Which data visualization approach will MOST accurately determine the optimal value of k?
Calculate the principal component analysis (PCA) components. Run the k-means clustering algorithm for a range of k by using only the first two PCA components. For each value of k, create a scatter plot with a different color for each cluster. The optimal value of k is the value where the clusters start to look reasonably separated.
Calculate the principal component analysis (PCA) components. Create a line plot of the number of components against the explained variance. The optimal value of k is the number of PCA components after which the curve starts decreasing in a linear fashion.
Create a t-distributed stochastic neighbor embedding (t-SNE) plot for a range of perplexity values. The optimal value of k is the value of perplexity, where the clusters start to look reasonably separated.
Run the k-means clustering algorithm for a range of k. For each value of k, calculate the sum of squared errors (SSE). Plot a line chart of the SSE for each value of k. The optimal value of k is the point after which the curve starts decreasing in a linear fashion.
Explanations:
PCA is a dimensionality reduction technique, but it may not always capture the optimal cluster structure. Using only the first two PCA components may not fully represent the data’s complexity, and the clustering may not be accurate.
The optimal value of k is not determined by the explained variance of PCA components, but by the behavior of the clustering algorithm’s performance (e.g., SSE). PCA doesn’t directly give information about k.
t-SNE is a technique for visualization and does not help determine the optimal number of clusters. It focuses on preserving pairwise distances, but it is not used to find the best value of k in clustering.
The sum of squared errors (SSE) plot is a standard method for determining the optimal k. The “elbow method” identifies the point where adding more clusters results in only a marginal improvement, indicating the optimal k.
I opine that the answer is:
Run the k-means clustering algorithm for a range of k. For each value of k, calculate the sum of squared errors (SSE). Plot a line chart of the SSE for each value of k. The optimal value of k is the point after which the curve starts decreasing in a linear fashion.