Dimensionality reduction by learning an invariant mapping

Dimensionality Reduction by Learning an Invariant Mapping Raia Hadsell,Sumit Chopra,Yann LeCun

The Courant Institute of Mathematical Sciences

New York University,719Broadway,New York,NY1003,USA.

https://www.sodocs.net/doc/1e6226733.html,/～yann

(November2005.To appear in CVPR2006)

Abstract

Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional mani-fold so that“similar”points in input space are mapped to nearby points on the manifold.Most existing techniques for solving the problem suffer from two drawbacks.First,most of them depend on a meaningful and computable distance metric in input space.Second,they do not compute a“func-tion”that can accurately map new input samples whose re-lationship to the training data is unknown.We present a method-called Dimensionality Reduction by Learning an Invariant Mapping(DrLIM)-for learning a globally co-herent non-linear function that maps the data evenly to the output manifold.The learning relies solely on neighbor-hood relationships and does not require any distance mea-sure in the input space.The method can learn mappings that are invariant to certain transformations of the inputs,as is demonstrated with a number of https://www.sodocs.net/doc/1e6226733.html,parisons are made to other techniques,in particular LLE.

1.Introduction

Modern applications have steadily expanded their use of complex,high dimensional data.The massive,high dimen-sional image datasets generated by biology,earth science, astronomy,robotics,modern manufacturing,and other do-mains of science and industry demand new techniques for analysis,feature extraction,dimensionality reduction,and visualization.

Dimensionality reduction aims to translate high dimen-sional data to a low dimensional representation such that similar input objects are mapped to nearby points on a man-ifold.Most existing dimensionality reduction techniques have two shortcomings.First,they do not produce a func-tion(or a mapping)from input to manifold that can be ap-plied to new points whose relationship to the training points is unknown.Second,many methods presuppose the exis-tence of a meaningful(and computable)distance metric in

the input space.

For example,Locally Linear Embedding(LLE)[15]lin-early combines input vectors that are identi?ed as neigh-bors.The applicability of LLE and similar methods to im-age data is limited because linearly combining images only makes sense for images that are perfectly registered and very https://www.sodocs.net/doc/1e6226733.html,placian Eigenmap[2]and Hessian LLE[8] do not require a meaningful metric in input space(they merely require a list of neighbors for every sample),but as with LLE,new points whose relationships with training samples are unknown cannot be processed.Out-of-sample extensions to several dimensionality reduction techniques have been proposed that allow for consistent embedding of new data samples without recomputation of all samples[3].

These extensions,however,assume the existence of a com-putable kernel function that is used to generate the neigh-borhood matrix.This dependence is reducible to the depen-dence on a computable distance metric in input space.

Another limitation of current methods is that they tend to cluster points in output space,sometimes densely enough to be considered degenerate solutions.Rather,it is sometimes desirable to?nd manifolds that are uniformly covered by samples.

The method proposed in the present paper,called Di-mensionality Reduction by Learning an Invariant Mapping (DrLIM),provides a solution to the above problems.Dr-LIM is a method for learning a globally coherent non-linear function that maps the data to a low dimensional manifold.

The method presents four essential characteristics:

?It only needs neighborhood relationships between

training samples.These relationships could come from

prior knowledge,or manual labeling,and be indepen-

dent of any distance metric.

?It may learn functions that are invariant to complicated

non-linear trnasformations of the inputs such as light-

ing changes and geometric distortions.

?The learned function can be used to map new samples

not seen during training,with no prior knowledge.

1

?The mapping generated by the function is in some sense“smooth”and coherent in the output space.

A contrastive loss function is employed to learn the param-eters W of a parameterized function G W,in such a way that neighbors are pulled together and non-neighbors are pushed apart.Prior knowledge can be used to identify the neighbors for each training data point.

The method uses an energy based model that uses the given neighborhood relationships to learn the mapping function.For a family of functions G,parameterized by W, the objective is to?nd a value of W that maps a set of high dimensional inputs to the manifold such that the euclidean distance between points on the manifold,D W( X1, X2)= ||G W( X1)?G W( X2)||2approximates the“semantic sim-ilarity”of the inputs in input space,as provided by a set of neighborhood relationships.No assumption is made about the function G W except that it is differentiable with respect to W.

1.1.Previous Work

The problem of mapping a set of high dimensional points onto a low dimensional manifold has a long history.The two classical methods for the problem are Principal Com-ponent Analysis(PCA)[7]and Multi-Dimensional Scal-ing(MDS)[6].PCA involves the projection of inputs to a low dimensional subspace that maximizes the variance.In MDS,one computes the projection that best preserves the pairwise distances between input points.However both the methods-PCA in general and MDS in the classical scaling case(when the distances are euclidean distances)-generate a linear embedding.

In recent years there has been a lot of activity in design-ing non-linear spectral methods for the problem.These methods involve solving the eigenvalue problem for a particular matrix.Recently proposed algorithms include ISOMAP(2000)by Tenenbaum et al.[1],Local Linear Em-bedding-LLE(2000)by Roweis and Saul[15],Laplacian Eigenmaps(2003)due to Belkin and Niyogi[2]and Hes-sian LLE(2003)by Donoho and Grimes[8].All the above methods have three main steps.The?rst is to identify a list of neighbors of each point.Second,a gram matrix is com-puted using this information.Third,the eigenvalue prob-lem is solved for this matrix.The methods differ in how the gram matrix is computed.None of these methods attempt to compute a function that could map a new,unknown data point without recomputing the entire embedding and with-out knowing its relationships to the training points.Out-of-sample extensions to the above methods have been pro-posed by Bengio et al.in[3],but they too rely on a prede-termined computable distance metric.

Along a somewhat different line Sch¨o elkopf et al.in 1998[13]proposed a non-linear extension of PCA,called Kernel PCA.The idea is to non-linearly map the inputs to a high dimensional feature space and then extract the prin-cipal components.The algorithm?rst expresses the PCA computation solely in terms of dot products and then ex-ploits the kernel trick to implicitly compute the high dimen-sional mapping.The choice of kernels is crucial:differ-ent kernels yield dramatically different embeddings.In re-cent work,Weinberger et al.in[11,12]attempt to learn the kernel matrix when the high dimensional input lies on a low dimensional manifold by formulating the problem as a semide?nite program.There are also related algorithms for clustering due to Shi and Malik[14]and Ng et al.[17].

The proposed approach is different from these methods; it learns a function that is capable of consistently mapping new points unseen during training.In addition,this function is not constrained by simple distance measures in the input space.The learning architecture is somewhat similar to the one discussed in[4,5].

Section2describes the general framework,the loss func-tion,and draws an analogy with a mechanical spring sys-tem.The ideas in this section are made concrete in sec-tion3.Here various experimental results are given and com-parisons to LLE are made.

