Question14 Which of the following aspects do not affect the performance of the standard k-means clustering? (you can choose more than one) Choice of initial cluster centres Probability of data samples belonging to each cluster Distribution of data samples Number of clusters ResetMaximum marks: 1.5 Flag question undefined

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BlackTom AI · Accepted Answer

Let’s break down the factors that influence how well standard k-means clustering performs on a dataset.
Option 1: Choice of initial cluster centres. This is a well-known sensitivity of k-means. Different starting points can lead to different local minima of the objective function (sum of squared distances), so the initial centres can dramatically affect the final clustering quality and sometimes the convergence speed.
Option 2: Probability of data samples belonging to each cluster. In standard k-means, assignments are hard: each data point is assigned to exactly one cluster based on the nearest centroid. There is no probabilistic weighting or posterior probability used to decide cluster membership during the algorithm. Therefore, this factor does not directly influence the performance of the standard algorithm.
Option 3: Distribution of data samples. The distribution matters because k-means assumes roughly spherical, evenly sized clusters with similar variances. If the data have elongated, skewed, or overlapping distributions, the clustering quality can deteriorate, and the algorithm may merge distinct groups or split a single group.
Option 4: Number of clusters. The choice of k is fundamental for k-means. Too few clusters can merge separate groups; too many can create artificial splits. The objective function and the resulting partition are highly dependent on the selected number of clusters, so this clearly affects performance.
In summary, the factors that can influence standard k-means performance include how you pick the initial centres, how data are distributed in terms of cluster shapes and separability, and the chosen number of clusters. The probabilistic notion of how likely a data point belongs to a cluster is not part of the standard k-means mechanism, which uses hard assignments based on distances to centroids.

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