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MISEP-- Linear and Nonlinear ICA Based on Mutual Information

MISEP-- Linear and Nonlinear ICA Based on Mutual Information
MISEP-- Linear and Nonlinear ICA Based on Mutual Information

Journal of Machine Learning Research4(2003)1297-1318Submitted10/02;Published12/03

MISEP–Linear and Nonlinear ICA Based on Mutual Information Lu′?s B.Almeida LUIS.ALMEIDA@INESC-ID.PT

INESC-ID,R.Alves Redol,9,

1000-029Lisboa,Portugal

Phone:+351-213100246

Fax:+351-213145843

Editors:Te-Won Lee,Jean-Franc?ois Cardoso,Erkki Oja and Shun-Ichi Amari

Abstract

Linear Independent Components Analysis(ICA)has become an important signal processing and data analysis technique,the typical application being blind source separation in a wide range of signals,such as biomedical,acoustical and astrophysical ones.Nonlinear ICA is less developed, but has the potential to become at least as powerful.

This paper presents MISEP,an ICA technique for linear and nonlinear mixtures,which is based on the minimization of the mutual information of the estimated components.MISEP is a generalization of the popular INFOMAX technique,which is extended in two ways:(1)to deal with nonlinear mixtures,and(2)to be able to adapt to the actual statistical distributions of the sources,by dynamically estimating the nonlinearities to be used at the outputs.The resulting MISEP method optimizes a network with a specialized architecture,with a single objective function:the output entropy.

The paper also brie?y discusses the issue of nonlinear source separation.Examples of linear and nonlinear source separation performed by MISEP are presented.

Keywords:ICA,Blind Source Separation,Nonlinear ICA,Mutual Information

1.Introduction

Linear Independent Components Analysis(ICA)and linear Blind Source Separation(BSS)have become,in the last years,relatively well established signal processing and data analysis techniques (good overviews can be found in work by Lee et al.,1998;Hyvarinen et al.,2001).Nonlinear ICA and nonlinear BSS,on the other hand,are techniques that are still largely under development,and have the potential to become rather powerful tools.Some work on nonlinear ICA has already been published(Burel,1992;Deco and Brauer,1995;Marques and Almeida,1996;Yang et al.,1998; Marques and Almeida,1999;Palmieri et al.,1999;Valpola,2000;Almeida,2000a;Harmeling et al., 2001;Martinez and Bray,2003).

In this paper we consider ICA as the problem of transforming a set of patterns o(vectors of size n,often called observations),whose components are not statistically independent from one another,into patterns y=F(o)whose components are as independent from one another as possible. In linear ICA the transformation F is restricted to be linear,while in nonlinear ICA there is no such restriction.In blind source separation one further assumes that the observations are the result of a mixture of statistically independent sources,s i,i.e.o=M(s),s i being the components of s. The purpose of BSS is the recovery of the sources from the observations,and ICA is one of the most commonly used techniques for performing this recovery.Once again,one distinguishes linear

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BSS,in which the mixture M is assumed to be linear,and nonlinear BSS,where there is no such assumption.In this paper we deal with linear and nonlinear ICA in the so called square case,in which the numbers of components of s,o and y are assumed to be the same.

An important ingredient of most ICA methods,both linear and nonlinear,is a measure of the mu-tual dependence of the extracted components y i.This measure is sometimes called contrast function (Comon,1994).Many ICA methods are based on the minimization of such a measure.Linear ICA is a relatively constrained problem,and therefore linear ICA methods do not need to be based on strict dependence measures.For example,some of these methods,which give rather good results in appropriate situations,are based only on cumulants up to the fourth order(Cardoso and Souloumiac, 1996;Hyv¨a rinen and Oja,1997).Nonlinear ICA,on the other hand,is rather unconstrained,and normally demands a good dependence measure.Some of the dependence measures that have been proposed are based on a quadratic“error”between probability densities(Burel,1992),on moments of all orders(Marques and Almeida,1996),on Renyi’s entropy(Marques and Almeida,1999)or on the mutual information of the estimated components(e.g.Deco and Brauer,1995;Taleb and Jutten, 1997;Almeida,2000a,b).The latter,the mutual information(MI)of the estimated components,is rather appealing as a dependence measure for several reasons.First of all,it is a strict dependence measure:it is always non-negative,and is zero only if the estimated components are statistically independent.We shall outline two other reasons for its appeal ahead.

The mutual information of the components of the vector y is de?ned as

H(y i)?H(y)

I(y)=∑

i

where H denotes Shannon’s entropy,for discrete variables,or Shannon’s differential entropy,H(y)=? p(y)log p(y)d y,for continuous variables,and p(y)denotes the joint probability density of the components of y.1This measure has the appealing property of being based on Shannon’s entropy, which is the most meaningful entropy measure in a large variety of situations.It also has the prop-erty of being insensitive to invertible transformations of the components.More speci?cally,if we de?ne z i=ψi(y i),where theψi are invertible,then I(z)=I(y).This property is intuitively sound, and is of great use in the derivation of algorithms,such as MISEP,based on the minimization of the mutual information,as we shall see ahead.Mutual information has been used as a criterion for ICA in several different ways(for examples of its use in linear ICA see work by Amari et al.1996; Haykin and Gupta1999;Almeida2000b;Taleb and Jutten1997;for nonlinear ICA examples see work by Yang et al.1998;Deco and Brauer1995;Almeida2000a).This paper’s central topic is the method of Almeida(2000a,b).

The use of mutual information as an ICA criterion raises dif?culties,that have been circum-vented by different authors in different ways.From(1)we see that the computation of the mutual information requires the knowledge of both the joint and the marginal distributions of the estimated sources.In practical situations,however,we usually have access only to a?nite set of mixture patterns o(the training set),from which we can obtain a?nite set of vectors of extracted compo-nents,y=F(o),given some candidate transformation F.The joint and marginal distributions of the components of y have to be estimated from this?nite set.

The need to estimate the joint density p(y)can be circumvented without resorting to approxi-mations,as described ahead.On the other hand,there is no known way of circumventing the need 1.We shall use the same notation,p(),to denote the statistical densities of all the random variables dealt with in this

paper.The argument used in the function will clarify which random variable is being considered.While this is a slight abuse of notation,it will help to keep expressions simpler and will not originate confusions.

