KMeans Clustering

Evaluating the Quality of Clustering

Once the K-means algorithm has converged, the quality of the clustering solution can be evaluated using various metrics, such as the sum of squared distances between each point and its assigned centroid. This metric is called the within-cluster sum of squares (WCSS). The lower the WCSS, the better the clustering solution. However, it's important to note that a low WCSS does not necessarily mean a good clustering solution, as the algorithm may have converged to a local minimum rather than the global minimum.

Limitations of K-means

K-means is a simple and computationally efficient algorithm, but it does have some limitations. One limitation is that it is sensitive to the initial choice of centroids. If the initial centroids are chosen poorly, the algorithm may converge to a suboptimal clustering solution. Another limitation is that K-means tends to converge to local optima rather than the global optimum, which may not be the best clustering solution. Various modifications and extensions to the algorithm have been proposed to address these issues, such as k-means++, which uses a smarter initialization scheme to choose the initial centroids.

Leveraging KMeans for Chicago Crime

The Chicago crime dataset covers the years 2001 through 2021 and is packed with information regarding criminal acts committed in the city. This includes the nature of the crime, when and where it took place, and more. The unsupervised machine learning approach known as K-means clustering may be used to organize data into coherent groups of comparable elements. Using K-means clustering to the Chicago crime dataset may help authorities see trends and patterns that can guide their work.

Loading and preprocessing the data is the initial stage in applying K-means clustering to the Chicago crime dataset. To prepare the data for clustering, you must first import it into a pandas DataFrame. In certain cases, this may need data cleaning, which includes the elimination of duplicates and missing values, the transformation of category variables into numerical ones, and the application of appropriate scale.

Data clustering is the next phase, and the number of clusters is up to you. A multitude of techniques, such as the elbow approach and silhouette analysis, may be used to zero down on the best number of clusters. To determine the optimal value of K, one may plot the within-cluster sum of squares (WCSS) vs the number of clusters and choose the point at which the WCSS decreases at a slower pace.

After the number of clusters has been decided upon, a distance metric must be selected in order to determine how closely individual data points relate to cluster centers. Although Euclidean distance is the most popular, alternative distance measures like Manhattan distance, cosine similarity, or Mahalanobis distance may be more appropriate for your data.

K-means clustering may be applied to the cleaned data with the specified number of clusters and distance metric. The scikit-learn package offers a Python version of the K-means clustering method. Besides the maximum number of iterations and the convergence tolerance level, you may choose a variety of additional hyperparameters.

When you've clustered your data, it's important to assess whether or not the resulting insights are meaningful and helpful. Scatter plots or heat maps may be used to visualize the clusters, and then their individual properties, such as the distribution of crime categories or the location of crimes, can be analyzed. K-means clustering's efficacy may be verified by comparing its findings to those of other clustering methods or with domain expertise.

Data Prepreparation

Kmeans For Spatial Clustering: Inorder to use the Spatial Data in the Crime Dataset with a characterization, the demographic/socio-economic dataset is used to Categorize Community Areas into Three Categories namely, Low Income, Moderate Income and High Income. These are now the Labels for the Dataset which are to be clustered together using Kmeans Clustering.

Data for 2-Dimensional KMeans ( Spatial Clustering )

KMeans Clustering on the Above Data

KMeans with Initial Clusters = 3

Using Starting with 3 Clusters because the dataset has the ground-truth pre-known. The 3 labels are categorized demographic status according to the community area. The labels are Low Income, Moderate Income and High Income. 

KMeans with Initial Clusters = 2

KMeans with Initial Clusters = 4

Data for 3-Dimensional KMeans

Results and Discussion for 3 Dimensional Clustering

In this analysis, Ward, District, and IUCR codes were used in K-means clustering on the Chicago Crime dataset. The term "ecosystem" refers to a group of people who work in the construction industry. We noticed a distinct divergence between clusters 0 and 2 based on the three-dimensional charts. Clusters 1 and 2 looked to be forced clusters that were split apart by K-means according to the threshold.

The analysis's findings imply that K-means clustering with a k value of 3 would be the best option for this dataset since it creates clear distinctions between the various groups. In example, the obvious distinction between clusters 0 and 2 shows that the crime patterns of these two groups vary significantly, but the forced distinction between clusters 1 and 2 suggests that these clusters may not be sufficiently dissimilar to warrant their distinction.

K-means clustering does, however, have limits, especially when the underlying data is complicated or the clusters have erratic sizes or forms. To validate the ideal number of clusters and assess the quality of individual clusters, it is advised to utilize K-means clustering in combination with other clustering validation approaches, such as the Silhouette method.

Data for n-Dimensional KMeans

Inference for the above

In the above n-dimensional Kmeans, the data is aggregated as counts for Crime Type in each hour of the day. In this case the clusters labels are the crime types which is greater than 3 dimensions so visually cannot be perceived to check if the clusters are performed correctly. Principal Component Analysis on the data is performed to visualise the clusters on a 2-Dimensional Plane. Looking at the plot, it is evident that the model has performed decently enough to produce some separation in the data points. The far right clusters are correctly aggregated as separate clusters because they doesn't have a closer neighbour. Rest of the plots seems to have clear centroids and the data points around them.

Conclusion

In conclusion, while K-means clustering can be a useful technique for identifying patterns and relationships in the Chicago Crime dataset, it may only be partially helpful due to the lack of data points that fit the conditions required for clustering. In particular, clustering requires that data points are similar to each other within clusters and different from data points in other clusters. However, in the case of the Chicago Crime dataset, there are no such variables that have a greater spread so that KMeans can be performed at optimum efficiency. 

Furthermore, K-means clustering may not always be the best choice for analyzing crime patterns in the city, as it may not account for the nuances and complexities of crime data, such as differences in crime patterns within individual Wards or the unique characteristics and challenges of different communities within a given district.

Therefore, while K-means clustering can provide some insights into crime patterns in the Chicago Crime dataset, it should be used with caution and in conjunction with other clustering validation techniques, such as the Silhouette method or hierarchical clustering, to ensure that the resulting clusters are meaningful and can be used to inform policy decisions and improve crime prevention strategies in the future. Additionally, it is important to carefully consider the variables used for clustering and to include relevant variables that provide a more comprehensive and nuanced understanding of crime patterns in the city.