average

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K

(x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



−

|S

_m

|

µ _m



 optimal

prototype µ _m

=

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K

(x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



−

|S

_m

|

µ _m



 optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K

(x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



−

|S

_m

|

µ _m



 optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K (x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



−

|S

_m

|

µ _m



 optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K (x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



−

|S

_m

|

µ _m





optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K (x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



− |S

_m

|µ

_m





optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K (x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



− |S

_m

|µ

_m



 optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K (x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



− |S

_m

|µ

_m



 optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

Prototype Optimization

with

S ₁ , · · · , S _M

being a partition of

{x _n },

{S

₁

,··· ,S

min_M

;µ

₁

,··· ,µ

_M

} N

X

n=1 M

X

m=1

J x _n ∈ S m K kx _n − µ _m k ²

• hard to optimize: joint combinatorial-numerical

optimization

• two sets

of

variables: will optimize alternatingly

if

S ₁ , · · · , S _M fixed, just unconstrained optimization

for each

µ _m

∇

_µ

_mE

_in

= −2

N

X

n=1

J x _n ∈ S m K (x _n − µ _m )

=

−2







 X

x

n

∈S

m

x _n



− |S

_m

|µ

_m



 optimal

prototype µ _m

=

average

of

x n

within

S m

for given

S ₁ , · · · , S _M

, each

µ _n

‘optimally computed’ as

consensus

within

S _m

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically

(different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

:

say, as

k

randomly chosen

x n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

m

until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

:

say, as

k

randomly chosen

x n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

m

until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

:

say, as

k

randomly chosen

x n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m

until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

:

say, as

k

randomly chosen

x n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

:

say, as

k

randomly chosen

x _n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

: say, as

k

randomly chosen

x _n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

: say, as

k

randomly chosen

x _n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

: say, as

k

randomly chosen

x _n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

k -Means: the most popular

clustering

algorithm through

alternating minimization

Radial Basis Function Network k -Means Algorithm

k -Means Algorithm

use k prototypes instead of M historically (different from k nearest neighbor, though)

k -Means Algorithm

1

initialize

µ ₁ , µ ₂ , . . . , µ _k

: say, as

k

randomly chosen

x _n

2 alternating optimization

of E

_in

: repeatedly

1 optimize S

₁

, S

₂

, . . . , S

_k

:

each x

_n

‘optimally partitioned’ using its closest µ

_i

2 optimize µ

₁

, µ

₂

, . . . , µ

_k

:

each µ

_n

‘optimally computed’ as consensus within S

_m until

converge

converge: no change of S ₁ , S ₂ , . . . , S _k

anymore

—guaranteed as E

_in decreases

during alternating minimization

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

_n

),y

n

)}to get

β

4

return g_RBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform

—like

autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

_n

),y

n

)}to get

β

4

return g_RBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform

—like

autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

n

),y

n

)}to get

β

4

return g_RBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform

—like

autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

n

),y

n

)}to get

β

4

return gRBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform

—like

autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

n

),y

n

)}to get

β

4

return gRBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform

—like

autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

n

),y

n

)}to get

β

4

return gRBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform—like autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

n

),y

n

)}to get

β

4

return gRBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform—like autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

RBF Network: a simple (old-fashioned) model

Radial Basis Function Network k -Means Algorithm

RBF Network Using k -Means

RBF Network Using k -Means

1

run

k -Means

with k = M to get

{µ _m }

2

construct transform

Φ(x) from RBF (say, Gaussian) at µ _m Φ(x)

= [RBF(x,

µ ₁

),RBF(x,

µ ₂

), . . . ,RBF(x,

µ _M

)]

3

run

linear model

on {(Φ(x

n

),y

n

)}to get

β

4

return gRBFNET(x) =

LinearHypothesis

(β,

Φ(x))

•

using

unsupervised learning (k -Means)

to assist

feature transform—like autoencoder

•

parameters: M (prototypes), RBF (such as γ of Gaussian)

Radial Basis Function Network k -Means Algorithm

Fun Time

For k -Means, consider examples

x _n

∈ R

²

such that all x

_n,1

and x

_n,2

are non-zero. When fixing two prototypes µ

₁

= [1, 1] and µ

₂

= [−1, 1], which of the following set is the optimal S

₁

?

1

{x

_n

:x

_n,1

>0}

2

{x

n

:x

_n,1

<0}

3

{x

n

:x

_n,2

>0}

4

{x

n

:x

_n,2

<0}

Reference Answer: 1

Note that S

₁

contains examples that are closer to µ

₁

than µ

₂

.

Hsuan-Tien Lin (NTU CSIE) Machine Learning Techniques 18/24

Radial Basis Function Network k -Means Algorithm

Fun Time

For k -Means, consider examples

x _n

∈ R

²

such that all x

_n,1

and x

_n,2

are non-zero. When fixing two prototypes µ

₁

= [1, 1] and µ

₂

= [−1, 1], which of the following set is the optimal S

₁

?

1

{x

_n

:x

_n,1

>0}

2

{x

n

:x

_n,1

<0}

3

{x

n

:x

_n,2

>0}

4

{x

n

:x

_n,2

<0}

Reference Answer: 1

Note that S

₁

contains examples that are closer to µ

₁

than µ

₂

.

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Beauty of k -Means

k = 4

usually works well

with

proper k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Difficulty of k -Means

k = 2 k = 4 k = 7

‘sensitive’ to

k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Difficulty of k -Means

k = 2 k = 4 k = 7

‘sensitive’ to

k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

Difficulty of k -Means

k = 2 k = 4 k = 7

‘sensitive’ to

k and initialization

Radial Basis Function Network k -Means and RBF Network in Action

RBF Network Using k -Means

k = 2 k = 4 k = 7

reasonable performance with

proper centers

Radial Basis Function Network k -Means and RBF Network in Action

RBF Network Using k -Means

k = 2 k = 4 k = 7

reasonable performance with

proper centers

Radial Basis Function Network k -Means and RBF Network in Action

RBF Network Using k -Means

k = 2 k = 4 k = 7

reasonable performance with

proper centers

Radial Basis Function Network k -Means and RBF Network in Action

在文檔中 Machine Learning Techniques (ᘤᢈ) (頁 93-140)