MISEP–L INEAR AND N ONLINEAR ICA

to estimate the marginal densities p(y i),or some equivalent description of the marginal distribu-tions.One of the main differences among the various MI-based ICA methods is the way in which this estimation is dealt with.For example,Amari et al.(1996);Haykin and Gupta(1999);Deco and Brauer(1995)use truncated series expansions of the densities,estimated from the y patterns. The well known INFOMAX method(Bell and Sejnowski,1995),although originally based on a different reasoning,can be interpreted as assuming some given,a-priori marginal distributions for the y i,as we shall see ahead.A?rst extension to INFOMAX(Lee et al.,1999)makes a binary decision on the form of each of these distributions.A more general extension(Taleb and Jutten, 1997)estimates the score functions(which can be seen as alternate descriptions of the marginal dis-tributions)by means of multilayer perceptrons,using as optimization criterion the quadratic error between the true and estimated score functions.MISEP(Almeida,2000a,b),described in this paper, is also based on INFOMAX,but estimates the marginal distributions in a different way,based on a maximum entropy criterion.It has the advantages that(1)both the independent component analysis itself and the estimation of the marginal distributions are performed by the same network,optimized according to a single criterion,and(2)that it is not limited to linear ICA,but can deal with nonlinear mixtures as well.

There is an important difference between linear and nonlinear ICA that we should emphasize before proceeding.Under rather unrestrictive assumptions,linear ICA has essentially a single solu-tion,except for possible permutations and scalings of the components(Comon,1994)).This makes ICA one of the most important tools for performing linear blind source separation,since it essen-tially gives a guaranty of recovering the original sources.In the nonlinear case,however,it can be easily shown that ICA has an in?nite number of solutions that are not related in any simple way to one another(Darmois,1953;Hyvarinen and Pajunen,1999;Marques and Almeida,1999).In a nonlinear BSS problem,an ICA technique,if used alone,can’t give any guaranty of recovering the original sources.This has led some people to think that nonlinear source separation was unsolvable, or at least that it couldn’t be solved by means of ICA techniques.This is a wrong view.What we have said means that nonlinear BSS is an ill-posed problem.But many other ill-posed prob-lems exist,with which we deal with relative ease.For example,probability density estimation,the training of classi?ers or the estimation of nonlinear regressors are ill-posed problems that we nor-mally don’t consider unsolvable.The solution to the ill-posedness is of the same kind in all cases: further knowledge has to be used.Fortunately,this knowledge often exists in practical situations. Frequently,this knowledge takes the form of some regularity assumption about the solution,and is applied to the problem through a suitable form of regularization.The same applies here,and we shall see in this paper several examples of nonlinear source separation performed through ICA.

A complementary note concerns the kinds of indeterminacies that we should expect in nonlinear blind source separation,even if proper regularization is used.In linear BSS these indeterminacies are just permutation and scaling.Here the permutation ambiguity remains,but we should expect the scaling ambiguity,which has the form y i=a i s i with arbitrary scale factors a i,to be extended to an ambiguity of the form y i=f i(s i),with arbitrary invertible nonlinear functions f i.In fact,if the sources s i are independent,so are f i(s i),and an ICA-based criterion can’t distinguish among them. Prior information may,or may not,help us to avoid these nonlinear transformations of the sources, depending on the speci?c situation.

The organization of this paper is as follows:Section2derives the MISEP method,by extending INFOMAX in the two directions indicated above.Results of linear and nonlinear ICA and BSS are

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presented in Section 3.Section 4brie?y discusses the issue of separability of nonlinear mixtures,and Section 5presents the paper’s conclusions.

2.The MISEP Method

In this section we start by brie?y reviewing INFOMAX,and then proceed to examine the MISEP method,both in its theoretical basis and in its implementation.

2.1INFOMAX –Brief Review

INFOMAX was originally presented as a maximum information preservation method,but can also be seen as a maximum likelihood one (Cardoso,1997)or as an MI-based one.It is this MI-based interpretation that interests us in this paper.

In Figure 1we show the form of the network that is used by INFOMAX.The separation function F ,being linear,performs just a product by a matrix.The ψi blocks are auxiliary,being used only during training.Each of them outputs a nonlinear,increasing function of its input,with values in

[0,1],i.e.z i =ψi (y i )with z i ∈[0,1].The system is trained by maximizing the output entropy H (z ).

F

o 1 ψ 2 o 2

ψ 1 y 1 y 2 z 1 z 2 Figure 1:Structure of the ICA systems studied in this paper.In the INFOMAX method the nonlin-

earities ψi are ?xed a-priori.In the MISEP method they are adaptive,being implemented by multilayer perceptrons.The ?gure illustrates the two-component case,but extension to a larger number of components is straightforward.

Since each z i is related to the corresponding y i by an invertible transformation,we have I (y )=I (z ).Assume now that we choose for each nonlinearity ψi the cumulative probability function (CPF)of the corresponding component y i .Then z i will have a uniform distribution in [0,1]and H (z i )=0.Consequently,

I (y )=I (z )

=∑i H (z i )?H (z )

(1)

=?H (z ),

Maximization of the output entropy H (z )will therefore be equivalent to the minimization of I (y ),the mutual information of the estimated https://www.wendangku.net/doc/7617776647.html,MAX can therefore be viewed as min-imizing this mutual information,wtih an a-priori choice of the estimated distributions of the com-ponents,performed through the choice of the ψnonlinearities.These should approximate the CPFs of the actual components as closely as possible.However,as said above,linear ICA is a rather con-strained problem,and therefore INFOMAX usually performs well even if the output nonlinearities

MISEP–L INEAR AND N ONLINEAR ICA

are only crude approximations to these cumulative functions.For example,it is known that logistic sigmoids can be used as nonlinearities for most unskewed,supergaussian distributions(Bell and Sejnowski,1995).

2.2MISEP–Theoretical Basis

MISEP uses the same basic network structure as INFOMAX(Figure1).But since it is also to be applicable to nonlinear mixtures,the separating block F shall now be nonlinear,with the capability to implement a relatively wide class of functions.We have often used a multilayer perceptron(MLP) to implement this block,but in some cases we’ve used a radial basis function network instead.

