On the Use of Bagging for Local Intrinsic Dimensionality Estimation
This work addresses a specific bottleneck in data mining and machine learning for more accurate local complexity characterization, representing an incremental improvement.
The paper tackles the problem of high variance in Local Intrinsic Dimensionality (LID) estimation due to limited data in small neighborhoods by proposing an ensemble approach using subbagging, which significantly reduces variance and mean squared error with controllable bias in broad hyper-parameter regions.
The theory of Local Intrinsic Dimensionality (LID) has become a valuable tool for characterizing local complexity within and across data manifolds, supporting a range of data mining and machine learning tasks. Accurate LID estimation requires samples drawn from small neighborhoods around each query to avoid biases from nonlocal effects and potential manifold mixing, yet limited data within such neighborhoods tends to cause high estimation variance. As a variance reduction strategy, we propose an ensemble approach that uses subbagging to preserve the local distribution of nearest neighbor (NN) distances. The main challenge is that the uniform reduction in total sample size within each subsample increases the proximity threshold for finding a fixed number k of NNs around the query. As a result, in the specific context of LID estimation, the sampling rate has an additional, complex interplay with the neighborhood size, where both combined determine the sample size as well as the locality and resolution considered for estimation. We analyze both theoretically and experimentally how the choice of the sampling rate and the k-NN size used for LID estimation, alongside the ensemble size, affects performance, enabling informed prior selection of these hyper-parameters depending on application-based preferences. Our results indicate that within broad and well-characterized regions of the hyper-parameters space, using a bagged estimator will most often significantly reduce variance as well as the mean squared error when compared to the corresponding non-bagged baseline, with controllable impact on bias. We additionally propose and evaluate different ways of combining bagging with neighborhood smoothing for substantial further improvements on LID estimation performance.