Solar Extreme Events 2005 prediction by

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Solar Extreme Events 2005 prediction by Singular
spectrum analysis and neurofuzzy models
1- locally linear neurofuzzy
1-1 outputs of locally linear models is as
follows
where
1-2 least square optimization
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2- Learning Algorithm Locally Linear Model Tree
(LOLIMOT)
1- Start with an initial model start with a
single LLM, which is a global linear 2- Find the
worst LLM 3- Check all divisions The worst LLM
is considered for further refinement. Divisions
in all dimensions are tried, and for each of the
divisions the following steps are carried
out 3-1- Construction of the multi-dimensional
membership functions for both generated hyper
rectangles Construction of all validity
functions. 3-2- Estimation of the rule consequent
parameters for newly generated LLMs. 3-3-
Calculations of the loss function for the current
overall model. 4- Find the best division The
best of the alternatives checked in step 3 is
selected, and the related validity functions and
LLMs are constructed. The number of LLM neurons
is incremented. 5- Test the termination
condition If the termination condition is met,
then stop, else go to step 2.
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3- Singular Spectrum Analysis
1- producing M-dimensional vectors from time
series
2- covariance matrix is calculated as
3- corresponding principal component (PC) are


4- time series is reconstructed by combining the
associated principal components
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4- SSALOLIMOT method
M principle component extracted and then for each
PC a LLNF model should train then next value
prediction of each PC obtained finally predicted
PCs combined for achievement to prediction of
main series.
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5- Proton Events 2005 prediction
Figure3- one-step prediction of proton density
with LOLIMOTSSA method (a)-16 July (b)-7 May
2005
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