2.Learning the Low Dimensional Mapping

The problem is to?nd a function that maps high dimen-sional input patterns to lower dimensional outputs,given neighborhood relationships between samples in input space. The graph of neighborhood relationships may come from information source that may not be available for test points, such as prior knowledge,manual labeling,etc.More pre-cisely,given a set of input vectors I={ X1,..., X P}, where X i∈?D,?i=1,...,n,?nd a parametric func-tion G W:?D?→?d with d?D,such that it has the following properties:

1.Simple distance measures in the output space(such as

euclidean distance)should approximate the neighbor-hood relationships in the input space.

2.The mapping should not be constrained to implement-

ing simple distance measures in the input space and should be able to learn invariances to complex trans-formations.

3.It should be faithful even for samples whose neighbor-

hood relationships are unknown.

2.1.The Contrastive Loss Function

Consider the set I of high dimensional training vectors X

i

.Assume that for each X i∈I there is a set S

X i

of train-ing vectors that are deemed similar to X i.This set can be computed by some prior knowledge-invariance to distor-tions or temporal proximity,for instance-which does not

depend on a simple distance.A meaningful mapping from high to low dimensional space maps similar input vectors to nearby points on the output manifold and dissimilar vectors to distant points.A new loss function whose minimization can produce such a function is now introduced.Unlike con-ventional learning systems where the loss function is a sum over samples,the loss function here runs over pairs of sam-ples.Let X1, X2∈I be a pair of input vectors shown to the system.Let Y be a binary label assigned to this pair.Y=0 if X1and X2are deemd similar,and Y=1if they are deemed dissimilar.De?ne the parameterized distance func-tion to be learned D W between X1, X2as the euclidean distance between the outputs of G W.That is,

D W( X1, X2)= G W( X1)?G W( X2) 2(1) To shorten notation,D W( X1, X2)is written D W.Then the loss function in its most general form is

L(W)=

P

i=1

L(W,(Y, X1, X2)i)(2)

L(W,(Y, X1, X2)i)=(1?Y)L S D i W +Y L D D i W (3) where(Y, X1, X2)i is the i-th labeled sample pair,L S is the partial loss function for a pair of similar points,L D the partial loss function for a pair of dissimilar points,and P the number of training pairs(which may be as large as the square of the number of samples).

L S and L D must be designed such that minimizing L with respect to W would result in low values of D W for similar pairs and high values of D W for dissimilar pairs.

Figure1.Graph of the loss function L against the energy D W. The dashed(red)line is the loss function for the similar pairs and the solid(blue)line is for the dissimilar pairs.

The exact loss function is

L(W,Y, X1, X2)=

(1?Y)1

2

{max(0,m?D W)}2(4)

where m>0is a margin.The margin de?nes a radius

around G W( X).Dissimilar pairs contribute to the loss

function only if their distance is within this radius(See?g-

ure1).The contrastive term involving dissimilar pairs,L D,

is crucial.Simply minimizing D W( X1, X2)over the set of

all similar pairs will usually lead to a collapsed solution,

since D W and the loss L could then be made zero by set-

ting G W to a constant.Most energy-based models require

the use of an explicit contrastive term in the loss function.

2.2.Spring Model Analogy

An analogy to a particular mechanical spring system is

given to provide an intuition of what is happening when

the loss function is minimized.The outputs of G W can be

thought of as masses attracting and repelling each other with

springs.Consider the equation of a spring

F=?KX(5)

where F is the force,K is the spring constant and X is the

displacement of the spring from its rest length.A spring

is attract-only if its rest length is equal to zero.Thus any

positive displacement X will result in an attractive force

between its ends.A spring is said to be m-repulse-only if its

rest length is equal to m.Thus two points that are connected

with a m-repulse-only spring will be pushed apart if X is

less than m.However this spring has a special property

that if the spring is stretched by a length X>m,then no

attractive force brings it back to rest length.Each point is

connected to other points using these two kinds of springs.

Seen in the light of the loss function,each point is connected

by attract-only springs to similar points,and is connected

by m-repulse-only spring to dissimilar points.See?gure2.

Consider the loss function L S(W, X1, X2)associated

with similar pairs.

L S(W, X1, X2)=

1

?W

=D W

?D W

?W

of L S gives the attractive force between the two points.

?D W

2

(max{0,m?D W})2(8)

Figure 2.Figure showing the spring system.The solid circles rep-resent points that are similar to the point in the center.The hol-low circles represent dissimilar points.The springs are shown as

red zigzag lines.The forces acting on the points are shown in blue arrows.The length of the arrows approximately gives the strength of the force.In the two plots on the right side,the x-axis is the distance D W and the y-axis is the value of the loss function.(a).Shows the points connected to similar points with attract-only springs.(b).The loss function and its gradient associated with similar pairs.(c)The point connected only with dissimilar points inside the circle of radius m with m-repulse-only springs.(d)Shows the loss function and its gradient associated with dis-similar pairs.(e)Shows the situation where a point is pulled by other points in different directions,creating equilibrium.

When D W >m ,

?L D

?W

=?(m ?D W )

?D W

?W

gives

the spring constant K and (m ?D W )gives the perturbation X .The negative sign denotes the fact that the force is re-pulsive only.Clearly the force is maximum when D W =0and absent when D W =m .See ?gure 2.

Here,especially in the case of L S ,one might think that simply making D W =0for all attract-only springs would put the system in equilibrium.Consider,however,?gure 2e.Suppose b 1is connected to b 2and b 3with attract-only springs.Then decreasing D W between b 1and b 2will in-crease D W between b 1and b 3.Thus by minimizing the

global loss function L over all springs,one would ultimately drive the system to its equilibrium state.

2.3.The Algorithm

The algorithm ?rst generates the training set,then trains the machine.

Step 1:For each input sample X

i ,do the following:(a)Using prior knowledge ?nd the set of samples

S X i ={ X j }p j =1,such that X j is deemed sim-ilar to X

i .(b)Pair the sample X

i with all the other training samples and label the pairs so that:

Y ij =0if X j ∈S X i ,and Y ij =https://www.sodocs.net/doc/1e6226733.html,bine all the pairs to form the labeled training set.

Step 2:Repeat until convergence:

(a)For each pair ( X

i , X j )in the training set,do i.If Y ij =0,then update W to decrease

D W = G W ( X

i )?G W ( X j ) 2ii.If Y ij =1,then update W to increase

D W = G W ( X

i )?G W ( X j ) 2This increase and decrease of euclidean distances in the out-put space is done by minimizing the above loss function.

3.Experiments

The experiments presented in this section demonstrate the invariances afforded by our approach and also clarify the limitations of techniques such as LLE.First we give details of the parameterized machine G W that learns the mapping function.