MISEP should be able to deal with a wide class of statistical distributions of the y i components. On the other hand,it needs to have good estimates of their CPFs,to be able to perform nonlinear ICA,which is much less constrained than its linear counterpart.We have therefore implemented theψnonlinearities by means of MLPs,which adaptively learn the CPFs during the training(again, other kinds of nonlinear blocks could have been used).

The F andψblocks,taken together,form a nonlinear network with a specialized architecture. The purposes of the training of the two kinds of blocks are very different:We want the F block to yield components that are as independent as possible,i.e.to minimize I(y),while eachψblock should approximate the CPF of its input as closely as possible.

We have already seen,in our analysis of INFOMAX,that the minimization of I(y)can be trans-lated into the maximization of the network’s output entropy.A key idea in MISEP is understanding that this same criterion will lead the output nonlinearities to approximate the desired CPFs.This is due to the fact that maximizing the output entropy will tend to lead the distribution of each z i to be uniform in[0,1],since the uniform distribution is the one which has maximum entropy in a?nite interval.More speci?cally,from(1)we can write

H(z i)=H(z)+I(y).

i

If we assume,for the moment,that the distributions of the y i are kept?xed,we see that maximizing H(z)will lead to the maximization of each of the marginal entropies H(z i),since each of them depends on a separate set of parameters(because theψi networks are separate from one another). Maximizing H(z i)will lead the distribution of z i to approach the uniform distribution in[0,1],as said above,and will leadψi to approach the CPF of y i,as desired,ifψi is constrained to be an increasing function with values in[0,1](we shall discuss later how to implement this constraint).

During a training procedure,the distributions of the y i will not remain?xed.One might wonder whether this would invalidate the reasoning given above.Note,however,that(1)the whole network will be trained by maximization of a single objective function(the output entropy),and therefore there is no danger of instability in the training,assuming that a well designed optimization procedure is used,and(2)when the training procedure approaches a maximum of the entropy and slows down, the statistics of the y i will change very slowly,and the reasoning above will be valid.Therefore,at convergence,theψi functions will be estimates of the CPFs of the components y i.

2.3Implementation

We’ll start by discussing how to implement the constraints on theψfunctions,and shall then de-scribe how to train the whole network using the output entropy as objective function.

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2.3.1C ONSTRAINING THEψMLP S

The MLPs that implement theψfunctions have to be constrained to yield increasing functions with

values in[0,1].There are several possibilities for doing this.Here we shall only describe the one that

we have found to be most effective(for other possibilities,and for a discussion of their drawbacks,

see work by Almeida,2000a,b,2001,2002).To implement these constraints we use,in theψMLPs,

hidden units with sigmoids which are increasing,with values in[0,1],and we use linear units at the

outputs.We normalize the Euclidean norm of the vector of weights leading into each output unit to √h,h being the number of hidden units connected to that output unit.With non-negative weights, 1/

this guarantees that the outputs will be in[0,1].If we use non-negative weights throughout these

networks,they will also be guaranteed to yield non-decreasing functions.In practice we have found

that instead of strictly enforcing non-negativity of the weights,it is preferable to enforce it in a soft

way:we initialize all weights with positive values,and the training procedure by itself tends to

keep them all positive,because a negative weight,among positive ones,would decrease the output

entropy.We have occasionally encountered negative weights during the training,but these normally

revert to positive values by themselves in a few iterations.

In actual implementations we have used,in the hidden layer,sigmoids with values in[?1,1].

This yieldsψfunctions with values in[?1,1],which are estimates of the CPFs re-scaled to this

interval.This still performs minimization of I(y),as can easily be checked.The use of these

sigmoids has the advantage of resulting in a faster training.

2.3.2M AXIMUM E NTROPY T RAINING

The whole network of Figure1is to be trained through maximization of the output entropy.This

is the same criterion that is used in INFOMAX,and the?rst steps in the derivation of our training

procedure closely follow those of INFOMAX.We use gradient-based optimization.The output

entropy can be written as

H(z)=H(o)+ log|det J|

where J=?z/?o is the Jacobian of the transformation performed by the network,and the angle

brackets denote expectation.The term H(o)doesn’t depend on the network’s parameters,and can

be omitted from the optimization.The remaining term,which is a statistical mean,will be approxi-

mated by the empirical mean,i.e.by the mean computed on the training set,

log|det J| ≈1K K∑

log det J k =E,

k=1

where J k denotes the value of J for the k-th training pattern,and K is the number of training patterns.

E will be our objective function.

Here we have to depart from the INFOMAX derivation,because our network is more general

than the one used there.We want to use a gradient method to maximize E,which is a function of

the Jacobians J k.Direct computation of the components of the gradient is very cumbersome and

inef?cient.However,from the theory of neural networks we know that,for any network,back-

propagation is a simple and ef?cient method to compute the gradient of a function of its outputs

relative to its weights(see,for example,work by Almeida,1997,especially Section C.1.2.3.1).The

network of Figure1doesn’t output the Jacobians,which are what our objective function depends

MISEP–L INEAR AND N ONLINEAR ICA

on.Therefore,to be able to ef?ciently compute the gradient of E,we need to?rst?nd a network that computes J k,and then backpropagate through that network.

The network that computes the Jacobians is essentially a linearized version of the network of Figure1.To illustrate how to obtain such a network,we shall assume speci?c structures for the F andψblocks.We’ll assume that the F block has a single hidden layer of sigmoidal units,linear output units,and no direct connections between input and output units.We’ll assume a similar structure for each of theψblocks:a single hidden layer of sigmoidal units,a single linear output unit,and no direct connections between input and output units.

