20191204 mbsj2019
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The document presents a mathematical model for dimensionality reduction. It defines vectors X1, X2, X3 to represent high-dimensional data. Matrices U and V are used to project the data into a lower-dimensional space. The model finds the optimal matrices U and V to minimize the difference between the original and projected data.
20191204 mbsj2019
- 11. " " X
- 12. " " X1 X2 X3 ^ ^ ^≃X + +
- 13. " " u1'◦v1' u2'◦v2' u3'◦v3' ++ X1 X2 X3 ^ ^ ^≃X + + =
- 14. " " u1'◦v1' u2'◦v2' u3'◦v3' ++= u1◦v1 u2◦v2 u3◦v3 λ1 λ2 λ3 = ++ X1 X2 X3 ^ ^ ^≃X + +
- 15. " " UΛVT = u1'◦v1' u2'◦v2' u3'◦v3' ++= u1◦v1 u2◦v2 u3◦v3 λ1 λ2 λ3 = ++ X1 X2 X3 ^ ^ ^≃X + +
- 16. " " ≃χ ̂χ1 ̂χ2 ̂χ3+ + = + + =
- 17. " "
- 18. " "
- 22. Tsuyuzaki K. et. al., 2019 (in prep.)
- 23. 1: AutoML Tsuyuzaki K. et. al., 2018
- 24. 1: AutoML
- 25. 2: w1 = 0.2 w2 = 0.3 w4 = 0.5 w3 = 0
- 26. 3: /
- 27. 4:
- 28. 5: