Positive semi-definite embedding for dimensionality reduction

This is the code associated to the following paper:

Michaël Fanuel, Antoine Aspeel, Jean-Charles Delvenne, Johan A.K. Suykens, Positive semi-definite embedding for dimensionality reduction and out-of-sample extensions, published in SIAM journal on mathematics for data science, https://arxiv.org/abs/1711.07271

Datasets

• The HTRU dataset was preprocessed and saved in .mat format. It is available in the Data folder.
• For the MNIST data, please download in the Data folder the following files:
  • train-images-idx3-ubyte.gz
  • train-labels-idx1-ubyte.gz
  • t10k-images-idx3-ubyte.gz
  • t10k-labels-idx1-ubyte.gz

Running demos

In the Demos folder, you can run the following scripts:

• interval_oos.m (Fig. 2 and Fig. 3)
• MNIST_embed_45.m (Fig. 4)
• wine_embed.m (Fig. 5)
• quasar_embed_classifier.m (Fig. 6)
• two_moons_plots.m (Fig. 7)
• two_moons_benchmark.m(Fig. 8)

Note that the eigenvalue decomposition of the diffusion embedding in two_moons_benchmark.m may fail to converge for a very small kernel bandwidth.

Dependencies

• MATLAB R2019b
• Statistics and Machine Learning Toolbox