Kernel RLS Experiment Result
Outline
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KRLS Abstract
KRLS Formula
Algorithm
Result
Abstract
• We want to predict the time series data(Santa
Fe) using KRLS algorithm. We compare the
predict outputs and the true data outputs
after 10 -step, which is so called 10-step
ahead prediction.
KRLS Formula
Basic Function:
ALD Threshold:
KRLS Formula (II)
Kernel Trick
KRLS Formula(III)
𝐸𝑎𝑢𝑔 (𝛼)= 0
coefficients
satisfying the approximate
linear dependence (ALD) condition if
<= v
If
> v , then we must expand the current dictionary
by augmenting it with
Alogrithm
Case1
• If
< = v or the dictionary’s space is full.
Go to Case1:
Define:
By matrix inversion Lemma, we have
(a recursive formula for 𝑃𝑡 )
Case1.cont
• Define:
Case2
• If
>= v and the dictionary’s space is not
full.
Go to Case2(Expand the dictionary
):
Case2.cont
Original Data
• Data: Sante Fe Lazer (1000 data)
• V=0.01
Prediction Result
Prediction GraphII
RMSE
• RMSE Formula:
• S={[(x1-x)^2+(x2-x)^2+......(xn-x)^2]/N}^0.5
• RMSE:43.5368(Max data 255,Min data 2)