3.1.Training Architecture

The learning architecture is similar to the one used in [4]and [5].Called a siamese architecture,it consists of two copies of the function G W which share the same set of pa-rameters W ,and a cost module.A loss module whose input is the output of this architecture is placed on top of it.The

input to the entire system is a pair of images ( X

1, X 2)and a label Y .The images are passed through the functions,

yielding two outputs G ( X

1)and G ( X 2).The cost module then generates the distance D W (G W ( X

1),G W ( X 2)).The loss function combines D W with label Y to produce the scalar loss L S or L D ,depending on the label Y .The pa-rameter W is updated using stochastic gradient.The gradi-ents can be computed by back-propagation through the loss,the cost,and the two instances of G W .The total gradient is the sum of the contributions from the two instances.

The experiments involving airplane images from the NORB dataset [10]use a 2-layer fully connected neural network as G W .The number of hidden and output units

used was20and3respectively.Experiments on the MNIST dataset[9]used a convolutional network as G W(?gure3). Convolutional networks are trainable,non-linear learning machines that operate at pixel level and learn low-level fea-tures and high-level representations in an integrated manner. They are trained end-to-end to map images to outputs.Be-cause of a structure of shared weights and multiple layers, they can learn optimal shift-invariant local feature detectors while maintaining invariance to geometric distortions of the input

image.

Figure3.Architecture of the function G W(a convolutional net-work)which was learned to map the MNIST data to a low dimen-sional manifold with invariance to shifts.

The layers of the convolutional network comprise a con-volutional layer C1with15feature maps,a subsampling layer S2,a second convolutional layer C3with30feature maps,and fully connected layer F3with2units.The sizes of the kernels for the C1and C3were6x6and9x9respec-tively.

3.2.Learned Mapping of MNIST samples

The?rst experiment is designed to establish the basic functionality of the DrLIM approach.The neighborhood graph is generated with euclidean distances and no prior knowledge.

The training set is built from3000images of the hand-written digit4and3000images of the handwritten digit9 chosen randomly from the MNIST dataset[9].Approxi-mately1000images of each digit comprised the test set. These images were shuf?ed,paired,and labeled according to a simple euclidean distance measure:each sample X i was paired with its5nearest neighbors,producing the set S X

i

.All other possible pairs were labeled dissimilar,pro-ducing30,000similar pairs and on the order of18million dissimilar pairs.

The mapping of the test set to a2D manifold is shown in?gure4.The lighter-colored blue dots are9’s and the darker-colored red dots are4’s.Several input test samples are shown next to their manifold positions.The4’s and9’s are in two somewhat overlapping regions,with an overall organization that is primarily determined by the slant angle of the samples.The samples are spread rather uniformly in the populated

region.Figure4.Experiment demonstrating the effectiveness of the Dr-LIM in a trivial situation with MNIST digits.A Euclidean near-est neighbor metric is used to create the local neighborhood rela-tionships among the training samples,and a mapping function is learned with a convolutional network.Figure shows the placement of the test samples in output space.Even though the neighborhood relationships among these samples are unknown,they are well or-ganized and evenly distributed on the2D manifold.

3.3.Learning a Shift-Invariant Mapping of MNIST

samples

In this experiment,the DrLIM approach is evaluated us-ing2categories of MNIST,distorted by adding samples that have been horizontally translated.The objective is to learn a2D mapping that is invariant to horizontal translations.

In the distorted set,3000images of4’s and3000im-ages of9’s are horizontally translated by-6,-3,3,and6 pixels and combined with the originals,producing a total of30,000samples.The2000samples in the test set were distorted in the same way.

First the system was trained using pairs from a euclidean distance neighborhood graph(5nearest neighbors per sam-ple),as in experiment1.The large distances between trans-lated samples creates a disjoint neighborhood relationship graph and the resulting mapping is disjoint as well.The out-put points are clustered according to the translated position of the input sample(?gure5).Within each cluster,however, the samples are well organized and evenly distributed.

For comparison,the LLE algorithm was used to map the distorted MNIST using the same euclidean distance neigh-borhood graph.The result was a degenerate embedding in which differently registered samples were completely sepa-rated(?gure6).Although there is sporadic local organiza-

Figure5.This experiment shows the effect of a simple distance-based mapping on MNIST data with horizontal translations added (-6,-3,+3,and+6pixels).Since translated samples are far apart,

the manifold has5distinct clusters of samples corresponding to the5translations.Note that the clusters are individually well-organized,however.Results are on test samples,unseen during training.

tion,there is no global coherence in the

embedding. Figure6.LLE’s embedding of the distorted MNIST set with hor-izontal translations added.Most of the untranslated samples are tightly clustered at the top right corner,and the translated samples

are grouped at the sides of the output.

In order to make the mapping function invariant to trans-lation,the euclidean nearest neighbors were supplemented with pairs created using prior knowledge.Each sample was paired with(a)its5nearest neighbors,(b)its4translations, and(c)the4translations of each of its5nearest neighbors. Additionally,each of the sample’s4translations was paired with(d)all the above nearest neighbors and translated sam-ples.All other possible pairs are labeled as dissimilar.

The mapping of the test set samples is shown in?gure7. The lighter-colored blue dots are4’s and the darker-colored red dots are9’s.As desired,there is no organization on the basis of translation;in fact,translated versions of a given character are all tighlty packed in small regions on the man-

ifold.

Figure7.This experiment measured DrLIM’s success at learning a mapping from high-dimensional,shifted digit images to a2D manifold.The mapping is invariant to translations of the input images.The mapping is well-organized and globally coherent. Results shown are the test samples,whose neighborhood relations are unknown.Similar characters are mapped to nearby areas,re-gardless of their shift.

3.4.Mapping Learned with Temporal Neighbor-

hoods and Lighting Invariance

The?nal experiment demonstrates dimensionality re-duction on a set of images of a single object.The object is an airplane from the NORB[10]dataset with uniform back-grounds.There are a total of972images of the airplane un-der various poses around the viewing half-sphere,and under various illuminations.The views have18azimuths(every 20degrees around the circle),9elevations(from30to70 degrees every5degrees),and6lighting conditions(4lights in various on-off combinations).The objective is to learn a globally coherent mapping to a3D manifold that is invariant to lighting conditions.A pattern based on temporal conti-nuity of the camera was used to construct a neighborhood

graph;images are similar if they were taken from contigu-ous elevation or azimuth regardless of lighting.Images may be neighbors even if they are very distant in terms of Eucli-den distance in pixel space,due to different lighting.

The dataset was split into660training images and a312 test images.The result of training on all10989similar pairs and206481dissimilar pairs is a3-dimensional manifold in the shape of a cylinder(see?gure8).The circumference of the cylinder corresponds to change in azimuth in input space,while the height of the cylinder corresponds to ele-vation in input space.The mapping is completely invariant to lighting.This outcome is quite https://www.sodocs.net/doc/1e6226733.html,ing only local neighborhood relationships,the learned manifold cor-responds globally to the positions of the camera as it pro-duced the dataset.

