Machine Learning: The Bare Math Behind Libraries Part 2 - Unsupervised learning

Second part of a talk about basics of Machine Learning. It covers: Hebbian learning, WTA, WTM and introduces the concept of Kohonen's network.

Transcript

1. achine Learning: The Bare Math Behind Libraries 30.04.2020 @CoffeeJUG by Piotr Czajka & Łukasz Gebel
2. Super Heroes & Super Powers continued
4. Agenda • History of unsupervised learning • Modern solutions • Q&A
5. Unsupervised learning
6. What? They can learn by themselves?
7. What? They can learn by themselves?
8. Why would we let them? • Less complex mathematical apparatus than in supervised learning. • It is similar to discovering world on your own.
9. Why would we let them? Used mostly for sorting and grouping when: • Sorting key can’t be easily figured out. • Data is very complex and finding the key is not trivial.
10. Idea behind – groups
11. Idea behind – groups
12. Idea behind – groups
13. Hebbian learning
14. Hebbian learning • Works similar to the nature • Great for beginners and biological simulations :) • Simple Hebbian learning algorithm Δ w ij =η⋅x ij ⋅y i Δ w ij −change of j weight of ineuron η−learningcoefficient x ij − jinput of ineuron y i −output of i neuron
15. Hebbian learning • Works similar to the nature • Great for beginners and biological simulations :) • Generalised Hebbian learning algorithm Δ w ij =F(x ij , y j ) Δ w ij −change of j weight of ineuron η−learningcoefficient x ij − jinput of ineuron y i −output of i neuron
16. Hebb’s neuron model w 1 w 2 w n w 0 Δ w ij =F(x ij , y j ) Σ x 1 x 2 x n ... 1 s y
17. Hebb’s neuron model 0.230 0.010 0.900 0.110 Δ w ij =F(x ij , y j ) Σ 0.200 0.300 0.100 1
18. Hebb’s neuron model 0.230 0.010 0.900 0.110 Δ w ij =F(x ij , y j ) Σ 1 0.046 0.003 0.090 0.110 0.200 0.300 0.100
19. Hebb’s neuron model 0.230 0.010 0.900 0.110 Δ w ij =F(x ij , y j ) Σ 1 0.046 0.003 0.090 0.110 0.249 0.200 0.300 0.100
20. Hebb’s neuron model 0.230 0.010 0.900 0.110 Δ w ij =F(x ij , y j ) Σ 1 0.046 0.003 0.090 0.110 0.249 0.562 0.562 0.200 0.300 0.100
21. Hebb’s neuron model 0.230 0.010 0.900 0.110 Δ w ij =F(x ij , y j ) Σ 1 0.562 0.200 0.300 0.100
22. Hebb’s neuron model 0.230 0.010 0.900 0.110 Δ w ij =F(x ij , y j ) Σ 1 0.562 +0.011 +0.016 +0.005 +0.056 0.300 0.100 0.200
23. Hebb’s neuron model 0.241 0.026 0.905 0.166 Δ w ij =F(x ij , y j ) Σ x 1 x 2 x 3 1
24. Demo
25. Imagine superhero teams
26. Marvel database to the rescue Intelligence Strength Speed Durability Energy projection Fighting skills Iron Man 6 6 5 6 6 4 Spiderman 4 4 3 3 1 4 Black Panter 5 3 2 3 3 5 Wolverine 2 4 2 4 1 7 Thor 2 7 7 6 6 4 Dr Strange 4 2 7 2 6 6 Hulk 2 7 3 7 5 4 Cpt. America 3 3 2 3 1 6 Mr Fantastic 6 2 2 5 1 3 Human Torch 2 2 5 2 5 3 Invisible Woman 3 2 3 6 5 3 The Thing 3 6 2 6 1 5 Luke Cage 3 4 2 5 1 4 She Hulk 3 7 3 6 1 4 Ms Marvel 2 6 2 6 1 4 Daredevil 3 3 2 2 4 5
27. Hebbian learning weaknesses • Unstable. • Prone to rise the weights ad infinitum. • Some groups can trigger no response. • Some groups may trigger response from too many neurons.
28. And now – self organising networks
29. Self organising?
30. Learning with concurrency • You try to generalize input vector in weights vector. • Instead of checking the reaction to input - you check distance between both vectors. • Ideally – each neuron specializes in one class generalization. • Two main strategies: – Winner Takes All (WTA) – Winner Takes Most (WTM)
31. Idea behind Neuron weights 3.0 2.0 2.0 Example 1.0 2.0 3.0
