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.

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: