A broad benchmark of intrinsic dimension estimators shows that no single method or set of hyperparameters works across datasets, and tuned benchmark scores frequently indicate overfitting rather than transferable accuracy.
A Novel Approach for Intrinsic Dimension Estimation
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abstract
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality. Finding the nearly optimal representation of the dataset in a lower-dimensional space (i.e. dimensionality reduction) offers an applicable mechanism for improving the success of machine learning tasks. However, estimating the required data dimension for the nearly optimal representation (intrinsic dimension) can be very costly, particularly if one deals with big data. We propose a highly efficient and robust intrinsic dimension estimation approach that only relies on matrix-vector products for dimensionality reduction methods. An experimental study is also conducted to compare the performance of proposed method with state of the art approaches.
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A Survey of Dimension Estimation Methods
A broad benchmark of intrinsic dimension estimators shows that no single method or set of hyperparameters works across datasets, and tuned benchmark scores frequently indicate overfitting rather than transferable accuracy.