CN107590505A - The learning method of joint low-rank representation and sparse regression - Google Patents
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Abstract
Combine low-rank representation and the learning method of sparse regression the invention discloses a kind of, the described method comprises the following steps：Feature extraction is carried out to the SUN data sets with iconic memory degree fraction label.By low-rank representation, one entirety of composition under same framework is placed on reference to sparse regression model two parts, builds joint low-rank representation and sparse regression model；Solves the problems, such as the mnemonic of automatic Prediction image using more vision self-adapting regression algorithms, the relation of characteristics of image and iconic memory degree is obtained under optimized parameter, and obtain relational result under optimized parameter, forecast database test machine iconic memory degree, and verify prediction result with relevant evaluation standard；The low-rank learning framework of present invention joint low-rank representation and sparse regression, the mnemonic of Accurate Prediction image-region.
Description
Technical field
The present invention relates to low-rank representation and sparse regression field, the memory degree for image is predicted, more particularly to joint is low
Order represents and the learning method of sparse regression.
Background technology
The mankind have the ability for remembeing thousands of images, but not all image is all stored in the same way
In the brain.Some representational pictures can be remembered at a glance, and other images are easy to disappear from memory.Image is remembered
Recall and be used to the measurement degree that image is remembered or passed into silence after a specific amount of time.Previous studies work it has been shown that
It is relevant to the memory of picture and the build-in attribute of image, i.e., to the memory of picture in different time intervals and not
With being uniformity between observer.In this case, just as study many other high vision attributes (such as popularity, interest,
Mood and aesthetics) as, some research work start to explore the potentially relevant property between picture material expression and iconic memory.
Analysis image mnemonic can be applied to be set in such as user-interface design, video frequency abstract, scene understanding and advertisement
In several fields such as meter.For example, can be by selecting significant image that mnemonic is used as into guiding standard to summarize figure
Image set closes or video.By improving memory of the consumer to target brand, unforgettable advertisement can be designed and help businessman to expand shadow
Ring power.
Recently, low-rank performance (LRR) has been successfully applied to multimedia and computer vision field.In order to preferably handle
Character representation problem, LRR are used for by the way that raw data matrix is decomposed into low-rank representation matrix, while eliminate incoherent thin
Section, disclose the bottom low-rank subspace structure in embedding data.Conventional method is typically not enough to carry out the processing of exceptional value.In order to
Solve this problem, there are some researchs also to focus on that sparse regression learns recently.
Carried out however, one of major defect of these methods is character representation and memory prediction two separated stages.
That is, when it is determined that for image mnemonic prediction combinations of features pattern when, the final performance of separate regression steps is main
Determined by the feature handled.Although bibliography [1] proposes the feature coding algorithm of joint low-rank and sparse regression to handle
Exceptional value.Equally, bibliography [2] develops a kind of joint figure insertion and sparse regression framework.But they are all for vision point
The design of class problem, rather than iconic memory prediction task.
The content of the invention
The invention provides a kind of learning method for combining low-rank representation and sparse regression, present invention joint low-rank representation and
The learning framework of sparse regression, the mnemonic of Accurate Prediction image-region are described below：
It is a kind of to combine low-rank representation and the learning method of sparse regression, it the described method comprises the following steps：
Feature extraction is carried out to the SUN data sets with iconic memory degree fraction label；
One entirety of composition under same framework, structure connection are placed on by low-rank representation and with reference to sparse regression model two parts
Close the model of low-rank and sparse regression；
Solves the problems, such as the mnemonic of automatic Prediction image using more vision self-adapting regression algorithms, under optimized parameter
Obtain the relation of characteristics of image and iconic memory degree；
The feature that combination image proposes, utilizes the relational result obtained under optimized parameter, forecast database test set figure
As memory degree, and prediction result is verified with relevant evaluation standard.
Methods described also includes：Obtain image mnemonic data set.
The feature includes：Scale invariant features transform feature, search tree feature, histograms of oriented gradients feature and
Structural similarity feature.
The joint low-rank and the model of sparse regression are specially：
Wherein：
X be input feature, A ∈ RD×DBe N number of sample low-rank projection matrix it is low to capture the bottom shared between sample
Order structure, E ∈ RN×DIt is to utilize L1Norm solves random error；w∈RD×1It is transformation matrix, by the sample after conversion and they
Memory score be associated, y be training sample label；It is the error function of definition；λ ＞ 0 are flat
Weigh parameter.