Viewing the weights of the network helps explain how the mapping learned illumination invariance(see?gure9). The concentric rings match edges on the airplanes to a par-ticular azimuth and elevation,and the rest of the weights are close to0.The dark edges and shadow of the wings,for example,are relatively consistent regardless of

lighting. Figure9.The weights of the20hidden units of a fully-connected neural network trained with DrLIM on airplane images from the

NORB dataset.Since the camera rotates360o around the airplane and the mapping must be invariant to lighting,the weights are zero except to detect edges at each azimuth and elevation;thus the con-

centric patterns.

For comparison,the same neighborhood relationships de?ned by the prior knowledge in this experiment were used to create an embedding using LLE.Although arbitrary neighborhoods can be used in the LLE algorithm,the al-gorithm computes linear reconstruction weights to embed the samples,which severely limits the desired effect of us-ing distant neighbors.The embedding produced by LLE is shown(see?gure10).Clearly,the3D embedding is not invariant to lighting,and the organization of azimuth and elevation does not re?ect the real topology neighborhood

graph.

Figure10.3d embedding of NORB images by LLE algorithm.The neighborhood graph was constructed to create invariance to light-ing,but the linear reconstruction weights of LLE force it organize the embedding by lighting.The shape of the embedding resembles a folded paper.The top image shows the’v’shape of the fold and the lower image looks into the valley of the fold.

4.Discussion and Future Work

The experiments presented here demonstrate that,unless prior knowledge is used to create invariance,variabilities such as lighting and registration can dominate and distort the outcome of dimensionality reduction.The proposed ap-proach,DrLIM,offers a solution:it is able to learn an in-variant mapping to a low dimensional manifold using prior knowledge.The complexity of the invariances that can be learned are only limited by the power of the parameterized function G W.The function maps inputs that evenly cover a manifold,as can be seen by the experimental results.It also faithfully maps new,unseen samples to meaningful lo-cations on the manifold.

The strength of DrLIM lies in the contrastive loss func-tion.By using a separate loss function for similar and dis-

Figure8.Test set results:the DrLIM approach learned a mapping to3d space for images of a single airplane(extracted from NORB dataset). The output manifold is shown under?ve different viewing angles.The manifold is roughly cylindrical with a systematic organization:along the circumference varies azimuth of camera in the viewing half-sphere.Along the height varies the camera elevation in the viewing sphere. The mapping is invariant to the lighting condition,thanks to the prior knowledge built into the neighborhood relationships.

similar pairs,the system avoids collapse to a constant func-

tion and maintains an equilibrium in output space,much as

a mechanical system of interconnected springs does.

The experiments with LLE show that LLE is most useful

where the input samples are locally very similar and well-

registered.If this is not the case,then LLE may give degen-

erate results.Although it is possible to run LLE with arbi-

trary neighborhood relationships,the linear reconstruction

of the samples negates the effect of very distant neighbors.

Other dimensionality reduction methods have avoided this

limitation,but none produces a function that can accept new

samples without recomputation or prior knowledge.

Creating a dimensionality reduction mapping using prior

knowledge has other uses.Given the success of the NORB

experiment,in which the positions of the camera were

learned from prior knowledge of the temporal connections

between images,it may be feasible to learn a robot’s posi-

tion and heading from image sequences.

References

[1]J.B.Tenenbaum,V.DeSilva,and https://www.sodocs.net/doc/1e6226733.html,ngford.A global

geometric framework for non linear dimensionality reduc-

tion.Science,290:2319–2323,2000.2

[2]M.Belkin and https://www.sodocs.net/doc/1e6226733.html,placian eigenmaps and spec-

tral techniques for embedding and clustering.Advances in

Neural Information Processing Systems,15(6):1373–1396,

2003.1,2

[3]Y.Bengio,J.F.Paiement,and P.Vincent.Out-of-sample ex-

tensions for lle,isomap,mds,eigenmaps,and spectral clus-

tering.Advances in Neural Information Processing Systems,

16,2004.In S.Thrun,L.K.Saul and B.Scholkopf,editors.

Cambrige,MA.MIT Press.1,2

[4]J.Bromley,I.Guyon,Y.LeCun,E.Sackinger,and R.Shah.

Signature veri?cation using a siamese time delay neural net-

work.J.Cowan and G.Tesauro(eds)Advances in Neural

Information Processing Systems,1993.2,4

[5]S.Chopra,R.Hadsell,and Y.LeCun.Learning a similarity

metric discriminatively,with applications to face veri?caton.

In Proceedings of the IEEE Conference on Computer Vision

and Pattern Recognition(CVPR-05),1:539–546,2005.2,4

[6]T.Cox and M.Cox.Multidimensional scaling.London:

Chapman and Hill,1994.2

[7]T.I.Jolliffe.Principal component analysis.New York:

Springer-Verlag,1986.2

[8] D.L.Donoho and C.E.Grimes.Hessian eigenmap:Lo-

cally linear embedding techniques for high dimensional data.

Proceedings of the National Academy of Arts and Sciences,

100:5591–5596,2003.1,2

[9]Y.LeCun,L.Bottou,Y.Bengio,and P.Haffner.Gradient-

based learning applied to document recognition.Proceed-

ings of the IEEE,86(11):2278–2324,1998.5

[10]Y.LeCun,F.J.Huang,and L.Bottou.Learning methods for

generic object recognition with invariance to pose and light-

ing.In Proceedings of the IEEE Conference on Computer

Vision and Pattern Recognition(CVPR-04),2:97–104,2004.

4,6

[11]K.Q.Weinberger and L.K.Saul.Unsupervised learning of

image manifolds by semide?nite programming.In Proceed-

ings of the IEEE Conference on Computer Vision and Pattern

Recognition(CVPR-04),2:988–995,2004.2

[12]K.Q.Weinberger,F.Sha,and L.K.Saul.Learning a kernel

matrix for nonlinear dimensionality reduction.In Proceed-

ings of the Twenty First International Conference on Ma-

chine Learning(ICML-04),pages839–846,2004.2

[13] B.Sch?o elkopf,A.J.Smola,and K.R.Muller.Nonlinear

component analysis as a kernel eigen-value problem.Neural

Computation,10:1299–1219,1998.2

[14]J.Shi and J.Malik.Normalized cuts and image segmenta-

tion.IEEE Transactions on Pattern Analysis and Machine

Intelligence(PAMI),pages888–905,2000.2

[15]S.T.Roweis and L.K.Saul.Nonlinear dimensionality re-

duction by locally linear embedding.Science,290.1,2

[16]P.Vincent and Y.Bengio.A neural support vector network

architecture with adaptive kernels.In Proc.of the Interna-

tional Joint Conference on Neural Networks,5,July2000.