A network for computing J k,assuming this structure,is shown in Figure2.The upper part of the?gure shows the network of Figure1,drawn in a different way.The A block represents the weight matrix of the hidden layer of F,and its output is the vector Ao(we’ll denote both the block and the corresponding matrix by the same letter,since this does not cause any confusion; we’ll also assume that o is augmented with a component o0=1,and that the matrix A includes a corresponding column with the bias terms of the hidden layer units;the same is assumed for vector y and matrix C,which appear later).The leftmostΦblock applies the hidden layer’s sigmoids to each of the components of Ao.Its outputs are the activations of the units of the hidden layer of F. Block

B corresponds to the weight matrix of the output units of F,and its output is y.Theψi blocks, taken together,form an MLP with a single hidden layer and with linear output units.This MLP is special,in that the weights corresponding to connections between units of differentψi blocks are always zero,but otherwise it is similar to F in structure.It is represented,in Figure2by the upper C,rightmostΦ,and D blocks.

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rightmostΦblock.To compute the sigmoid derivatives,the twoΦ′blocks need to receive the input activations of the corresponding hidden units from the upper part.This information is transferred through the gray arrows.

The output of the lower part of the network is the Jacobian of the transformation performed by the upper part(for the speci?c observation pattern being input at o),and is given by

J=DΦ′r CBΦ′l A,

whereΦ′r andΦ′l denote,respectively,the rightmost and leftmostΦ′diagonal matrices of Figure2.

Once we have a network that outputs the Jacobian,the computation of the derivatives of the ob-jective function relative to the network’s weights essentially amounts to a backpropagation through this network.There are still a few details that are worth emphasizing,however.

The input to the backpropagation is made into the lower part of the network,and consists of

?E

= J?1 T.

?J

Nothing is input into the upper part,because E doesn’t depend on z,i.e.?E/?z=0.

The backpropagation must be performed along all of the network’s paths.This means that there will be backpropagation along the gray arrows into the upper part,and this propagation will proceed backward through the upper part.Backpropagation through most blocks is rather straightforward, but theΦ′ones are somewhat unusual.Figure3-a)shows a unit of one of these blocks,propagating in the forward direction.It is governed by

h i j=φ′(s i)g i j,

where g i j denotes a generic input into the block from the left arrow,s i is the corresponding input from the gray arrow,and h i j is the corresponding output towards the right arrow.The backward propagation is governed by the partial derivatives

?h i j

=φ′(s i)

?g i j

?h i j

=φ′′(s i)g i j.

?s i

The backpropagation unit is therefore as depicted in Figure3-b),where each box denotes a product by the indicated value.Note that since the forward unit has two inputs,the backward unit has two outputs,one leading left in the lower part of Figure2and the other leading upward along the gray arrow.

All the network’s weights,except the hidden units’biases,are shared by the upper and lower parts of the network.Since the lower part is linear and propagates matrices,it can be seen as n identical networks,each one propagating one of the columns of the identity matrix.Therefore the lower part’s weights can also be seen as being shared among these n networks.The normal procedure for handling shared weights should be used:the partial derivatives relative to all the weight’s instances are added,and the sum constitutes the partial derivative relative to the shared weight.

We should note that the method for computing the gradient of E that we have presented,despite having been described in detail for a speci?c network structure,is in fact rather general,being

MISEP–L INEAR AND N ONLINEAR ICA

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Figure4:Bottom:

Figure5:speech mixture.The was used,although it training.

Figure6network’s output by theψblocks.we used had a somewhat probability function.

Figures8-11noise.Note the rather blocks.

With two able to per-form a good subgaus-sian,bimodal to the absolute a local min-

MISEP–L INEAR AND N ONLINEAR ICA

Figure6:speech

(note the

set. Figure7:Top:noise.

a re-scaling

of the

imum of the13),and sometimes to14).Local optima are a when there is more methods can converge to

3.2Nonlinear ICA

This section gives examples of nonlinear ICA tests.We?rst present several examples using two-component mixtures,and then a test with a four-component mixture.To illustrate the versatility of the MISEP method,the same network was used in all of the two-component cases.The F block had20arctangent hidden units,10of which were connected to each of the block’s output units.It also had direct connections between input and output units,to be able to perfectly implement linear

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Figure8:Separation of a supergaussian and a subgaussian signal.Top:source signals.Middle: mixtures.Bottom:separated signals.Samples are shown as unconnected dots for better

visibility of the bimodal character of the noise.

Figure9:Scatter plots of the separation of a supergaussian and a subgaussian signal.Left:source signals.Right:mixtures.

separation,if necessary.Eachψblock had a single hidden layer with two arctangent units,and a linear output unit.Each training set had1000mixture vectors.

Figure15shows the separation of a nonlinear mixture of two speech signals,which are super-gaussian.The mixture was of the form

o1=s1+a(s2)2(2)

o2=s2+a(s1)2(3) With the value of a that was used,the signal to noise ratio(SNR)of o1relative to s1was7.8dB, and the SNR of o2relative to s2was10.4dB.After nonlinear separation,the SNR of y1relative to s1 became16.4dB and the SNR of y2relative to s2was17.4dB.The average improvement was of7.8 dB.Linear ICA,on the other hand,did not yield any improvement in the components of y,relative to those of o.This was expected:the speci?c mixture that was used had no“linear part”,as can be seen both from the mixture equations and from the scatter plot,Figure15-a).This kind of mixture was chosen speci?cally to evaluate the nonlinear capabilities of the method,since the linear part of the separation was known to be relatively easy to handle.

MISEP–L INEAR AND N ONLINEAR ICA

Figure10:Left:sepa-

distribution). Figure11:by the

ψof the CPFs, Figures16a subgaus-sian,and of two one source is multimodal,may get trapped.

In a larger

(sources3and the form

[s i s j+(s j)2].

o i=s i+a i∑

j=i

Figure19gives examples of scatter plots of the mixture components.Note that in a4-dimensional distribution,pairwise scatter plots don’t always give a full idea of the distribution.For example, in the center and right-hand plots of Figure19the supergaussian components appear somewhat “fuzzy”because these are projections from a4-dimensional space into a2-dimensional one.In the 4-dimensional space the supergaussian components remain as sharp as the corresponding sources.

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Figure12:Separation of the mutual

plot of outputs of theψnets.

Figure13:Separation of the mutual in-formation.plot of outputs of

theψnets estimated by theψ

nets.

The a i coef?cients that was clearly visible(and that is best for the method to still be able to of the degree of nonlinearity that not simply ICA.

