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Greg Heath
Guest
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 Posted: Tue Nov 11, 2008 8:20 pm Post subject: Re: RBF vs. MLP |
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On Nov 11, 3:01 pm, Greg Heath <he...@alumni.brown.edu> wrote:
| Quote: | On Nov 8, 2:41 pm, paulvbi...@gmail.com wrote:
QUESTION:
Is anyone familiar with work done on two hidden layer
MLP-RBF models?
***********************************************
Dear Greg
Never heard of them but nice idea
I guess I need to dig out all my sigmoid papers!
I recall a conference abstract w.r.t. this model.
I think it was a pre-2003 NIPS conference ... maybe
in the 90's.
|
A quick search of the archives in Google Groups
lead to the FAQ and this paragraph:
RBF networks are most often used with a single hidden
layer. But an extra, linear hidden layer before the
radial hidden layer enables the network to ignore
irrelevant inputs (see How do MLPs compare with RBFs?")
The linear hidden layer allows the RBFs to take
elliptical, rather than radial (circular), shapes in
the space of the inputs. Hence the linear layer gives
you an elliptical basis function (EBF) network. In the
hill and valley example, an ORBFUN network requires
nine hidden units (37 weights) to get the test RMSE below .01, but by
adding a linear hidden layer, you
can get an essentially perfect fit with three linear
units followed by two radial units (20 weights).
Hope this helps.
Greg
P.S. NOTE: Linear, not sigmoidal! |
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Greg Heath
Guest
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| Posted: Tue Nov 11, 2008 8:30 pm Post subject: Re: RBF vs. MLP |
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On Oct 29, 9:32 pm, Leon <le...@poczta.onet.pl> wrote:
| Quote: | I am rather new to NN, and as the starting point I am reading now
Bishop's book on NN. I am now in the middle, but I am very curios now
about one issue, when MLP is better and when RBF. Can anybody mention
some methodological guidelines of when MLP and when RBF would be better.
I think I will get an answer when I get to the end of Bishop's book,
but I would be interested to see opinions from people in this group.
|
Take a good look at the FAQ.
Especially
ftp://ftp.sas.com/pub/neural/FAQ2.html#A_mlpvsrbf
and
ftp://ftp.sas.com/pub/neural/FAQ3.html#A_hl
Hope this helps.
Greg |
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Guest
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| Posted: Tue Nov 11, 2008 9:24 pm Post subject: Re: RBF vs. MLP |
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|
On Nov 11, 3:20 pm, Greg Heath <he...@alumni.brown.edu> wrote:
| Quote: | On Nov 11, 3:01 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 8, 2:41 pm, paulvbi...@gmail.com wrote:
QUESTION:
Is anyone familiar with work done on two hidden layer
MLP-RBF models?
***********************************************
Dear Greg
Never heard of them but nice idea
I guess I need to dig out all my sigmoid papers!
I recall a conference abstract w.r.t. this model.
I think it was a pre-2003 NIPS conference ... maybe
in the 90's.
A quick search of the archives in Google Groups
lead to the FAQ and this paragraph:
RBF networks are most often used with a single hidden
layer. But an extra, linear hidden layer before the
radial hidden layer enables the network to ignore
irrelevant inputs
|
Nice ! but irrelevant to the given RBF centre I would expect might be
best giving therefore a lot of weights to determine ie Nc*Nv where Nc
is the number of basis functions and Nv is the number of variables.
If just to all the centres may not give enough discrimination of the
inputs however low weight count, ie just Nv
thanks Greg
best
Paul |
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Greg Heath
Guest
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| Posted: Wed Nov 12, 2008 3:29 pm Post subject: Re: RBF vs. MLP |
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|
On Nov 11, 4:24 pm, paulvbi...@gmail.com wrote:
| Quote: | On Nov 11, 3:20 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 11, 3:01 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 8, 2:41 pm, paulvbi...@gmail.com wrote:
QUESTION:
Is anyone familiar with work done on two hidden layer
MLP-RBF models?
***********************************************
Dear Greg
Never heard of them but nice idea
I guess I need to dig out all my sigmoid papers!
I recall a conference abstract w.r.t. this model.
I think it was a pre-2003 NIPS conference ... maybe
in the 90's.