[17] A.Y.Ng,M.Jordan,and Y.Weiss.On spectral clustering:

Analysis and an algorithm.Advances in Neural Information

Processing Systems,14:849–856,2002.2

人教版九年级全册英语重点语法知识点复习提纲

人教版九年级全册英语重点语法知识点复习提纲 一. 介词by的用法（Unit-1重点语法） 1. 意为“在……旁”，“靠近”。 Some are singing and dancing under a big tree. Some are drawing by the lake. 有的在大树下唱歌跳舞。有的在湖边画画儿。 2. 意为“不迟于”，“到……时为止”。 Your son will be all right by supper time. 你的儿子在晚饭前会好的。 How many English songs had you learned by the end of last term? 到上个学期末你们已经学了多少首英语歌曲? 3. 表示方法、手段,可译作“靠”、“用”、“凭借”、“通过”、“乘坐”等。 The monkey was hanging from the tree by his tail and laughing. 猴子用尾巴吊在树上哈哈大笑。 The boy’s father was so thankful that he taught Edison how to send messages by railway telegraph. 孩子的父亲是那么的感激,于是他教爱迪生怎样通过铁路电报来传达信息。 4. 表示“逐个”，“逐批”的意思。 One by one they went past the table in the dark. 他们一个一个得在黑暗中经过这张桌子。 5. 表示“根据”，“按照”的意思。 What time is it by your watch? 你的表几点了? 6. 和take , hold等动词连用，说明接触身体的某一部分。 I took him by the hand. 我拉住了他的手。

初中英语代词用法全解及练习含答案

1、人称代词顺口溜：人称代词有两类，一类主格一类宾；主格代词本领大，一切动作由它发；宾格代词不动脑，介动之后跟着跑。 2、物主代词顺口溜：物主代词不示弱，带着‘白勺’来捣乱；形容词性物主代，抓住名词不放松； 1、人称代词的主格在句子中作主语或主语补语。一般在句首，动词前。 例如：John waited a while but eventually he went home. 约翰等了一会儿，最后他回家了。 John hoped the passenger would be Mary and indeed it was she. 约翰希望那位乘客是玛丽，还真是她。 说明：在复合句中，如果主句和从句主语相同，代词主语要用在从句中，名词主语用在主句中。在电话用语中常用主格。 例如：When he arrived, John went straight to the bank. 约翰一到就直接去银行了。 I wish to speak to Mary. This is she. 我想和玛丽通话，我就是玛丽。 2、人称代词的宾格在句中作宾语或表语，在动词或介词后。 例如：Do you know him？(作宾语) 你认识他吗？ Who is knocking at the door？It’s me. (作表语) 是谁在敲门？是我。 说明：单独使用的人称代词通常用宾格，即使它代表主语时也是如此。 例如：I like English. Me too. 我喜欢英语。我也喜欢。 3、注意：在动词be 或to be 后的人称代词视其前面的名词或代词而定。 例如：I thought it was she.我以为是她。(主格----主格) I thought it to be her.(宾格----宾格) I was taken to be she.我被当成了她。(主格----主格) They took me to be her.他们把我当成了她。(宾格----宾格) 4、人称代词并列时的排列顺序 1）单数人称代词并列作主语时，其顺序为： 第二人称→第三人称→第一人称 即you and I he/she/it and I you, he/she/it and I 顺口溜：第一人称最谦虚，但若错误责任担，第一人称学当先。 例如：It was I and John that made her angry. 2）复数人称代词作主语时，其顺序为： 第一人称→第二人称→第三人称 即we and you you and they we, you and they

With的用法全解

With的用法全解 with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词 +动词不定式； 5. with或without-名词/代词 +分词。 下面分别举例： 1、 She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语）

2、 With the meal over ， we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。） The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语）He could not finish it without me to help him.（without+代词 +不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语） Without anything left in the with结构是许多英 语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 二、with结构的用法 with是介词，其意义颇多，一时难掌握。为帮助大家理清头绪，以教材中的句子为例，进行分类，并配以简单的解释。在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件（详见上述例句）。 1.带着，牵着…… (表动作特征)。如： Run with the kite like this.

人教版初中英语中考英语语法总结

中考英语语法总结 一、祈使句结构 1 祈使句结构 祈使句用以表达命令，要求，请求，劝告等。 1）祈使句有两种类型，一种是以动词原形开头，在动词原形之前加do (但只限于省略第二人称主语的句子)。 Take this seat. Do be careful. 否定结构： Don't move. Don't be late. 2）第二种祈使句以let开头。 Let 的反意疑问句 a. Let's 包括说话者 Let's have another try，shall we / shan't we = Shall we have another try b. Let us 不包括说话者 Let us have another try，will you / won't you = Will you please let us have another try

否定结构： Let's not talk of that matter. Let us not talk of that matter. 二、感叹句结构 感叹句结构 感叹句通常有what, how引导，表示赞美、惊叹、喜悦、等感情。 what修饰名词，how 修饰形容词，副词或动词，感叹句结构主要有以下几种： 掌握它的搭配，即掌握了感叹句的重点。 How +形容词+ a +名词+ 陈述语序 How+形容词或副词+ 陈述语序 What +名词+ 陈述语序 What+a+形容词+名词+ 陈述语序 What+ 形容词+复数名词+ 陈述语序 What+ 形容词+不可数名词+ 陈述语序 How clever a boy he is! How lovely the baby is! What noise they are making! What a clever boy he is!

初三英语语法知识点

1) leave的用法 1.“leave+地点”表示“离开某地”。例如： When did you leave Shanghai? 你什么时候离开上海的？ 2.“leave for+地点”表示“动身去某地”。例如： Next Friday, Alice is leaving for London. 下周五，爱丽斯要去伦敦了。 3.“leave+地点+for+地点”表示“离开某地去某地”。例如：Why are you leaving Shanghai for Beijing? 你为什么要离开上海去北京？ 2) 情态动词should“应该”学会使用

should作为情态动词用，常常表示意外、惊奇、不能理解等，有“竟会”的意思，例如： How should I know? 我怎么知道？ Why should you be so late today? 你今天为什么来得这么晚？ should有时表示应当做或发生的事，例如： We should help each other.我们应当互相帮助。 我们在使用时要注意以下几点： 1. 用于表示“应该”或“不应该”的概念。此时常指长辈教导或责备晚辈。例如： You should be here with clean hands. 你应该把手洗干净了再来。 2. 用于提出意见劝导别人。例如： You should go to the doctor if you feel ill. 如果你感觉不舒服，你最好去看医生。

3. 用于表示可能性。should的这一用法是考试中常常出现的考点之一。例如： We should arrive by supper time. 我们在晚饭前就能到了。 She should be here any moment. 她随时都可能来。 3) What...? 与Which...? 1. what 与which 都是疑问代词，都可以指人或事物，但是what仅用来询问职业。如： What is your father? 你父亲是干什么的？ 该句相当于： What does your father do? What is your father's job? Which 指代的是特定范围内的某一个人。如：

with的用法大全

with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。 下面分别举例：

1、 She came into the room，with her nose red because of cold.(with+名词+形容词，作伴随状语) 2、 With the meal over ， we all went home.(with+名词+副词，作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语，作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.(with+名词+不定式，作伴随状语) He could not finish it without me to help him.(without+代词 +不定式，作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词，作伴随状语) 6、Without anything left in the cupboard， she went out to get something to eat.(without+代词+过去分词，作为原因状语) 二、with结构的用法 在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件(详见上述例句)。

