Choosing Techniques and Limitations

As with dimensionality reduction techniques themselves, there is no gold standard intrinsic dimensionality estimator. Instead, questions need to be asked prior to using an intrinsic dimensionality estimator so as to help the user gain a meaningful and useful result. 

As such, care should be taken when seeking to embed a dataset into higher dimensions. The performance of spectral dimensionality reduction methods, and in fact nonlinear dimensionality reduction methods in general, is called into question in such cases. 

This chapter has briefly outlined various approaches to estimating intrinsic dimensionality of a dataset. There is an attractiveness in using an intrinsic dimensionality estimation that comes as part of a spectral dimensionality reduction algorithm (as shown in Sect. 4.2. However, this may not always be available as many algorithms 

Murase, H. Columbia Object Image Library (COIL-20). Tech, rep., Technical Report CUCS-005-96. (1996) 

Strange, H., Zwiggelaar, R. Classification performance related to intrinsic dimensionality in mammographic image analysis. In Proceedings of the Thirteenth Annual Conference on Medical Image Understanding and Analysis, pp. 219-223 (2009) 

---