# 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.

**WEBPAGE: **
Elements of Dimensionality Reduction and Manifold Learning (Amazon)

Manifold Learning and Dimensionality Reduction are vast areas of study in Math and Computer Science. The task is to find ways to determine the essential relationships and structure of a dataset. Researchers in this area 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. After all, some form of Encoder-Decoder neural network could always be devised as a replacement.
While such systems work well given the right training process and enough data, 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.

We have an exciting group of work which has been published in recent years on this topic which you can see below in the Publications list.

### Upcoming Textbook on Manifold Learning!

This work has culiminated recently in the graduation of my first Doctoral student, Benyamin Ghojogh, in April 2021 with his thesis encompassing many of these advances.
Dr. Ghojogh continued as a postdoc in my lab until 2022 and now works in industry. In late 2022 we will publish, via Springer, a new textbook on **“Manifold Learning and Dimensionality Reduction”** (Ghojogh et al., 2023) written in collaboration with Prof. Ali Godsi andd Prof. Fakhri Karray.

## Our Papers on Manifold Learning

- Weighted Fisher Discriminant Analysis in the Input and Feature SpacesIn
*International Conference on Image Analysis and Recognition (ICIAR-2020)*. Springer, Póvoa de Varzim, Portugal (virtual). Jun, 2020. - Theoretical Insights into the Use of Structural Similarity Index In Generative Models and Inferential AutoencodersIn
*International Conference on Image Analysis and Recognition (ICIAR-2020)*. Springer, Póvoa de Varzim, Portugal (virtual). Jun, 2020. - Instance Ranking and Numerosity Reduction Using Matrix Decompositionand Subspace LearningIn
*Canadian Conference on Artificial Intelligence*. Springer’s Lecture Notes in Artificial Intelligence., Kingston, ON, Canada. 2019. - Locally Linear Image Structural Embedding for Image Structure Manifold LearningIn
*International Conference on Image Analysis and Recognition (ICIAR-19)*. Waterloo, Canada. 2019. - Image Structure Subspace Learning Using Structural Similarity IndexIn
*International Conference on Image Analysis and Recognition (ICIAR-19)*. Waterloo, Canada. 2019. - Principal Component Analysis Using Structural Similarity Index for ImagesIn
*International Conference on Image Analysis and Recognition (ICIAR-19)*. Waterloo, Canada. 2019. - Principal Sample Analysis for Data ReductionIn
*2018 IEEE International Conference on Big Knowledge (ICBK)*. Singapore. 2018.