A quick search of the archives in Google Groups
lead to the FAQ and this paragraph:
RBF networks are most often used with a single hidden
layer. But an extra, linear hidden layer before the
radial hidden layer enables the network to ignore
irrelevant inputs
Nice ! but irrelevant to the given RBF centre I would expect might be
best giving therefore a lot of weights to determine ie Nc*Nv where Nc
is the number of basis functions and Nv is the number of variables.
If just to all the centres may not give enough discrimination of the
inputs however low weight count, ie just Nv
|
I see it from another perspective:
The main job of the linear layer is to
create the equivalent of nonidentical EBF
hidden nodes. Whether or not the resulting
equivalent EBF net is satisfactorially better
than a RBF net, has to be determined using
whatever criterion is dear to the heart of
the user.
However, the two main points to be emphasized
here are:
1. If an EBF is preferable, using the linear-
RBF combination seems simpler than a single EBF
hidden layer.
2. The linear-RBF combination more easily
and more transparently, reduces the effect of
redundant and/or irrelevant inputs.
Hope this helps.
Greg |
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Guest
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| Posted: Wed Nov 12, 2008 5:16 pm Post subject: Re: RBF vs. MLP |
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|
On Nov 12, 10:29 am, Greg Heath <he...@alumni.brown.edu> wrote:
| Quote: | On Nov 11, 4:24 pm, paulvbi...@gmail.com wrote:
On Nov 11, 3:20 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 11, 3:01 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 8, 2:41 pm, paulvbi...@gmail.com wrote:
QUESTION:
Is anyone familiar with work done on two hidden layer
MLP-RBF models?
***********************************************
Dear Greg
Never heard of them but nice idea
I guess I need to dig out all my sigmoid papers!
I recall a conference abstract w.r.t. this model.
I think it was a pre-2003 NIPS conference ... maybe
in the 90's.
A quick search of the archives in Google Groups
lead to the FAQ and this paragraph:
RBF networks are most often used with a single hidden
layer. But an extra, linear hidden layer before the
radial hidden layer enables the network to ignore
irrelevant inputs
Nice ! but irrelevant to the given RBF centre I would expect might be
best giving therefore a lot of weights to determine ie Nc*Nv where Nc
is the number of basis functions and Nv is the number of variables.
If just to all the centres may not give enough discrimination of the
inputs however low weight count, ie just Nv
I see it from another perspective:
The main job of the linear layer is to
create the equivalent of nonidentical EBF
hidden nodes. Whether or not the resulting
equivalent EBF net is satisfactorially better
than a RBF net, has to be determined using
whatever criterion is dear to the heart of
the user.
However, the two main points to be emphasized
here are:
1. If an EBF is preferable, using the linear-
RBF combination seems simpler than a single EBF
hidden layer.
2. The linear-RBF combination more easily
and more transparently, reduces the effect of
redundant and/or irrelevant inputs.
Hope this helps.
Greg
|
******************************************
Dear Greg
My words were not clear
Would you have a weighted linear equation in the inputs for each
centre or just an over all one
If you have one for each centre you have a "whack of weights" ie
Nv*NC and not doubt this would be effective
if you just have one weighted linear equation "feeding" all the
centres, would you have enough "power" to perform discrimination of
the inputs as this is now applied only one to all the input/output
space
best wishes
Paul |
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Greg Heath
Guest
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| Posted: Thu Nov 13, 2008 5:27 pm Post subject: Re: RBF vs. MLP |
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On Nov 12, 12:16 pm, paulvbi...@gmail.com wrote:
| Quote: | On Nov 12, 10:29 am, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 11, 4:24 pm, paulvbi...@gmail.com wrote:
On Nov 11, 3:20 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 11, 3:01 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 8, 2:41 pm, paulvbi...@gmail.com wrote:
QUESTION:
Is anyone familiar with work done on two hidden layer
MLP-RBF models?
***********************************************
Dear Greg
Never heard of them but nice idea
I guess I need to dig out all my sigmoid papers!
I recall a conference abstract w.r.t. this model.
I think it was a pre-2003 NIPS conference ... maybe
in the 90's.