The network that the one used in the previous tests.Of40hidden units, divided into four sets It also had direct connections between input and output units.Each of the fourψblocks had two hidden units.Figure 20shows scatter plots of the extracted components.We see that the system was able to recover the sources quite well,although not perfectly.

Regarding convergence speed,the two-source nonlinear ICA tests,with batch-mode training and with training sets of1000patterns,normally converged in less than400epochs.On a400MHz Pentium processor running a Matlab implementation of the method,these400epochs took less than 4minutes.The four-source results were obtained in1000epochs,also with a training set of1000 patterns.These1000epochs took less than20minutes on the same processor.

MISEP–L INEAR AND N ONLINEAR ICA

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true

BSS

are

MLP

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Figure

Figure

are,for

within a

A

kinds of

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MISEP–L INEAR AND N ONLINEAR ICA

Figure18:Separation of a nonlinear mixture of four signals,two subgaussian and two supergaus-sian.Left:scatter plot of the two subgaussian sources(#1and2).Center:scatter plot

of a subgaussian and a supergaussian source(#1and3).Right:scatter plot of the two

supergaussian sources(#3and4).

Figure19:Separation of a nonlinear mixture of four signals,two subgaussian and two supergaus-sian.Left:scatter plot of mixture components1and2.Center:scatter plot of mixture

components1and3.Right:scatter plot of mixture components3and4.

with the present form of MISEP(although it may become separable with future improvements). In this unseparable example the two sources are supergaussian,and the mixture is quadratic,as in(2)and(3),but the a coef?cient is given a large value.The scatter plot of the mixture,as well as the scatter plots of the extracted components at various stages along the optimization,are shown in Figure21.In somewhat loose terms,we can say that the system wrongly aligned the two outer“half-branches”of the sources with each other,these having become the horizontal extracted component.The two inner half-branches ended up being almost merged together,and essentially formed the vertical extracted component.Although the original sources are strongly mixed in the extracted components,these components are almost independent from each other after the2000 epochs shown(and the objective function was still slowly improving at that point).

This an example of a case in which ICA was approximately achieved,but source separation was not.It is a case where the mixture was,in our terms,too unsmooth,deviating too much from a linear one.With this mixture,MISEP consistently failed to separate the sources.On the other

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Figure20:Separation of a nonlinear mixture of four signals,two subgaussian and two supergaus-sian.Left:scatter plot of extracted components1and2.Center:scatter plot of extracted

components1and3.Right:scatter plot of extracted components3and4.

Figure21:A case in which ICA was achieved,but source separation was not.The leftmost scatter plot shows the mixture components.Then,from left to right,the scatter plots show the

extracted components after45,150,330and2000training epochs,respectively. hand,in the cases reported in Section3,the method consistently was able to perform separation,5 when tried with different initializations of the MLP’s weights and,in the cases where sources were randomly generated,also when tried with different realizations of the sources,obeying the same source distributions.

A question that may asked regarding the structure of Figure1(and one that was actually asked by one of our anonymous reviewers),is why theψblocks are needed.It is true that,in principle,one could simply use the F block,with its outputs bounded within a hypercube,and maximize its output entropy.A uniform distribution of y in that hypercube would result,if the F block were?exible enough,and therefore the y i would be independent from one another.

This issue is related to the smoothness one,and that is why it is discussed here.The key phrase in the above reasoning is“if the F block were?exible enough.”Excluding situations in which all the sources have close-to-uniform distributions,the F block will have to perform a rather unsmooth transformation to?t the extracted components uniformly into a hypercube.Given the above discussion on the need of the smoothness constraint for achieving source separation,we see that we can’t expect this unsmooth F to be able to recover the original sources in such a situation, 5.In the situations involving two bimodal sources,separation was always achieved when the system converged to

the absolute minimum of the mutual information.However,the system sometimes converged to local minima,as previously mentioned.

MISEP–L INEAR AND N ONLINEAR ICA

even though it will yield independent components.By separating the unmixing F block from the ψones(which have the purpose of turning each component into a uniformly distributed one),we can keep a smooth F(even applying explicit regularization to it if appropriate),while allowing the ψblocks to perform the transformation of the y i into uniformly distributed variables,these blocks being allowed to be rather unsmooth if necessary.The structuring of the network into separate F andψblocks thus gives it a much greater ability to perform nonlinear source separation.

5.Conclusions

We have presented MISEP,a method for performing ICA by minimizing the mutual information of the estimated components.Some of the features of the method are:

?It is able to perform both linear and nonlinear ICA.

?It adapts to the statistical distributions of the estimated components.It can therefore deal with

a wide range of source distributions.

?It uses a single network to perform both the ICA operation and the estimation of the distribu-tions of the sources.This network is optimized according to a single objective function,the output entropy.

We have presented experimental results that show the capability of MISEP to perform both linear and nonlinear ICA.We have also shown examples in which blind source separation was performed on relatively smooth nonlinear mixtures,using this smoothness as an assumption to handle the ill-posedness of nonlinear source separation.The smoothness regularization that we used in the experiments presented in this paper was only the one implicitly performed by MLPs with small initial weights and with relatively few hidden units.

MISEP is not the only currently available alternative for nonlinear ICA/BSS.Some other meth-ods that deserve mention are those described by Yang et al.(1998);Marques and Almeida(1999); Valpola(2000);Harmeling et al.(2001);Martinez and Bray(2003).We shall not make detailed comparisons with these methods here.But we wish to emphasize that we believe that,among the currently available nonlinear ICA/BSS methods,MISEP is the one of the very few that simultane-ously have the following qualities:

?having a relatively simple implementation,

?being quite?exible in terms of the kinds of nonlinear separating networks that it can use,?being able to handle a large variety of source distributions,

?not needing to rely on temporal structure of the sources,

?being able to easily incorporate various forms of regularization,

?being relatively ef?cient in computational terms.

On the other hand,it is clear from the discussion and the examples presented in this paper that MISEP,in its present form,can only perform source separation when the nonlinearities involved

A LMEIDA

in the mixture are not too strong.In this respect,especially the method of Harmeling et al.(2001) seems to be more powerful(although it may have drawbacks in some other aspects).