32. Example 1.0 2.0 3.0 Idea behind Distance 2.0 0.0 -1.0 Neuron weights 3.0 2.0 2.0 d i =w i −x i Euclidiandistance √∑ i=1 n d i 2 =√5
33. Distance 2.0 0.0 -1.0 Idea behind Neuron weights 3.0 2.0 2.0 Learning coefficient η=0.100 Learning Step 0.2 0.0 -0.1 Δ w i =η⋅d i Example 1.0 2.0 3.0 d i =w i −x i Learning coefficient η=0.100
34. Idea behind Distan ce 2.0 0.0 -1.0 Neuron weights 2.8 = 3.0 – 0.2 2.0 = 2.0 – 0.0 2.1 = 2.0 -(-0.1) Exam ple 1.0 2.0 3.0 d i =w i −x i Learning coefficient η=0.100 Learning Step 0.2 0.0 -0.1 w' i =w i −Δw i Δ w i =η⋅d i Example 1.0 2.0 3.0 Learning Step 0.2 0.0 -0.1 Δ w i =η⋅d i Distance 2.0 0.0 -1.0 d i =w i −x i
35. Idea behind Neuron weights 2.8 2.0 2.1
36. Idea behind – initial setup 1 2 3
37. Idea behind – mid learning 1 2 3
38. Idea behind – homeostasis 1 2 3
39. Demo time
40. Learning with concurrency • Gives more diverse groups. • Less prone to clustering (than Hebb’s). • Searches wider spectrum of answers. • First step to more complex networks.
41. Learning with concurency - weaknesses • WTA – works best if teaching examples are evenly distributed in solution space. • WTM – works best if weights’ vectors are evenly distributed in solution space. • Still can stick to local optimum.
42. Teuvo Kohonen’s SOM Created by this nice guy here
43. Kohonen’s self-organizing map • The most popular self-organizing network with concurrency algorithm. • It teaches groups of neurons with WTM alghoritm • Special features: – Neurons are organised in a grid – Nevertheless – they are treated as a single layer
44. Kohonen’s self-organizing map w ij (s+1)=w ij (s)+Θ(k best ,i , s)⋅η(s)⋅(I j (s)−w ij (s)) s−epochnumber k best −best neuron w ij (s)− j weight of ineuron Θ(k best ,i,s)−neighbourhood function η(s)−learning coefficient for sepoch I j (s)− jchunk of example for s epoch
45. SOM model By Mcld - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10373592
46. Common weaknesses of artificial neuron systems • We are still dependant on randomized weights. • All algorithms can stick to local optimum.
47. Summary • Grouped superheroes using historical algorithm.
48. Summary • Grouped superheroes using recent algorithms.
49. Call to Action! • Implement WTA algorithm in your favourite programming language • Add ranking to WTA to create WTM algorithm. • Don’t care about performance • Check how it works – generate your data sets, get simple ones from the Internet • You’ll gain intuition and understand basic mathematical aparathus • If you feel comfortable try coding self-organising map from WTM.
50. Call to Action! • Play with Machine Learning and become superhero ;)
51. Bibliography • Presentation + code: https://bitbucket.org/medwith/public/downloads/mluvr-coffeJugPart2.zip • https://www.coursera.org/learn/machine-learning • https://www.coursera.org/specializations/deep-learning • Math for Machine Learning - Amazon Training and Certification • Linear and Logistic Regression - Amazon Training and Certification • Grus J., Data Science from Scratch: First Principles with Python • Patterson J., Gibson A., Deep Learning: A Practitioner's Approach • Trask A., Grokking Deep Learning • Stroud K. A., Booth D. J, Engineering Mathematics • https://github.com/massie/octave-nn- neural network Octave implementation • https://www.desmos.com/calculator/dnzfajfpym - Nanananana … Batman equation ;) • https://xkcd.com/605/ - extrapolating ;) • http://dilbert.com/strip/2013-02-02 - Dilbert & Machine Learning
52. Thank you