Manifold Learning

Manifold learning looks at ways to automatically extract meaningful features, dimensions or subspaces from data in order to build better models, expand data, reduce data, etc.

Manifold Learning and Dimensionality Reduction are vast areas of study in the Math and Computer Science fields. The task is quite simply to find ways to extact the essential nature out of a dataset. looks at ways to automatically extract meaningful features, dimensions or subspaces from data in order to build better models, expand data, reduce data, etc.

The recent focus on Deep Learning seems to raise the question whether dedicated research on Manifold Learning and Dimensionality Reduction are still required as their own pursuit since some form of Encoder-Decoder neural network could always be devised as a replacement. While such systems work well, there is also certainly a role to be played by interpretable models built on solid statistical concepts.

Extraction of lower-dimensional representations of data can allow more compact storage or transmission and also improve the performance of other ML tasks such as classification and regres_sion, as the more compact representation must necessarily encode the most important relationships to maintain accuracy.

This is an exciting group of work which has published in several good conferences so far (Ghojogh et al., 2020)-(Ghojogh et al., 2020),(Ghojogh et al., 2019)-(Ghojogh et al., 2019), and in particular (Ghojogh & Crowley, 2018):

Ghojogh, B., & Crowley, M. (2018). Principal Sample Analysis for Data Reduction. 2018 IEEE International Conference on Big Knowledge (ICBK), 350–357.

This work has culiminated recently in the completion of my first Doctoral student, Benyamin Ghojogh, in April 2021 with his thesis encompassing many of these advances. Dr. Ghojogh continues as a postdoc now with my lab and we have an approved book deal with Springer for a textbook due out later in 2021 on “Manifold Learning and Dimensionality Reduction” which we are writing in collaboration with Prof. Ali Gosi andd Prof. Fakhri Karray.

Our Papers on Manifold Learning

  1. Acceleration of Large Margin Metric Learning for Nearest Neighbor Classification Using Triplet Mining and Stratified Sampling
    Poorheravi, Parisa, Ghojogh, Benyamin, Gaudet, Vincent, Karray, Fakhri, and Crowley, Mark
    Journal of Computational Vision and Imaging Systems 2021
  2. Generative Locally Linear Embedding
    Ghojogh, Benyamin, Ghodsi, Ali, Karray, Fakhri, and Crowley, Mark
    2021
  3. Batch-Incremental Triplet Sampling for Training Triplet Networks Using Bayesian Updating Theorem
    Sikaroudi, Milad, Ghojogh, Benyamin, Karray, Fakhri, Crowley, Mark, and Tizhoosh, H. R.
    In 25th International Conference on Pattern Recognition (ICPR) 2021
  4. QQE
    Quantile–Quantile Embedding for distribution transformation and manifold embedding with ability to choose the embedding distribution
    Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark
    Machine Learning with Applications (MLWA) 2021
  5. Weighted Fisher Discriminant Analysis in the Input and Feature Spaces
    Ghojogh, Benyamin, Sikaroudi, Milad, Tizhoosh, H.R., Karray, Fakhri, and Crowley, Mark
    In International Conference on Image Analysis and Recognition (ICIAR-2020) 2020
  6. Theoretical Insights into the Use of Structural Similarity Index In Generative Models and Inferential Autoencoders
    Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark
    In International Conference on Image Analysis and Recognition (ICIAR-2020) 2020
  7. Generalized Subspace Learning by Roweis Discriminant Analysis
    Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark
    In International Conference on Image Analysis and Recognition (ICIAR-2020) 2020
  8. Instance Ranking and Numerosity Reduction Using Matrix Decompositionand Subspace Learning
    Ghojogh, Benyamin, and Crowley, Mark
    In Canadian Conference on Artificial Intelligence 2019
  9. Locally Linear Image Structural Embedding for Image Structure Manifold Learning
    Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark
    In International Conference on Image Analysis and Recognition (ICIAR-19) 2019
  10. Image Structure Subspace Learning Using Structural Similarity Index
    Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark
    In International Conference on Image Analysis and Recognition (ICIAR-19) 2019
  11. Principal Component Analysis Using Structural Similarity Index for Images
    Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark
    In International Conference on Image Analysis and Recognition (ICIAR-19) 2019
  12. Principal Sample Analysis for Data Reduction
    Ghojogh, Benyamin, and Crowley, Mark
    In 2018 IEEE International Conference on Big Knowledge (ICBK) 2018