Many issues remain open,regarding the MISEP method,and will be addressed in future work. Some of them are:

?To further study the method in blind and semi-blind source separation settings,clarifying the kinds of mixtures that can be separated,the kinds of prior information that can be used,and the role of regularization.

?Finding ways to measure the quality of the separation that is obtained.The measures currently used for linear ICA will probably not be appropriate,due to the possibility that the separated components are nonlinearly transformed relative to the original sources,as discussed in the end of Section1.

?To make the method able to deal with stronger nonlinearities.

?To study the behavior of the method with larger numbers of sources and with noisy observa-tions.It can be mentioned that preliminary results with up to10sources have already been obtained.These will be reported in a forthcoming paper(Almeida,2003b).

?To study the extension of the method to under-and over-determined situations,to non-stationary and non-instantaneous mixtures,etc.

?The application of the method to real-life problems.An application to a real-life nonlinear image separation problem has already started to show promising results,although these are still in too early a stage to be reported here.

Acknowledgments

The author wishes to acknowledge the anonymous reviewers for their comments,which helped to signi?cantly improve the quality of this paper.This work was partially supported by Praxis project P/EEI/14091/1998and by the European IST project BLISS.

References

L.B.Almeida.Multilayer perceptrons.In E.Fiesler and R.Beale,editors,Handbook of Neural Computation.Institute of Physics,Oxford University Press,1997.Available electronically at http://neural.inesc-id.pt/?lba/papers/AlmeidaHNNC.ps.zip.

L.B.Almeida.Linear and nonlinear ICA based on mutual information.In Proc.Symp.2000on Adapt.Sys.for Sig.Proc.,Commun.and Control,Lake Louise,Alberta,Canada,2000a.

L.B.Almeida.Simultaneous MI-based estimation of independent components and of their distri-butions.In Proc.Second Int.Worksh.Independent Component Analysis and Blind Signal Sepa-ration,pages169–174,Helsinki,Finland,2000b.

国际汉语教师资格证面试真题回忆及问题集锦

国际汉语教师资格证面试真题回忆 一、 英语问题: 1 小学汉语课上,一个学生突然对你说“老师!我讨厌你!你给了那么多作 业balabala”,你怎么办? 汉语问题 1:司马光砸缸的故事,俄罗斯孔院的学生们觉得司马光只是勇敢,并不聪明~因 为石头砸缸,可能伤害了缸里的孩子~作为教师,你应该怎么办? 汉语问题 2:学生问问题,汉语老师说汉语里就这样说,就这样记。请评价。 英语问题:一个阿富汗的女孩在中国,因为戴了头巾,处处引起围观~她受不了中国人的 注目礼,迫于压力放弃汉语学习回国了,汉语老师应该怎么办? 二、 中文问题1:一个学生老是迟到捣乱,你批评了他,并要他道歉第二天他的妈妈来了, 说迟到是因为她有事造成的,需要你道歉。 中文问题2: .作为一个对外汉语老师你很忙很忙,你如何提升生自己? 英文问题1:一个学生课堂上突然哭了怎么办? 英语问题2:中国四大发明之一的火药害死了很多人怎么解释。 三、 中文问题1:在宗教国家,做包子,没放猪肉,但还是有老师不满意,因为她是素食主 义者,中国教师知道后觉得自己费力不讨好,很伤心。怎么解决? 中文问题2:小李出国后做助教只能批改作业做一些教辅工作自认为大材小用如何看待 这个问题怎么解决 英语问题1:你的班级里一个七岁的孩子取笑其他的孩子,大家都开始起哄,你认为是 为什么?应该怎么解决? 英语问题2:中国老师出国后下班时间呆在学校上网备课引起其他老师不满为什么怎么 解决? 试讲的语法点是:试讲是:动词重叠了的用法有的......有的 四、 中文问 :1:一个是一个老师去外国教学,教学对象年龄,水平参差不齐,有的学生对汉 语有热情,有的对汉语不感冒,校长也不信任他,校长还认为开展汉语活动没有必要,但是你认为很重要,问要是你是这位老师你会怎么办。 中文问题2:某老师很擅长活跃课堂气氛,其他老师向他请教,但是该老师总是在公开 场合批评其他老师,引起其他老师的反感,久而久之不愿意和他接触,期末考试之后,他发现其他老师带的班级和他带的班级成绩差不多,他该怎么办? 英语问题1:是你班的同学总是爱迟到,全班必须等迟到的同学来了之后才能上课,你 该什么办。 英语问题2:龙在中西方的意思不同,你如何在跨文化交际中给同学们讲解。 语法点:除了......以外,动词的重叠,条件复句只要就,假设复句要是就。 问题集锦 1、请问,你如何教学生钱数的表达? 2、请问,“这件衣服是紫的。”和“这件衣服是紫色的。”一样吗? 3、请问,“这件衣服是蓝色。”正确吗? 4、如果你们班学生水平参差不齐,你如何开展你的教学? 5、你如何教声调? 6、如果你的学生只会简单的汉字,你怎么教他们组词? 7、美国人到华人家里做客,家里又爷爷奶奶,作为汉语教师,你会告诉他什么?

国际汉语教师证面试语法点总结

语法点总结 1. “是”字句:A是B a)表示事物等于什么或属于什么,在等于的句子中,A/B 可互换,此外不可互换。李白是这首诗的作者。b)表示事物的特征、质料、情况。孩子是双眼皮。 c)表示事物的存在。遍地是牛羊。 d)副词,放在谓语动词、形容词前,表肯定。 重读时表“的确、确实” ,不能省略(他的性格是变了。);不重读时表一般肯定,能省略。 2. 趋向动词:上下进出回过起vs 来去(13 个) 上来,上去,下来,下去,进来,进去,出来,出去,回来,回去,过来,过去,起来 3. 指示代词 a)这、那:这是近指,那是远指,二者并举指代众多的人或事物,是虚指(不图这不图那) b)每、各:是分指,每侧重个体相同的一面,各侧重不同的一面。某、另:指不确定的人或事物,某是不定指,另是旁指。 4. 语气词 a)的:表陈述。 b)了:表陈述(树叶黄了。);表祈使(别说话了。) c)呢:表陈述(我不辛苦,你才辛苦呢。);表疑问(去呢还是不去?) d)吧:表疑问(天晴了吧?);表祈使(我们走吧。) e)吗:表疑问(你去过北京吗?) f)啊:表陈述(他不去呀。);表祈使(来呀。);表疑问(谁呀?);表感叹(是他啊!) 5. 定语标记“的” a)音节上:单音节adj 做定一般不加(红花,绿叶)。 单音节n 做定一定加(人的性格,花的颜色)。 双音节的adj 但中心语是单音节的常加(黄河的水)。用不用都可以时,讲究音节的调整,看 读起来顺不顺口。 b)意义上:表领属,谁的,可加可不加(小明的书包,他姐姐) 定语是代词而中心语是和它有关的人或集体时,可不加)表性质,什么, 不加(世界地图,汉语词典) 描写说明,怎么样的,加(明亮的双眼)