A quick search of the archives in Google Groups
lead to the FAQ and this paragraph:
RBF networks are most often used with a single hidden
layer. But an extra, linear hidden layer before the
radial hidden layer enables the network to ignore
irrelevant inputs
Nice ! but irrelevant to the given RBF centre I would expect might be
best giving therefore a lot of weights to determine ie Nc*Nv where Nc
is the number of basis functions and Nv is the number of variables.
If just to all the centres may not give enough discrimination of the
inputs however low weight count, ie just Nv
I see it from another perspective:
The main job of the linear layer is to
create the equivalent of nonidentical EBF
hidden nodes. Whether or not the resulting
equivalent EBF net is satisfactorially better
than a RBF net, has to be determined using
whatever criterion is dear to the heart of
the user.
However, the two main points to be emphasized
here are:
1. If an EBF is preferable, using the linear-
RBF combination seems simpler than a single EBF
hidden layer.
2. The linear-RBF combination more easily
and more transparently, reduces the effect of
redundant and/or irrelevant inputs.
Hope this helps.
Greg
******************************************
Dear Greg
My words were not clear
Would you have a weighted linear equation in the
inputs for each centre or just an over all one
If you have one for each centre you have a "whack of weights" ie
Nv*NC and not doubt this would be effective
if you just have one weighted linear equation "feeding" all the
centres, would you have enough "power" to perform discrimination of
the inputs as this is now applied only one to all the input/output
space
|
My words were not clear either. By "nonidentical"
I meant nonidentical effective inverse covariance
matrices in addition to the obviously nonidentical
centers. This obviously requires an initial
layer with Nv*Nc weights. However, during or after
training iterations, some of the weights could be
eliminated.
My original emphasis was on the simple creation of
effective EBFs. I considered the automatic filtering
of redundant and/or irrelevant inputs as a bonus.
However, for certain problems, the latter is more
important.
Hope this helps.
Greg |
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Guest
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| Posted: Thu Nov 13, 2008 7:21 pm Post subject: Re: RBF vs. MLP |
|
|
On Nov 13, 12:27 pm, Greg Heath <he...@alumni.brown.edu> wrote:
| Quote: | On Nov 12, 12:16 pm, paulvbi...@gmail.com wrote:
On Nov 12, 10:29 am, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 11, 4:24 pm, paulvbi...@gmail.com wrote:
On Nov 11, 3:20 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 11, 3:01 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 8, 2:41 pm, paulvbi...@gmail.com wrote:
QUESTION:
Is anyone familiar with work done on two hidden layer
MLP-RBF models?
***********************************************
Dear Greg
Never heard of them but nice idea
I guess I need to dig out all my sigmoid papers!
I recall a conference abstract w.r.t. this model.
I think it was a pre-2003 NIPS conference ... maybe
in the 90's.
A quick search of the archives in Google Groups
lead to the FAQ and this paragraph:
RBF networks are most often used with a single hidden
layer. But an extra, linear hidden layer before the
radial hidden layer enables the network to ignore
irrelevant inputs
Nice ! but irrelevant to the given RBF centre I would expect might be
best giving therefore a lot of weights to determine ie Nc*Nv where Nc
is the number of basis functions and Nv is the number of variables.
If just to all the centres may not give enough discrimination of the
inputs however low weight count, ie just Nv
I see it from another perspective:
The main job of the linear layer is to
create the equivalent of nonidentical EBF
hidden nodes. Whether or not the resulting
equivalent EBF net is satisfactorially better
than a RBF net, has to be determined using
whatever criterion is dear to the heart of
the user.
However, the two main points to be emphasized
here are:
1. If an EBF is preferable, using the linear-
RBF combination seems simpler than a single EBF
hidden layer.
2. The linear-RBF combination more easily
and more transparently, reduces the effect of
redundant and/or irrelevant inputs.
Hope this helps.
Greg
******************************************
Dear Greg
My words were not clear
Would you have a weighted linear equation in the
inputs for each centre or just an over all one
If you have one for each centre you have a "whack of weights" ie
Nv*NC and not doubt this would be effective
if you just have one weighted linear equation "feeding" all the
centres, would you have enough "power" to perform discrimination of
the inputs as this is now applied only one to all the input/output
space
My words were not clear either. By "nonidentical"
I meant nonidentical effective inverse covariance
matrices in addition to the obviously nonidentical
centers. This obviously requires an initial
layer with Nv*Nc weights. However, during or after
training iterations, some of the weights could be
eliminated.
|
**********
yes do a full model run and then eliminate under some reasonable
"throw out" criterion
***********
| Quote: |
My original emphasis was on the simple creation of
effective EBFs. I considered the automatic filtering
of redundant and/or irrelevant inputs as a bonus.
