This document summarizes a presentation on Locality Preserving Projections (LPP), a dimensionality reduction technique. LPP preserves the local neighborhood structure of the data when projecting it to a lower-dimensional space. It constructs an adjacency graph representing the connections between nearby data points, chooses weights for these connections, and computes eigenmaps to perform the dimensionality reduction while maintaining locality. LPP is compared to Principal Component Analysis (PCA), the most common dimensionality reduction method, which aims to preserve global variance rather than local neighborhood structure.

1. CS404 : Pattern Recognition
Locality Preserving Projections
07-November-2016

2. Presenters
P Jishnu Jaykumar
201352005@iiitvadodara.ac.in
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Vivek Kumar Singh
201352015@iiitvadodara.ac.in

3. Paper Overview
Authors
● Xiaofei He and
● Partha Niyogi
From
● Computer Science Department
● The University of Chicago
● Chicago, IL 60615
Resource Link

4. Before proceeding, 2 simple questions
1. Has anyone of you ever heard about dimensionality reduction
techniques ?
2. If yes, then do you know why they are used ?

5. Dimensionality reduction (In CS/IT context)
● What is it ?
○ In machine learning and statistics, dimensionality reduction or
dimension reduction is the process of reducing the number of random
variables under consideration, via obtaining a set of principal variables.
■ Courtesy : https://en.wikipedia.org/wiki/Dimensionality_reduction
○ Simply, removing the redundant information(among the random variables)
and keeping the important information (principal variables) that will be
sufficient enough to represent the original data.

6. Dimensionality reduction (In CS/IT context)
● Why is it needed ?
◆ It helps in data compressing and reducing the storage space required.
◆ It fastens the time required for performing same computations. Less dimensions leads to less
computing, also less dimensions can allow usage of algorithms that are unfit for a large number of
dimensions.
◆ It takes care of multicollinearity that improves the model performance. It removes redundant features.
For example: there is no point in storing a value in two different units (meters and inches).
● Don’t throw tomatoes towards us. This is just an example for the convenience of explanation. ..

7. Some common
DR Techniques.
1. Multidimensional scaling
2. Linear discriminant analysis
3. High Correlation
4. Backward feature elimination
5. Factor Analysis
6. Missing Values
7. Low Variances
8. Principal Component Analysis (PCA)
9. And many more ...
To learn more about this techniques
Click here.

8. Our topic : Locality Preserving Projection (LPP)
● An overview
○ It is one of the DR techniques.
○ Obviously, it is the topic of our presentation as well as
the topic of the research paper which we read.
○ As the name suggests, this technique preserves the
information of its local region and thereby provides a
helping hand in dimensionality reduction.

9. Locality Preserving Projection (LPP)
● Algorithm
◆ .

10. Constructing the adjacency graph

11. Constructing the adjacency graph
A Graphical look

12. Choosing the weights

13. EigenMaps

14. EigenMaps - Continues...

15. Evaluating criteria

16. Comparison between PCA and LPP.

17. Any Queries?

18. References
● http://www.machinelearning.org/proceedings/icml2005/papers/036_Statisti
cal_HeEtAl.pdf
● http://papers.nips.cc/paper/2359-locality-preserving-projections.pdf
● https://www.youtube.com/watch?v=BgMFBqrtCwo

19. Thank you ...