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中国文化与跨文化交际习题 壹中外文化及跨文化交际基础 一、填空题 1.佛教传入中国后建立的第一座寺庙是位于洛阳的。 2.唐代着名书法家柳公权最擅长的字体是。 3.明代戏曲家汤显祖的影响最大的作品是。 4.明末清初来华欧洲传教士最早把孔子介绍到西方,今天“孔子”的英译是,即是保留了当时的译法。 5.在西汉武帝时期,儒生提出“罢黜百家,独尊儒术”,为儒家学说在后世的正统地位奠定了基础。 6.举行赏菊、登高、佩茱萸等礼俗活动的传统节日是。 7.唐僧玄奘所着记录他周游百余国经历的书名为。 8.中国少数民族创造了优秀的文化,与汉族早期长篇史诗不发达的情况不同,少数民族中往往流传着反映其早期历史的长诗,《嘎达梅林》就是族的着名史诗。 9.是明代修撰的最大的类书。 10.提出“知行合一”、“致良知”等主张的明代着名思想家是。 11.中国古代着名水利工程南北大运河是在时期开始修建的。 12.京剧的人物角色一般分为生、旦、、丑等四类。 13.被誉为“诗圣“的唐代着名诗人是。 14.洋务运动时期清政府创办的官方外语学校叫做。 15.唐代时期,日本派遣了大批留学生和学问僧来华学习,这些人在中文和日文中都被称为。 16.二十四节气歌谣里,“夏满芒夏暑相连”中的“满”指的是。 17.人们用“吴带当风”来形容唐代着名画家在人物画方面所取得的成就。 18.王勃《滕王阁序》中“秋水共长天一色”的前一句是。 19.中国的最高司法机关是。 20.1861年,清政府在北京设立了正式的处理外交事务的机构,叫做。 21.甲午战争失败后,清政府被迫与日本签订条约,割让台湾、澎湖列岛和辽东半岛等。

国际汉语教师资格证CETTIC人社部认证解读

对外汉语教师培训考试海外输出基地https://www.wendangku.net/doc/7617776647.html, 国际汉语教师资格证CETTIC人社部认证解读 教师节国际汉语教师受瞩目 九月十号举国共庆教师节,教师中还有一群特殊的群体也备受国人的尊重,那便是国际汉语教师,他们帮助外国友人更好的了解中国文化,更流利地说中文,从容在中国生活工作。24岁的林欢从小就对国际汉语教师的职业充满期待。她希望也能像许多优秀的前辈一样。 带着对中国历史文化的充分自信,在国内外结识不同国家的朋友,教授他们纯正的中文发音,告诉他们中国的风俗习惯,让他们理解中国厚德载物,热情好热的传统品德,从而更加地了解中国,与中国人成为互相信任的朋友。 林欢知道,想成为国际汉语教师,必须拥有相关的资质,才能获得老外的信任,更便于他人发现自己。同时资质越高,教学能力越优秀的人也能接触到更为有学问、出色的学生,在中国的博硕留学生,各个行业的精英人才,跨国公司的经理人、总裁等,与这些出色的人才教学相长,也能给教师们带来许多精彩的正能量和学识。 在一段时间的综合培训和考试后,林欣获得了国内对外汉语教师最高规格认证证书CETTIC 职业培训证书,CETTIC是对外汉语教学行业唯一的、合法的、国家级的资格证书。“老外比较相信专业的教学能力,拥有这个证书的汉语老师们都深受老外学员的喜欢。这个证书,代表的是一种能力的提升和被认可,在实际的工作中,这张证书也为我赢得了很多学生。”林欣分享经验时这样说道。 那么,持CETTIC证书的国际汉语教师们是如何脱颖而出的呢? 首先,国际汉语教师资格证CETTIC属于“全国1+N复合型人才培训项目”,由人力资源和社会保障部中国就业培训技术指导中心推出,是以最先进、最实用、最丰富高效的教学技术教授给汉语教师。对于汉语老师的学识思路和实践能力都能有极大的提高。 再者,CETTIC证书是职业教育法里规定的三个一级证书“学历证书、职业鉴定证(OSTA)、职业培训证书(CETTIC)”之一,具有法律效应,各大高校都悉知和认可,是求职和获得晋升的最佳证明,CETTIC证书已经成为行业的风向标,众多追求卓越教学能力的国际汉语教师们都志在必得。 要培养出这些对外汉语行业的精英,让他们更好地在国际舞台传播中国文化,发挥自身的激情和热量,当然需要行业顶尖的培训导师和培训方案。提到这个,汉语老师们自然地会想起业内一流的上海IPA对外汉语教师培养基地。学校受到国家认可,获得独家授权的CETTIC 培训资质,多年来已经培养了30000多位优秀的国际汉语教师,他们在各个平台,感受着跨国文化的碰撞,感受多元交流的快乐。 文章来源国际汉语教师资格证CETTIC认证学校儒森汉语 最近活动 权威导师对外汉语教学试听体验开始啦,试听截止到2014年9月30日,我校面向想当对外

