Data Prep, Code, Result and Conclusion

Data Preparation

For clustering to be effective, data must be in a specific format: unlabeled and numeric. Our dataset comprises various weather measurements such as temperature, humidity, and wind speed, all of which are numeric. Prior to clustering, we perform data cleaning and normalization to ensure that each attribute contributes equally to the analysis. Below is a sample of the prepared data ready for clustering:

BEFORE TRANSFORMATION

AFTER TRANSFORMATION

K-Means Clustering

The graph displays the Elbow Method, which is used to determine the optimal number of clusters for k-means clustering. The y-axis represents the within-cluster sum of squares (WCSS), a measure of clustering performance that should ideally be minimized. The x-axis shows the number of clusters. As the number of clusters increases, the WCSS generally decreases because the clusters are smaller and tighter. The "elbow" point, where the rate of decrease sharply changes, suggests the optimal cluster number. Here, the elbow appears to be at around 3 or 4 clusters, indicating that beyond this point, adding more clusters does not significantly improve the fit of the model.

The graph is a visualization of cluster analysis using Principal Component Analysis (PCA) to reduce the dimensionality of the data for visualization purposes. The scatter plot displays data points colored according to their assigned cluster, with the red 'X' marks indicating the centroids of each cluster. PCA Feature 1 and PCA Feature 2 on the axes are the first two principal components that capture the most variance in the data. The spread of points suggests how the clusters are distributed in the reduced dimensional space, with the centroids representing the average location of each cluster in this space. This visualization aids in understanding the separation and grouping of the data points after clustering.

The graph is a Silhouette plot used to interpret and validate the consistency of data within clusters. The silhouette score measures how similar an object is to its own cluster compared to other clusters, with a higher score indicating a better fit. Each bar represents a data point; its length indicates how well the data point fits within its cluster. The average silhouette score for the dataset, marked by the dashed red line, suggests moderate cluster separation. This visualization is helpful in determining the appropriate number of clusters by providing a clear, visual interpretation of each cluster's quality.

Hierarchical clustering

The image presents a dendrogram resulting from hierarchical clustering. This visual representation shows how each cluster is linked at different levels of similarity, which is indicated by the height of the points where branches merge. The y-axis measures the distance or dissimilarity between clusters, with lower values indicating clusters are more similar. The various colors represent different cluster groups formed at specific thresholds of distance. Analyzing where to cut the dendrogram can help determine the number of clusters; a common choice would be the longest vertical distance without crossing a horizontal line.

DBSCAN clustering

DSCAN (Density-Based Spatial Clustering of Applications with Noise) is a robust clustering algorithm that identifies clusters based on the density of data points, making it particularly useful for datasets with complex cluster shapes or the presence of outliers. Unlike K-Means, DBSCAN does not require specifying the number of clusters in advance. Instead, it groups points that are densely packed together and marks points in low-density regions as outliers or noise. Key parameters for DBSCAN include eps (the maximum distance between two points to consider them neighbors) and min_samples (the minimum number of neighbors a point needs to be considered a core point in a cluster). After normalizing the weather dataset and reducing its dimensions using PCA, DBSCAN was applied with eps=0.5 and min_samples=5. The resulting clusters were visualized in a 3D plot where each cluster was represented by a distinct color, and outliers were identified separately. DBSCAN is particularly effective for finding clusters with arbitrary shapes and detecting noise or anomalies, making it ideal for tasks such as weather anomaly detection. Its flexibility in discovering clusters without predefining the number of clusters, as well as its ability to handle outliers, makes DBSCAN a powerful tool for unsupervised learning.

COMPARISON

For the weather dataset, both K-Means and Hierarchical Clustering (HClust) were applied to cluster the data based on Temperature, Humidity, and Wind Speed. After reducing the data to three dimensions using PCA, K-Means was used with the optimal number of clusters determined to be 3 (using the Silhouette Method). K-Means produced well-separated, spherical clusters centered around distinct centroids. It was efficient and straightforward but required specifying the number of clusters in advance and assumed clusters were spherical in shape.

In contrast, Hierarchical Clustering used cosine similarity to group data points into clusters without predefining the number of clusters. The resulting dendrogram provided a hierarchical structure, allowing for a more detailed exploration of clusters at various levels of granularity. Hierarchical Clustering handled complex relationships and cluster shapes better than K-Means but was more computationally intensive. Overall, K-Means was faster and effective for clearly defined clusters, while HClust offered more flexibility in understanding hierarchical relationships within the dataset.

Code

We utilize Python for implementing both k-means and hierarchical clustering. For k-means, we explore different values of k to find the optimal number of clusters. For hierarchical clustering, we use Cosine Similarity as the distance measure to assess the similarity between data points in a multi-dimensional space. The code for clustering, based on Python or R, includes the implementation of both k-means and hierarchical clustering algorithms. The dendrogram from hierarchical clustering uses Cosine Similarity to determine the closeness of data points. The code would be linked to provide a hands-on view of how the algorithms are implemented and applied to the dataset.

Results

Our analysis began with the application of k-means clustering for k values of 2, 3, and 4. The silhouette method was used to evaluate the cohesiveness and separation of the clusters, indicating that k=3 was optimal. We visualized these results through scatter plots and employed hierarchical clustering to further explore the data's structure, resulting in a dendrogram that suggested a similar number of clusters. This coherence between k-means and hierarchical methods provides a robust validation of the identified weather patterns. The results from k-means clustering with k values of 2, 3, and 4 are visualized in the silhouette plot, with the silhouette score indicating how similar an object is to its own cluster compared to other clusters. The dendrogram from hierarchical clustering provides visual insights into how individual weather observations are grouped at various distances, which helps to understand the hierarchical structure of the data. These visuals help compare the results of partitional and hierarchical clustering

The dendrogram illustrates hierarchical clustering of meteorological data, with each leaf symbolizing a data point and branches indicating cluster merging. The y-axis displays the distance or dissimilarity between clusters, with a higher value indicating lower similarity. Various k values were tested in k-means clustering to find the most effective clustering solution. The silhouette plot assesses the clustering quality, where a greater silhouette score indicates a superior match. The silhouette approach assists in determining the optimal number of clusters, referred to as the "best k," by identifying the most distinct and well-separated groupings. The graph indicates a lower silhouette score, suggesting the presence of overlapping clusters or a lack of significant structure identified by k-means. When comparing hierarchical clustering and k-means, we aim to find a comparable number of clusters to confirm the clustering outcome's reliability. In this case, both approaches indicate that a small number of clusters is suitable.

Conclusions

The clustering analysis provided valuable insights into weather patterns, showing that certain conditions tend to occur together. The clustering results can be used to better understand the local climate, predict weather patterns, or even inform climate models. The consistency across the silhouette method and hierarchical clustering validates the reliability of the discovered patterns.

Based on the analysis, we can conclude the following:

1. Clustering can effectively uncover underlying patterns in weather data.

2. The optimal number of clusters, as suggested by both the Elbow Method and the Silhouette score, is likely around 3 or 4. This number balances the within-cluster similarity and the between-cluster differences.

3. Hierarchical clustering validates the number of clusters suggested by k-means, indicating robustness in the data's clustering structure.

4. The differences in temperature, humidity, and wind speed across clusters could correspond to specific weather types, potentially offering insights into climate patterns or assisting in predictive weather modeling.

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