Nonlinear Dimensionality Compression Algorithm

A Nonlinear Dimensionality Compression Algorithm is a dimensionality reduction algorithm that uses a non-linear model (to solve a dimensionality reduction task).

• Example(s):
  • Non-Linear Independent Component Analysis.
  • Non-Linear Principal Component Analysis.
  • Multidimensional Scaling.
  • Non-metric MDS.
  • Locally-Linear Embedding.
  • Isomap.
  • a Manifold Dimensionality Compression Algorithm, such as Laplacian Eigenmaps.
  • …
• Counter-Example(s):
  • a Linear Dimensionality Reduction Algorithm.
• See: Principal Curves, Pairwise Distance Algorithm, Sammon Projection, Manifold Learning Algorithm, t-Distributed Stochastic Neighbor Embedding (t-SNE) Algorithm.

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References

2011

• http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction
  • High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension then the data can be visualised in the low dimensional space.
    Below is a summary of some of the important algorithms from the history of manifold learning and nonlinear dimensionality reduction. Many of these non-linear dimensionality reduction methods are related to the linear methods listed below. Non-linear methods can be broadly classified into two groups: those that provide a mapping (either from the high dimensional space to the low dimensional embedding or vice versa), and those that just give a visualisation. In the context of machine learning, mapping methods may be viewed as a preliminary feature extraction step, after which pattern recognition algorithms are applied. Typically those that just give a visualisation are based on proximity data - that is, distance measurements.

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