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v1.0 可编辑可修改 2018 年对外汉语教师资格证考试真 题 第一部分 中国文化 一、填空题 2. “人性本恶”还是“人性本善”儒家中的孟子与荀子的观点存在着根本的对立, 持“人 3. 明代废爵 __著有《乐律全书》,他提出的“十二平均律”是对古代音乐理论的巨大贡献。 【答案】朱载堉 4. 封禅是古代帝王在泰山祭祀天地的仪式,历史上第一个封禅的皇帝是 _______ 。 【答案】 秦始皇 10. 历史上共有十个皇帝亲往曲阜祭祀孔子,最早的是 11. 汉族政权最早主动接受异族文化的重大事件是“ __________ 胡服骑射”。 【答案】赵武 灵王 12. 在殷墟王陵出土的 ______ 鼎,代表了殷商时期青铜器制作的最高水平。 【答案】司母 1. 自秦至今,我国一直沿用的行政区划单位是 答案】县 性本恶”观点的是 答案】荀子 5. 明清科考有三级考试,在北京外的各省城举行的考试称为 6. 被称为“最大的碑刻艺术博物馆”是西安 的 7. 现存最古老的宗祠是位于山西省闻喜县的 8. 被誉为“天下第一行书”的书法作品是《 9. 明代画家 __ 被称为“大写意”画家。 试”。 【答案】乡 ___ 。 【答案】碑林 ____ 祠。 【答案】裴氏 》。 【答案】《兰亭集序》 / 《兰亭序》 答 案】徐渭 答案】汉高祖 / 刘邦

13. 著名的蛋壳黑陶高柄杯是______ 文化时期制作的器物。【答案】龙山 14. 历史上,发生了四次大规模的灭佛事件,佛教称之为四次“法难”,而史学界简略地称 之为——“ ________ ”。【答案】三武一宗 15. 中国传统的祥瑞动物中,“四灵”指的是麟、龙、凤、龟,再加上__,则称为“五灵”。【答案】虎 16. 清代出现的以满族菜为主,沿袭明代宫廷风格的菜肴,被称为“ _____________ ”。【答案】满汉全席 17. 中国书画史上,将书、画、金、石结合在一起的杰出代表是清代书画家_______ 。【答案】吴昌硕 第二部分现代汉语 一、填空题 1.在语音四要素中,由外力大小或振幅大小决定的是。 2.在普通话语音系统中,“ bà(爸)”和“ pà(怕)”这两个音节起首辅音的发音区别在于。 3. “勇敢”中,“勇”的韵母属于呼。 4. 根据“六书”理论,“灯”字属于。 5. 从所记录的语言单位来看,现代汉字属于。 6. 在先秦汉语中,“兵”的基本义是“兵器”;而在现代汉语中,“兵”的基本义则是“ 7. 从句类角度来看,“谁也不可能两次踏进同一条河”这句话是。 8. 在现代汉语中,“香波”是外来词,所采取的翻译方法是。 9. 动态助词“着”的语法意义是。

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附件1: 《国际汉语教师证书》 考试大纲 (试行) 孔子学院总部/国家汉办 2014年10月

目录 一、《国际汉语教师证书》考试介绍 (1) (一)考试对象 (1) (二)考试用途 (1) (三)报考条件 (1) (四)考试时间和报名 (1) (五)考试内容和方式 (1) (六)成绩与证书 (2) 二、《国际汉语教师证书》考试范围与结构 (2) (一)考试范围 (2) (二)考试结构 (5) 三、考试样题 (6) (一)笔试 (7) (二)面试 (11)

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国际汉语教师资格证报考条件 国际汉语教师资格证全称就是“国际认证协会职业资格证书-------IPA国际注册汉语教师资格证”,历年称为“对外汉语教师资格证书”,此证书由美国IPA国际认证协会组织并颁发,考取此证书的人便有资格从事对外汉语教育事业,成为国际对外汉语教师。 IPA国际注册对外汉语教师资格考试是中华人民共和国人力资源和社会保障部授权举行的,认定具有从事对外国人进行汉语教学资格的考试。今后,只有具备对外汉语教师资格证,才能在国内和国外从事对外汉语教学。 IPA国际注册对外汉语教师资格证由IPA国际认证协会组织和颁发,学员可以报考中级和高级。建议如果学生的条件具备,可以直接考高级考试。 报考IPA国际注册对外汉语教师资格证的条件: A、专科以上学历,不限专业; B、外语水平证书:英语最低四级以上、雅思5.0、公共英语三级等(需在有效期内);其它的外语专业如:韩语、日语等小语种都可以; C、普通话二级甲等证书(此证书由上海语委培训和颁发,每个月都有培训和考试) IPA国际注册对外汉语教师资格证这个证书在国外认可吗? 1、IPA国际注册对外汉语教师资格证唯一获得中国驻美国大使馆的全面认证,并由中国使领馆代表签字。 2、IPA国际注册对外汉语教师资格证获得国家人事部的认可。学员可申请获得国家人事部企业经营管理人才库资格证书。 3、IPA国际注册对外汉语教师资格证获得了美国联邦政府的全面认可,并得到美国国务卿的签字。 4、IPA国际注册对外汉语教师资格证获得了美国教育部的认可,并得到当地政府教育部和法律部门的认可。

IPA国际注册对外汉语教师资格证与出国留学工作 IPA国际注册对外汉语教师资格证是唯一获得中国驻美国大使馆的全面认证。凭借IPA国际注册对外汉语教师资格证,学员可申请获得中国驻美大使馆对学员的证书及学历鉴定,为出国留学及工作创造“护身符”。 国际认证协会International Profession Certification Association(简称IPA)是资质驻京际认证机构。是中国区唯一经美国国务院签印并由中国驻美国大使馆认证认可的国际认证协会。 目前赴外从事对外汉语教师工作的七种途径: 1. 中国与其他国家之间有合作项目,双方有协议,由中国按照对方要求派出人员; 2. 国家汉办与国外机构有协议,国家公派提供汉语教师, 3. 国外大学自己贴招聘启事,直接向国内招聘; 4. 还有部分是校际之间的合作交流项目; 5. 孔子学院招募志愿者。 6. 出国留学兼职做对外汉语老师,表现优秀者可以在当地大学或中学任教。 7.参加儒森汉语海外汉语教师输出项目出国从事兼职/全职对外汉语教师工作。

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目录

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