CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical...
Transcript of CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical...
![Page 1: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/1.jpg)
CMSE 820
Mathematical Foundations of Data Science
Instructor: Matthew Hirn
![Page 2: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/2.jpg)
Data science• Process data
• Extract information from data
• Make predictions using data
• Large amounts of data (“Big Data”)
• Often high dimensional (“Curse of Dimensionality”)
![Page 3: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/3.jpg)
Data science
Signal processing: Processing, extracting, and transferring information contained in multitude different formats, broadly referred to as signals.
![Page 4: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/4.jpg)
Some examples of data science in use From data to knowledge
• Recommend movies on Netflix or products on Amazon
• Object recognition in images or automatic image tagging
• Community detection in social networks (e.g., Facebook)
• Automatic medical diagnosis and treatment recommendation
![Page 5: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/5.jpg)
Object recognition
Guang-Tong Zhou, Tian Lan, Weilong Yang, and Greg Mori
![Page 6: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/6.jpg)
Predictive vs descriptive
![Page 7: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/7.jpg)
Supervised vs unsupervised machine learning
![Page 8: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/8.jpg)
Classification
Training phase:
{(x1
, y
1
), . . . , (xn, yn)}| {z }labeled data
⇢ X ⇥ Y 7! f : X ! Y, f(xi) = yi| {z }classification model
, |Y| < 1
Testing phase:
x 2 X| {z }new data
7! classification model ) f(x) = y 2 Y| {z }classification result
![Page 9: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/9.jpg)
Classification
![Page 10: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/10.jpg)
Example: MNIST
![Page 11: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/11.jpg)
Example: CalTech 101
![Page 12: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/12.jpg)
Regression
Similar to classification, but the model f can have an infinite range!
For example, Y = R or [0, 1]
![Page 13: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/13.jpg)
Regression
![Page 14: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/14.jpg)
Clustering
![Page 15: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/15.jpg)
Clustering
![Page 16: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/16.jpg)
Example: Bickley jetRalf Banisch
![Page 17: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/17.jpg)
Dimensionality reduction
![Page 18: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/18.jpg)
Dimensionality reduction
![Page 19: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/19.jpg)
Principal Component Analysis
![Page 20: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/20.jpg)
Manifold learning
![Page 21: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/21.jpg)
Example: Lip motions in speech
![Page 22: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/22.jpg)
Example: Lip motions in speech
Stéphane Lafon, Yosi Keller, and Ronald R. Coifman
![Page 23: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/23.jpg)
Example: Chemistry
Sandip De, Albert P. Bartók, Gábor Csanyi and Michele Ceriotti
![Page 24: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/24.jpg)
Compressed sensing
![Page 25: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/25.jpg)
Example: Single pixel camera
Digital Signal Processing Group
Kelly Lab
Department of Electrical and Computer Engineering
Rice University
![Page 26: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/26.jpg)
Syllabus
![Page 27: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/27.jpg)
My information
• instructor: Matthew Hirn • office: 2507F, Engineering Building • email: [email protected] • phone: (517) 432-0611 • course webpage: MSU Desire2Learn (D2L) course page
![Page 28: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/28.jpg)
Office hours
• Tuesday, 3:00 - 4:00 PM
• Friday, 3:00 - 4:00 PM
• By appointment
![Page 29: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/29.jpg)
Grading
• Homework exercises: 35%
• Midterm: 15%
• Project: 15%
• Final Exam: 35%
![Page 30: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/30.jpg)
Exam dates
• Midterm: Thursday, March 2 (in class)
• Final: Thursday, May 4, 7:45 AM - 9:45 AM (same place)
• These are cumulative, closed book exams
![Page 31: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/31.jpg)
Exercises• Will be posted on D2L on a rolling basis
• After each class, anywhere from zero to a few exercises
• Generally due one week after they are posted
• Some will be programming (MATLAB)
• Others will be mathematical proofs
• All solutions must be typed and submitted online through D2L
![Page 32: CMSE 820 Mathematical Foundations of Data Science · 2017. 1. 11. · CMSE 820 Mathematical Foundations of Data Science Instructor: Matthew Hirn. Data science](https://reader035.fdocuments.in/reader035/viewer/2022070215/61286d71bf040d091369ddf6/html5/thumbnails/32.jpg)
Project
• Opportunity to explore an application of the mathematical theory we will develop
• Will be developed over stages throughout the semester