However, for certain problems, the latter is more
important.
|
yes I agree and truly very important
You get a stronger method with the EBFs and therefore can be more
assured when "throwing out" a given input
very good Greg
Paul |
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tomhoo
Guest
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| Posted: Thu Nov 13, 2008 11:01 pm Post subject: Re: RBF vs. MLP |
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On Nov 4, 10:38 am, Leon <le...@poczta.onet.pl> wrote:
| Quote: | Greg Heath wrote:
On Oct 29, 9:32 pm, Leon <le...@poczta.onet.pl> wrote:
I am rather new to NN, and as the starting point I am reading now
Bishop's book on NN. I am now in the middle, but I am very curios now
about one issue, when MLP is better and when RBF. Can anybody mention
some methodological guidelines of when MLP and when RBF would be better.
I think I will get an answer when I get to the end of Bishop's book,
but I would be interested to see opinions from people in this group.
Have both algorithms in your bag of tricks and try both.
However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or
MDS.
After a while, based on visual representations,you will have a "feel"
for which
one might be better.
Hope this helps.
Greg
Yes, visualisation always gives a good insight into the problem. After
reading the paper suggested in this thread by Gavin I have a feeling
that (in case of regression) RBF seems to be better when there are hills
in the target value, and MLP learns better when the target value is more
smooth and looks like a plateau. In the classification problem probably
the shape of the decision boundary would play the same role. The problem
with RBFs is that we may need a huge number of basis functions. Exactly
this makes a problem in a spiral domain. Well, overall I think I start
understanding the issue.
Leon
|
I'm trying to visualize your two, different surface types.
Can you elaborate a little on "hills" and "plateaus?"
In particular, a plateau is a flat surface that is at a higher
elevation than surrounding terrain. If looking for global minima, the
location would definitely not be on the plateau but rather somewhere
on the surrounding terrain.
Thanks in advance,
Tom |
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tomhoo
Guest
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| Posted: Thu Nov 13, 2008 11:03 pm Post subject: Re: RBF vs. MLP |
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On Nov 3, 3:07 am, Greg Heath <he...@alumni.brown.edu> wrote:
| Quote: | On Oct 29, 9:32 pm, Leon <le...@poczta.onet.pl> wrote:
I am rather new to NN, and as the starting point I am reading now
Bishop's book on NN. I am now in the middle, but I am very curios now
about one issue, when MLP is better and when RBF. Can anybody mention
some methodological guidelines of when MLP and when RBF would be better..
I think I will get an answer when I get to the end of Bishop's book,
but I would be interested to see opinions from people in this group.
Have both algorithms in your bag of tricks and try both.
However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or
MDS.
After a while, based on visual representations,you will have a "feel"
for which
one might be better.
Hope this helps.
Greg
|
More and more people are mentioning "visualizing the data." I don't
think the FAQ really get into this. (If I missed the section, I
appologize for my haste.)
Might this not be a good sub-section to add to the FAQ? maybe under
"Visualization of Data" and perhaps "RBF's"
Thanks
Tom |
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Greg Heath
Guest
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| Posted: Fri Nov 14, 2008 4:14 pm Post subject: Re: RBF vs. MLP |
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|
On Nov 13, 6:01 pm, tomhoo <tom...@gmail.com> wrote:
| Quote: | On Nov 4, 10:38 am, Leon <le...@poczta.onet.pl> wrote:
Greg Heath wrote:
On Oct 29, 9:32 pm, Leon <le...@poczta.onet.pl> wrote:
I am rather new to NN, and as the starting point I am reading now
Bishop's book on NN. I am now in the middle, but I am very curios now
about one issue, when MLP is better and when RBF. Can anybody mention
some methodological guidelines of when MLP and when RBF would be better.
