K) eigenvectors to form a projection matrix.
6. Project each sample into the reduced space.

The first principal component captures the greatest possible variance. Each subsequent component captures as much remaining variance as possible while being orthogonal to the earlier components.

As an example, the lecture considers combining repeated multispectral and hyperspectral observations. Because hyperspectral images may contribute many more channels, PCA could reduce their dimensionality so they can be used more manageably alongside multispectral data. The appropriate reduction and subsequent classifier depend on the analysis; the lecture presents this as a question to consider rather than prescribing one answer.

4. Unsupervised Change Detection

Change detection is an important earth-observation task. Before deep learning, unsupervised approaches were often preferred because labeled examples could be difficult to obtain. The lecture previews classical techniques and notes that later course material will treat change detection in more depth.

Change Vector Analysis (CVA)

• Compare pixel vectors from two dates.
• Compute a change vector from the difference between the two temporal vectors.
• Use the vector’s magnitude to indicate how much change occurred; its direction can provide information about the type of change.
• For binary change detection, threshold the magnitude:
  • Above the threshold: classify the pixel as changed.
  • Below the threshold: classify the pixel as unchanged.

Extensions

• Robust CVA: Addresses possible misregistration between pre-change and post-change images. Instead of comparing only corresponding pixels, it compares a pixel with pixels in a local neighborhood of the other image.
• Object-based change detection: Uses image objects rather than relying only on pixel-by-pixel comparisons. A simple object representation is a superpixel, a relatively homogeneous image region. The method can compare average spectral values or features extracted from corresponding superpixels.
• Partial Change Vector Analysis: Extends the object-based idea by representing a location with features from superpixels at multiple scales. These multiscale features can be combined, compared between dates, and used to calculate change magnitude.

The discussion emphasizes that multiscale information is important in image analysis and connects these classical approaches to ideas used in later deep-learning methods.

Speakers and Sources

• Speaker: One lecturer welcomes the class, explains the material, and gives the examples. The subtitles do not provide the lecturer’s name.
• Other voices: No other speakers are identifiable in the subtitles.
• Sources and tools mentioned: A 2004 remote-sensing segmentation work (not named in the subtitles) and scikit-learn, which provides the k-means implementation used in the example.