(完整版)人教版初中英语语法完整总结

1 . (see 、hear 、notice 、find 、feel 、listen 从句感觉/对什么有信心，自信 to 、look at ( 感官动词)+（sb. ）+do sth. eg : I am/ feel confident of myspoken English. eg:I like watching monkeys jump. I feel that I can pass the test . 2 . （比较级and 比较级）表示越来越怎么样18. be + doing 表：1现在进行时2将来时 eg:the more the more 越来越多19 . be able to (+ v 原) = can (+ v 原）能够?? 3. a piece of cake =easy 小菜一碟（容易）eg : She is able to sing .= She can sing. 4 . agree with sb赞成某人20. be able to do sth. 能够干什么 5 . all kinds of 各种各样a kind of 一样e g :she is able to sing . 6 . all over the world = the whole world 整个21. be afraid to do (of sth 恐惧，害怕??世界eg : I'm afraed to go out at night . 7. along with 同??一道，伴随??I'm afraid of dog. eg : I will go along with you. 我将和你一起去22. be allowed to do 被允许做什么 The students planted trees along with their eg: I'm allowed to watch TV. 我被允许看电视teachers. 学生同老师们一起种树I should be allowed to watch TV. 我应该被允 8. as soon as 一怎么样就怎么样 许看电视 9 . as you can see 你是知道的(正如你所见)23. be angry with sb 生某人的气 10 . ask for ??求助向?要?（直接接想要的东e g : Don't be angry with me. 西）24. be angry with(at) sb for doing sth 12. ask sb to do sth询问某人某事 为什么而生某人的气 ask sb not to do 叫某人不要做某事25. be as ?原级?as 和什么一样 13 . at the age of 在??岁时eg : She is as tall as me. 她和我一样高 eg ：I amsixteen. = I am at the age of sixteen . 26. be ashamed to 14. at the beginning of ????的起初；??27. be away from远离 的开始28. be away from 从??离开 15. at the end of + 地点/+时间最后；尽头；末29. be bad for对什么有害 尾eg : Reading books in the sun is bad for your eg : At the end of the day eyes. 在太阳下看书对你的眼睛不好 16. at this time of year 在每年的这个时候30. be born 出生于 17. be /feel confident of sth /that clause + 31. be busy doing sth 忙于做什么事

九年级英语全册所有必考语法点都在这里了,初三都在看!

一. 介词by的用法 1. 意为“在……旁”，“靠近”。 Some are singing and dancing under a big tree. Some are drawing by the lake. 有的在大树下唱歌跳舞。有的在湖边画画儿。 2. 意为“不迟于”，“到……时为止”。 Your son will be all right by supper time. 你的儿子在晚饭前会好的。 How many English songs had you learned by the end of last term? 到上个学期末你们已经学了多少首英语歌曲? 3. 表示方法、手段,可译作“靠”、“用”、“凭借”、“通过”、“乘坐”等。 The monkey was hanging from the tree by his tail and laughing. 猴子用尾巴吊在树上哈哈大笑。 The boy’s father was so thankful that he taught Edison how to send messages by railway telegraph. 孩子的父亲是那么的感激,于是他教爱迪生怎样通过铁路电报来传达信息。 4. 表示“逐个”，“逐批”的意思。 One by>他们一个一个得在黑暗中经过这张桌子。 5. 表示“根据”，“按照”的意思。 What time is it by your watch? 你的表几点了? 6. 和take , hold等动词连用，说明接触身体的某一部分。 I took him by the hand. 我拉住了他的手。 7. 用于被动句中，表示行为主体,常译作“被”、“由”等。

with用法归纳

with用法归纳 （1）“用……”表示使用工具，手段等。例如： ①We can walk with our legs and feet. 我们用腿脚行走。 ②He writes with a pencil. 他用铅笔写。 （2）“和……在一起”，表示伴随。例如： ①Can you go to a movie with me? 你能和我一起去看电影'>电影吗？ ②He often goes to the library with Jenny. 他常和詹妮一起去图书馆。 （3）“与……”。例如： I’d like to have a talk with you. 我很想和你说句话。 （4）“关于，对于”，表示一种关系或适应范围。例如： What’s wrong with your watch? 你的手表怎么了？ （5）“带有，具有”。例如： ①He’s a tall kid with short hair. 他是个长着一头短发的高个子小孩。 ②They have no money with them. 他们没带钱。 （6）“在……方面”。例如： Kate helps me with my English. 凯特帮我学英语。 （7）“随着，与……同时”。例如： With these words, he left the room. 说完这些话，他离开了房间。 [解题过程] with结构也称为with复合结构。是由with+复合宾语组成。常在句中做状语，表示谓语动作发生的伴随情况、时间、原因、方式等。其构成有下列几种情形： 1.with+名词(或代词)+现在分词 此时，现在分词和前面的名词或代词是逻辑上的主谓关系。 例如:1)With prices going up so fast, we can't afford luxuries. 由于物价上涨很快，我们买不起高档商品。（原因状语） 2)With the crowds cheering, they drove to the palace. 在人群的欢呼声中，他们驱车来到皇宫。（伴随情况） 2.with+名词(或代词)+过去分词 此时，过去分词和前面的名词或代词是逻辑上的动宾关系。