I think I will get an answer when I get to the end of Bishop's book,
but I would be interested to see opinions from people in this group.
Have both algorithms in your bag of tricks and try both.
However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or
MDS.
After a while, based on visual representations,you will have a "feel"
for which
one might be better.
Hope this helps.
Greg
Yes, visualisation always gives a good insight into the problem. After
reading the paper suggested in this thread by Gavin I have a feeling
that (in case of regression) RBF seems to be better when there are hills
in the target value, and MLP learns better when the target value is more
smooth and looks like a plateau. In the classification problem probably
the shape of the decision boundary would play the same role. The problem
with RBFs is that we may need a huge number of basis functions. Exactly
this makes a problem in a spiral domain. Well, overall I think I start
understanding the issue.
Leon
I'm trying to visualize your two, different surface types.
Can you elaborate a little on "hills" and "plateaus?"
In particular, a plateau is a flat surface that is at a higher
elevation than surrounding terrain. If looking for global minima, the
location would definitely not be on the plateau but rather somewhere
on the surrounding terrain.
Thanks in advance,
|
Not sure exactly what you mean. The first layer
is linear, not sigmoidal, so all it does is rotate
and scale. The second layer is a superposition of
elliptical Gaussians, which, if they are close and
broad enough, can even represent a flat surface
with small bumps.
The search for local/global minima is in weight
space. I have no idea what that will look like.
Hope this helps.
Greg |
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tomhoo
Guest
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| Posted: Tue Nov 18, 2008 3:10 pm Post subject: Re: RBF vs. MLP |
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|
It helps a little, however, I need a chapter somehwere explaining from
basics Data Visualization and RBF-v-MLP selection as per your post:
"However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or
MDS.
After a while, based on visual representations,you will have a "feel"
for which
one might be better."
Perhaps a new chapter for the FAQ?
Thanks
Tom |
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| Back to top |
Greg Heath
Guest
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| Posted: Tue Nov 18, 2008 5:10 pm Post subject: Re: RBF vs. MLP |
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|
On Nov 13, 6:03 pm, tomhoo <tom...@gmail.com> wrote:
| Quote: | On Nov 3, 3:07 am, Greg Heath <he...@alumni.brown.edu> wrote:
On Oct 29, 9:32 pm, Leon <le...@poczta.onet.pl> wrote:
I am rather new to NN, and as the starting point I am reading now
Bishop's book on NN. I am now in the middle, but I am very curios now
about one issue, when MLP is better and when RBF. Can anybody mention
some methodological guidelines of when MLP and when RBF would be better.
I think I will get an answer when I get to the end of Bishop's book,
but I would be interested to see opinions from people in this group.
Have both algorithms in your bag of tricks and try both.
However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or MDS.
After a while, based on visual representations,you will have a "feel"
for which one might be better.
More and more people are mentioning "visualizing the data." I don't
think the FAQ really get into this. (If I missed the section, I
appologize for my haste.)
|
Visualizing data is a topic that is independent of NNs.
It falls more into the "elementary statistics" bag for which
there are a plethora of references.
Typical are
1. Scatter plots to visualize simple pairwise correlations
a. yk vs xi
b. xj vs xi
2. Projections on PCA planes
a. Covariance matrix
b. Correlation matrix
3. Color coding of projections
a. clusters
b. classes
4. Other planar projections
a. SOM
b. LDA
c. MDS
| Quote: | Might this not be a good sub-section to add to the FAQ? maybe under
"Visualization of Data"
|
Not without the more important tutorials on statistical data
preparation
(data verification, outlier detection and mitigation,
multicollinearity
detection and mitigation, linear and nonlinear transformations, etc).
Since all of these topics are adequately covered in stats
texts, a short list of excellent references would be useful.
| Quote: | and perhaps "RBF's"
|
What does that have to do with data visualization?
Or .. are you referring to visualizing intermediate
(e.g., hidden node) and final results?
Hope this helps.
Greg |
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Greg Heath
Guest
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| Posted: Tue Nov 18, 2008 5:29 pm Post subject: Re: RBF vs. MLP |
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On Nov 18, 10:10 am, tomhoo <tom...@gmail.com> wrote:
| Quote: | It helps a little, however, I need a chapter somehwere explaining from
basics Data Visualization and RBF-v-MLP selection as per your post:
"However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or MDS.
