Nonlineat Data Analytics
For all the work (reading summary, homework, report, slids, .tex files, etc.) need to be submitted electronically,
please send directly to both the TA and the instructor via email. If you have handwritten homework or printed work,
please submit at the beginning of the class.
Reading summary and homework should be submitted before class on the due date. All resources
(including lecture slides, homework, starter files, hw solution,
articles) can be found under the "Resources" tab.
The topics to cover and the homework to be assigned are subject to change.
| Date | Topics | Due & Assign Date |
|---|---|---|
| Overview May 22 |
Why we need nonlinear data analysis? Similarity measurements for nonlinear data Introduction to cell phone data Introduction to rigid motion |
Assign:
● Hw 1
● Reading summary 1: HMOG: New Behavioral Biometric Features for Continuous Authentication of Smartphone Users Due: None |
| May 24 |
Intro to UAV’s data, cell phone’s data, and other robotic data Their common mathematical representations The set of rotations and translations and the set of rigid motions Euler angles Unit Quaternions | Assign: ● Hw 2 Due: None |
| May 27 | None |
Assign:
None Due: ● Project Proposal (via email by 11:59 pm) |
| May 29 |
Introduction to manifold Examples of manifolds (focus on SO(3)) Introduction of Lie group idea (focus on SO(n)) Introduction to Lie algebra (focus on Lie algebra of SO(3)) Homogeneous representation of Rigid motions |
Assign:
● Hw 3 Due: ● Hw 1 ● Hw 2 ● Reading summary 1 |
| May 31 |
Detailed motivations of nonlinear data analysis Specific force Sensor errors Moving frames (Coordinate frames) Angular velocity (Pitch, roll, yaw) Exponential and log maps Applications of exponential and log maps to analyze cell phone data |
Assign:
None Due: None |
| June 3 |
Cell phone data in quaternion representations Gyroscope measurement models Accelerometer measurement models Choosing the state and modeling its dynamics Model for the prior Resulting probabilistic models |
Assign:
● Hw 4 Due: ● Hw 3 |
| June 7 |
No class. Work on your project. Please submit your midterm progress report to both TA and instructor via email by 11:59 pm. Please check on the "Final Project" tab for submission requirements. |
Midterm progress report due (via email by 11:59 pm) |
| June 10 |
Rigid motion SE(3) |
Assign:
None Due: ● Hw 4 |
| June 14 |
Review matrix exponential and define matrix logarithm Christoffel symbols and the compatibility equations From directional derivative to covariant derivative |
Assign:
● Hw 5 Due: None |
| June 17 |
The first fundamental form Riemannina metric |
Assign:
● Hw 6 Due: ● Hw 5 |
| June 21 |
Polynomial PCA Principal Curves and Surfaces ISOMAP LLE (Local Linear Embedding) Spectral Clustering |
Assign:
● Hw 7 Due: ● Hw 6 |
| June 24 |
No class. Work on your project. Please submit your draft of final project report to both TA and instructor via email by 11:59 pm. Please check on the "Final Project" tab for submission requirements. |
Assign:
None Due: ● Hw 7 (via email by 11:59 pm) ● Draft of final project report due (via email by 11:59 pm) |
| June 28 | Final Project Presentation (in class) | Final project presentation slides due (via email by 11:59 pm) |
| July 1 |
No class. Please submit your final project report to both TA and instructor via email by 11:59 pm. Please check on the "Final Project" tab for submission requirements. |
Final project due (via email by 11:59 pm) |