人教版英语九年级语法知识点

1. by + doing 通过……方式如：by studying with a group by 还可以表示："在…旁","靠近","在…期间"、"用,""经过","乘车"等如：I live by the river. I have to go back by ten o'clock. The thief entered the room by the window. The student went to park by bus. 2. talk about 谈论，议论，讨论 如：The students often talk about movie after class. 学生们常常在课后讨论电影。talk to sb. === talk with sb. 与某人说话 3. 提建议的句子： ①What/ how about +doing sth.? 如：What/ How about going shopping? ②Why don't you + do sth.? 如：Why don't you go shopping? ③Why not + do sth. ? 如：Why not go shopping? ④Let's + do sth. 如：Let's go shopping ⑤Shall we/ I + do sth.? 如：Shall we/ I go shopping? 4. a lot 许多常用于句末如：I eat a lot. 我吃了许多。 5. too…to 太…而不能常用的句型too+adj./adv. + to do sth. 如：I'm too tired to say anything. 我太累了，什么都不想说。 6. aloud, loud与loudly的用法三个词都与"大声"或"响亮"有关。 ①aloud是副词,重点在出声能让人听见,但声音不一定很大, 常用在读书或说话上。通常放在动词之后。aloud没有比较级 形式。如: He read the story aloud to his son.他朗读那篇故事给他儿子听。 ②loud可作形容词或副词。用作副词时,常与speak, talk, laugh等动词连用,多用于比较级,须放在动词之后。如: She told us to speak a little louder. 她让我们说大声一点。 ③loudly是副词,与loud同义,有时两者可替换使用,但往往 含有令人讨厌或打扰别人的意思,可位于动词之前或之后。 如: He does not talk loudly or laugh loudly in public. 他不当众大声谈笑。 7. not …at all 一点也不根本不如： I like milk very much. I don't like coffee at all. 我非常喜欢牛奶。我一点也不喜欢咖啡。 not经常可以和助动词结合在一起，at all 则放在句尾 8. be / get excited about sth.=== be / get excited about doing sth. === be excited to do sth. 对…感兴奋如： I am / get excited about going to Beijing.=== I am excited to go to Beijing. 我对去北京感到兴奋。 9. ①end up doing sth 终止做某事，结束做某事如： The party ended up singing. 晚会以唱歌而结束。 ②end up with sth. 以…结束如： The party ended up with her singing. 晚会以她的歌唱而告终。 10. first of all 首先. to begin with 一开始later on 后来、随 11. also 也、而且（用于肯定句）常在句子的中间 either 也（用于否定句）常在句末 too 也(用于肯定句) 常在句末 12. make mistakes 犯错如：I often make mistakes. 我经常犯错。

初三英语语法知识点归纳

初中英语语法速记口诀大全 很多同学认为语法枯燥难学，其实只要用心并采用适当的学习方法，我们就可以愉快地学会英语，掌握语法规则。笔者根据有关书目和多年教学经验，搜集、组编了以下语法口诀，希望对即将参加中考的同学们有所帮助。 一、冠词基本用法 【速记口诀】 名词是秃子，常要戴帽子， 可数名词单，须用a或an， 辅音前用a，an在元音前， 若为特指时，则须用定冠， 复数不可数，泛指the不见， 碰到代词时，冠词均不现。 【妙语诠释】冠词是中考必考的语法知识之一，也是中考考查的主要对象。以上口诀包括的意思有：①名词在一般情况下不单用，常常要和冠词连用；②表示不确指的可数名词单数前要用不定冠词a或an，确指时要用定冠词the；③如复数名词表示泛指，名词前有this，these，my，some等时就不用冠词。 二、名词单数变复数规则 【速记口诀】 单数变复数，规则要记住， 一般加s，特殊有几处： 末尾字母o，大多加s， 两人有两菜，es不离口， 词尾f、fe，s前有v和e； 没有规则词，必须单独记。 【妙语诠释】①大部分单数可数名词变为复数要加s，但如果单词以/t蘩/、/蘩/、/s/发音结尾(也就是单词如果以ch，sh，s，x等结尾)，则一般加es；②以o结尾的单词除了两

人(negro，hero)两菜(tomato，potato) 加es外，其余一般加s；③以f或fe结尾的单词一般是把f，fe变为ve再加s；④英语中还有些单词没有规则，需要特殊记忆，如child—children，mouse—mice，deer—deer，sheep—sheep，Chinese—Chinese，ox—oxen，man—men，woman—women，foot—feet，tooth —teeth。 三、名词所有格用法 【速记口诀】 名词所有格，表物是“谁的”， 若为生命词，加“’s”即可行， 词尾有s，仅把逗号择； 并列名词后，各自和共有， 前者分别加，后者最后加； 若为无生命词，of所有格， 前后须倒置，此是硬规则。 【妙语诠释】①有生命的名词所有格一般加s，但如果名词以s结尾，则只加“’”；②并列名词所有格表示各自所有时，分别加“’s”，如果是共有，则只在最后名词加“’s”；③如果是无生命的名词则用of表示所有格，这里需要注意它们的顺序与汉语不同，A of B要翻译为B的A。 四、接不定式作宾语的动词 【速记口诀】 三个希望两答应，两个要求莫拒绝； 设法学会做决定，不要假装在选择。 【妙语诠释】三个希望两答应：hope，wish，want，agree，promise 两个要求莫拒绝：demand，ask，refuse 设法学会做决定：manage，learn，decide 不要假装在选择：petend，choose 五、接动名词作宾语的动词

with用法小结

with用法小结 一、with表拥有某物 Mary married a man with a lot of money . 马莉嫁给了一个有着很多钱的男人。 I often dream of a big house with a nice garden . 我经常梦想有一个带花园的大房子。 The old man lived with a little dog on the lonely island . 这个老人和一条小狗住在荒岛上。 二、with表用某种工具或手段 I cut the apple with a sharp knife . 我用一把锋利的刀削平果。 Tom drew the picture with a pencil . 汤母用铅笔画画。 三、with表人与人之间的协同关系 make friends with sb talk with sb quarrel with sb struggle with sb fight with sb play with sb work with sb cooperate with sb I have been friends with Tom for ten years since we worked with each other, and I have never quarreled with him . 自从我们一起工作以来，我和汤姆已经是十年的朋友了，我们从没有吵过架。 四、with 表原因或理由 John was in bed with high fever . 约翰因发烧卧床。 He jumped up with joy . 他因高兴跳起来。 Father is often excited with wine . 父亲常因白酒变的兴奋。 五、with 表“带来”，或“带有,具有”，在…身上，在…身边之意

comparison的用法解析大全

comparison的用法解析大全 comparison的意思是比较，比喻，下面我把它的相关知识点整理给大家，希望你们会喜欢！ 释义 comparison n. 比较;对照;比喻;比较关系 [ 复数 comparisons ] 词组短语 comparison with 与…相比 in comparison adj. 相比之下;与……比较 in comparison with 与…比较，同…比较起来 by comparison 相比之下，比较起来 comparison method 比较法 make a comparison 进行比较 comparison test 比较检验 comparison theorem 比较定理 beyond comparison adv. 无以伦比 comparison table 对照表 comparison shopping 比较购物;采购条件的比较调查 paired comp arison 成对比较 同根词 词根： comparing adj. comparative 比较的;相当的 comparable 可比较的;比得上的 adv. comparatively 比较地;相当地 comparably 同等地;可比较地 n.

comparative 比较级;对手 comparing 比较 comparability 相似性;可比较性 v. comparing 比较;对照(compare的ing形式) 双语例句 He liked the comparison. 他喜欢这个比喻。 There is no comparison between the two. 二者不能相比。 Your conclusion is wrong in comparison with their conclusion. 你们的结论与他们的相比是错误的。 comparison的用法解析大全相关文章： 1.by的用法总结大全

