The document provides several examples of machine learning techniques, including:
i) Examples of applying K-SVD dictionary learning to signals with noise and comparing it to other methods like FFT.
ii) Examples of using K-SVD regression to predict future values and comparing its performance to other models like k-NN and local AR models.
iii) Further examples of K-SVD for tasks like source separation and its use in other algorithms for problems like system identification and time series prediction.
37. my bachelor examples...
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38. my bachelor examples...
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39. my bachelor examples...
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AR: x = (x(1), . . . , x(t))T ∈ X ⊂ Rt
a = (a(1), . . . , a(t))T ∈ A ⊂ Rt
x(t + 1) = a x + N (0, σ )
T 2
0 t t+1
40. my bachelor examples...
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AR: x = (x(1), . . . , x(t))T ∈ X ⊂ Rt
ARIMA Example
a = (a(1), . . . , a(t))T ∈ A ⊂ Rt
230
observed value
x(t + 1) = a x + N (0, σ )
predicted value
T
2*SE 2
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0 0 5 10 15 t t+1
20 25 30 35
Time
41. my bachelor examples...
i) ˜
X Xr
ii) AR &
X ar = g(Xr )
x(t + 1) = ar x + N (0, σ )
˜ T 2
|˜(t + 1) − x(t)| → Ck
x ˜
Xr
˜
X
42. my bachelor examples...
i) ˜
X Xr
ii) AR &
X ar = g(Xr )
x(t + 1) = ar x + N (0, σ )
˜ T 2
|˜(t + 1) − x(t)| → Ck
x ˜
Xr
˜
X
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43. my bachelor examples...
Monthly Data Daily Data
240
250
240
230
230
220
220
E
E
210
210
200
200
June 15th 13:00
190
190
Day Hour