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The following relationship can be seen between spectral entropy and clustering:
A large eigenvalue indicates the variance of the data in the corresponding direction.
On the other hand, a large spectral entropy indicates that the variance is spread fairly evenly across multiple directions.
Conversely, a small spectral entropy indicates that a few directions dominate.
In the impact on clustering, when entropy is high, data spreads in many directions, making clustering difficult.
Conversely, when entropy is low, data tends to concentrate in a specific direction, making cluster boundaries clearer and making clustering easier.
In other words, the spectral entropy of the covariance matrix measures the diversity of the spread of the data and evaluates the clarity of the clusters.
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IEEE/ICACT20260379 Slide.15
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