人教版九年级英语各单元知识点总结

九年级英语全册各单元知识点总结 Unit 1 How can we become good learners? 一、短语： 1.have conversation with sb. 同某人谈话 2.connect …with… 把…和…连接/联系起来 3.the secret to… ……的秘诀 4.be afraid of doing sth./to do sth. 害怕做某事 5.look up 查阅 6.repeat out loud 大声跟读 7.make mistakes in 在……方面犯错误8.get bored 感到厌烦 9.be stressed out 焦虑不安的10.pay attention to 注意；关注 11.depend on 取决于；依靠12.the ability to do sth. 做某事的能力 二、知识点： 1. by + doing：通过……方式（by是介词，后面要跟动名词，也就是动词的ing形式）； 2. a lot：许多，常用于句末； 3. aloud, loud与loudly的用法，三个词都与“大声”或“响亮”有关。 ①aloud是副词，通常放在动词之后。 ①loud可作形容词或副词。用作副词时，常与speak, talk, laugh等动词连用，多用于比较级， 须放在动词之后。 ①loudly是副词，与loud同义，有时两者可替换使用，可位于动词之前或之后。 4. not …at all：一点也不，根本不，not经常可以和助动词结合在一起，at all 则放在句尾； 5. be / get excited about sth.：对…感到兴奋； 6. end up doing sth：终止/结束做某事；end up with sth.：以…结束； 7. first of all：首先（这个短语可用在作文中，使得文章有层次）； 8. make mistakes：犯错make a mistake 犯一个错误； 9. laugh at sb.：笑话；取笑（某人）（常见短语） 10. take notes：做笔记/记录； 11. native speaker 说本国语的人； 12. make up：组成、构成； 13. deal with：处理、应付； 14. perhaps = maybe：也许； 15. go by：（时间）过去； 16.each other：彼此； 17.regard… as … ：把…看作为…； 18.change… into…：将…变为…； 19. with the help of sb. = with one's help 在某人的帮助下（注意介词of和with，容易出题） 20. compare … to …：把…比作… compare with 拿…和…作比较； 21. instead：代替，用在句末，副词； instead of sth / doing sth：代替，而不是（这个地方考的较多的就是instead of doing sth，也就是说如果of后面跟动词时，要用动名词形式，也就是动词的ing形式） 22.Shall we/ I + do sth.? 我们/我…好吗？ 23. too…to：太…而不能，常用的句型是too+形容词/副词+ to do sth.

With_复合结构详解

介词With 复合结构讲解及练习 with复合结构的作用：with复合结构在句子中作状语，表示原因、时间、条件、伴随、方式等. 1）We sat on the dry grass with our backs to the wall.（作伴随状语） 2）She could not leave with her painful duty unfulfilled.（作原因状语） 3）He lay in bed with his head covered.（作方式状语） 4）Jack soon fell asleep with the light still burning.（作伴随状语） 5）I won't be able to go on holiday with my mother being ill.（作原因状语） 6）He sat with his arms clasped around his knees.（作方式状语） 注：with复合结构在句子中还可以作定语，阅读下面的句子。 1）There was a letter for Lanny with a Swiss stamp on it.（作定语修饰letter） 2）It was a vast stretch of country with cities in the distance.（作定语修饰a stretch of country）1) with +宾语+ 现在（短分词语） When mother went into the house, she found her baby was sleeping in bed, with his lips moving. 当妈妈走进房子的时候，她发现自己的孩子正睡在床上，嘴唇一直在动。 My aunt lives in the room with the windows facing south. 我姑妈住在那间窗户朝南开的房间。 With winter coming on，it's time to buy warm clothes 2)with +宾语+ 过去分词（短语） With more and more forests damaged ,some animals and plants are facing the danger of dying out. 由于越来越多的森林遭到破坏，一些动植物正面临着灭绝的危险。 With his legs broken, he had to lie in bed for a long time. 他双腿都断了，只得长时间躺在床上。 3) with +宾语+ 不定式（短语） * With so many children to look after, the nurse is busy all the time. 有这么多的孩子需要照顾，保育员一直都很忙。 *With a lot of papers to correct, M r. Li didn’t attend the party. 李老师有许多试卷需要批改，所以没有参加聚会。 4) with +宾语+ 副词 * You should read with the radio off. 在看书的时候应该把收音机关掉。 * With the temperature up, we had to open all the windows. 气温上升，我们不得不打开所有的窗户。 5) with +宾语+形容词 *With the window open, I felt a bit cold. 窗户开着，我感到有点冷。 * It was cold outside , the boy ran into the room with his nose red. 外面天气很冷，那个男孩跑进了屋子时，鼻子红红的。 6) with +宾语+ 介词短语 * The woman with a baby in her arms is getting on the bus. 怀里抱着婴儿的那位妇女正在上车。 * John starts to work very clearly in the morning and goes on working until late in the afternoon with a break at midday . 约翰早上开始工作，中午稍作休息后又接着工作到下午稍晚些时候。

人教版初中英语语法完整总结(最新最全)

1 .(see 、hear 、notice 、find 、feel 、listen to 、 look at (感官动词)+（sb.）+do sth. eg:I like watching monkeys jump. 2 .（比较级 and 比较级）表示越来越怎么样eg:the more the more 越来越多 3. a piece of cake =easy 小菜一碟（容易） 4 .agree with sb 赞成某人 5 .all kinds of 各种各样 a kind of 一样 6 .all over the world = the whole world 整个世界 7. along with同……一道，伴随…… eg : I will go along with you.我将和你一起去The students planted trees along with their teachers. 学生同老师们一起种树 8. as soon as 一怎么样就怎么样 9 .as you can see 你是知道的(正如你所见) 10 .ask for ……求助向…要…（直接接想要的东西） 12. ask sb to do sth 询问某人某事 ask sb not to do 叫某人不要做某事 13 .at the age of 在……岁时 eg：I am sixteen. = I am at the age of sixteen . 14.at the beginning of …… ……的起初；……的开始 15. at the end of +地点/+时间最后；尽头；末尾 eg : At the end of the day 16.at this time of year 在每年的这个时候 17. be /feel confident of sth /that clause +从句感觉/对什么有信心，自信 eg : I am / feel confident of my spoken English. I feel that I can pass the test . 18. be + doing 表：1 现在进行时 2 将来时 19 .be able to (+ v 原) = can (+ v 原）能够…… eg : She is able to sing .= She can sing. 20. be able to do sth. 能够干什么 eg :she is able to sing . 21. be afraid to do (of sth 恐惧，害怕…… eg : I'm afraed to go out at night . I'm afraid of dog. 22. be allowed to do 被允许做什么 eg: I'm allowed to watch TV. 我被允许看电视 I should be allowed to watch TV. 我应该被允许看电视 23. be angry with sb 生某人的气 eg : Don't be angry with me. 24. be angry with(at) sb for doing sth 为什么而生某人的气 25.be as…原级…as 和什么一样 eg : She is as tall as me. 她和我一样高 26.be ashamed to 27.be away from 远离 28. be away from 从……离开 29. be bad for 对什么有害 eg : Reading books in the sun is bad for your eyes. 在太阳下看书对你的眼睛不好 30. be born 出生于 31.be busy doing sth 忙于做什么事