After a while, based on visual representations,you will have a "feel"
for which one might be better."
Perhaps a new chapter for the FAQ?
|
MLPs and RBFs are universal approximators. Users should have
software for both. For most problems either one will work.
So, as far as getting results, choosing which one is not a
big deal.
However, I neither enourage the blind "black box" approach
nor presentation of results without interpretaion. No
statistical technique should be used without considering
whatever a priori information is available.
I consider data visualizations as part of the "a priori"
info. For a beginner my advice is
1. Find some traditional demo data (see the FAQ)
2. Visualize the data
3. Design both MLPs and RBFs
4. Compare
Hope this helps.
Greg |
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| Back to top |
tomhoo
Guest
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| Posted: Wed Nov 19, 2008 8:45 pm Post subject: Re: RBF vs. MLP |
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|
On Nov 18, 12:29 pm, Greg Heath <he...@alumni.brown.edu> wrote:
| Quote: | On Nov 18, 10:10 am, tomhoo <tom...@gmail.com> wrote:
It helps a little, however, I need a chapter somehwere explaining from
basics Data Visualization and RBF-v-MLP selection as per your post:
"However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or MDS.
After a while, based on visual representations,you will have a "feel"
for which one might be better."
Perhaps a new chapter for the FAQ?
MLPs and RBFs are universal approximators. Users should have
software for both. For most problems either one will work.
So, as far as getting results, choosing which one is not a
big deal.
However, I neither enourage the blind "black box" approach
nor presentation of results without interpretaion. No
statistical technique should be used without considering
whatever a priori information is available.
I consider data visualizations as part of the "a priori"
info. For a beginner my advice is
1. Find some traditional demo data (see the FAQ)
2. Visualize the data
3. Design both MLPs and RBFs
4. Compare
Hope this helps.
Greg
|
As far as visualization, y=f(x,y) is about the limit of my spacial
dimensions, 2 at a time.
I have no idea how to visualize multi dimensional data.
I could amass some statistics based on Euclidean distances within my
population, but I question its usefullness.
There may be ways to project onto a plane....(?) How? Which plane?
Lots of speculation but nothing useful - not my area - but sounds like
that are standard methods to use here.
Thanks
Tom |
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| Back to top |
Greg Heath
Guest
|
| Posted: Thu Nov 20, 2008 10:35 am Post subject: Re: RBF vs. MLP |
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|
On Nov 19, 3:45 pm, tomhoo <tom...@gmail.com> wrote:
| Quote: | On Nov 18, 12:29 pm, Greg Heath <he...@alumni.brown.edu> wrote:
On Nov 18, 10:10 am, tomhoo <tom...@gmail.com> wrote:
It helps a little, however, I need a chapter somehwere explaining from
basics Data Visualization and RBF-v-MLP selection as per your post:
"However, before using either one, obtain a visual representation
of the data (color coded for a classifier) via coordinate projections,
PCA or MDS.
After a while, based on visual representations,you will have a "feel"
for which one might be better."
Perhaps a new chapter for the FAQ?
MLPs and RBFs are universal approximators. Users should have
software for both. For most problems either one will work.
So, as far as getting results, choosing which one is not a
big deal.
However, I neither enourage the blind "black box" approach
nor presentation of results without interpretaion. No
statistical technique should be used without considering
whatever a priori information is available.
I consider data visualizations as part of the "a priori"
info. For a beginner my advice is
1. Find some traditional demo data (see the FAQ)
2. Visualize the data
3. Design both MLPs and RBFs
4. Compare
Hope this helps.
Greg
As far as visualization, y=f(x,y) is about the limit of my spacial
dimensions, 2 at a time.
I have no idea how to visualize multi dimensional data.
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I gave a list several replies ago.
| Quote: | I could amass some statistics based on Euclidean distances within my
population, but I question its usefullness.
There may be ways to project onto a plane....(?) How? Which plane?
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Reread my post.
| Quote: | Lots of speculation but nothing useful - not my area - but sounds like
that are standard methods to use here.
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Most statistical software has them. Got to sci.stat.* and ask for
free or cheap software references that yield data visualization plots.
Hope this helps.
Greg |
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