The beneficial effect of technical scheme provided by the invention is：
1st, combine low-rank representation and sparse regression to predict for image mnemonic, wherein disclosing using inferior grade constraint
The immanent structure of embedded initial data, exceptional value and redundancy are removed using sparse constraint, when low-rank representation and sparse time
When returning common execution, the shared low-rank representation of all features can capture the internal structure of feature, so as to improve the standard of prediction
True rate；
2nd, the present invention returns (MAR) algorithm based on more vision self-adaptings, solves the optimization of object function with Fast Convergent
Problem.
Brief description of the drawings
Fig. 1 is the flow chart of joint low-rank representation and the learning method of sparse regression；
Fig. 2 is the database images sample for indicating iconic memory degree fraction；
Fig. 3 is algorithmic statement figure；
Fig. 4 is pair of the prediction result of single class image attributes feature and all properties feature prediction result under this method framework
Than figure.
Embodiment
To make the object, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing to embodiment party of the present invention
Formula is described in further detail.
Embodiment 1
The feature of image is studied and iconic memory degree is predicted, the embodiment of the present invention proposes a kind of joint
The learning method of low-rank representation and sparse regression, referring to Fig. 1, this method comprises the following steps：
101：Obtain image mnemonic data set；
Wherein, the image mnemonic data set[1]Comprising from SUN data sets[11]2,222 images.The note of image
Recall score to obtain by Amazon Mechanical Turk Visual Memory Game, image mnemonic is from 0 to 1
Successive value.Value is higher, and image is more difficult to remember.Sample image with various memory scores is as shown in Figure 2.
102：Feature extraction is carried out respectively to the SUN data sets with iconic memory degree fraction label；
Wherein, the feature of extraction includes：SIFT (Scale invariant features transform, Scale-invariant feature
Transform, SIFT), Gist (search tree, Generalized Search Trees), HOG (histograms of oriented gradients,
Histogram of Oriented Gradient) and SSIM (structural similarity, structural similarity
Index)) feature, 4 kinds of features together constitute property data base.
103：Low-rank representation and sparse regression model two parts are placed on one entirety of composition under same framework, structure
JLRSR (joint low-rank and sparse regression) model；
104：(MAR) algorithm, which is returned, using more vision self-adaptings solves the problems, such as the mnemonic of automatic Prediction image,
The relation of characteristics of image and iconic memory degree is obtained under optimized parameter；
105：Combination image feature, utilize the relational result obtained under optimized parameter, forecast database test set image
Memory degree, and verify prediction result with relevant evaluation standard.
In summary, the embodiment of the present invention is constrained to disclose original number by above-mentioned steps 101- steps 105 using low-rank
According to immanent structure and using sparse constraint remove feature exceptional value and redundancy, when low-rank representation and sparse regression are total to
During with performing, the shared low-rank representation of all features can not only capture the global structure of all mode, and can represent back
The requirement returned；Because the object function worked out is unsmooth, it is difficult to solve, therefore (MAR) algorithm is returned using various visual angles are adaptive
Solving the problems, such as the mnemonic of automatic Prediction image, solves optimization problem with Fast Convergent.
Embodiment 2
The scheme in embodiment 1 is further introduced with reference to specific calculation formula, it is described below：
201：Image mnemonic data set[1]Comprising from SUN data sets[17]2,222 images；
Wherein, the data set is known to those skilled in the art, and the embodiment of the present invention is not repeated this.
202：Picture progress feature extraction to the SUN data sets with iconic memory degree fraction label, the SIFT of extraction,
Gist, HOG and SSIM feature constitutive characteristic storehouse.
This database includes the picture under 2222 various environment, and iconic memory degree point has all been marked per pictures
Number, accompanying drawing 2 illustrate the sample that memory degree fraction picture is indicated in database.Character representation isDiRepresent such
The dimension of feature, contained image number (2222) in N representation databases.These feature constitutive characteristic storehouses B={ B1,...,BM}。
203：Establish JLRSR and (Joint Low-Rank and Sparse Regression, combine low-rank and sparse time
Return) model, low-rank representation and sparse regression are combined on the basis of the feature of extraction, establishes more robust character representation and accurate
Regression model.General framework defined in JLRSR models is as follows：
Wherein, F (A, w) is used as predicting the loss function of error；L (A, E) represents the feature coding based on low-rank representation
Device；G (A) is for solving the problems, such as the figure regularization of over-fitting expression.A is the mapping matrix of low-rank representation；W is low-rank feature
Represent the linear dependence between output memory degree fraction；E is sparse error constraint portions.
Image mnemonic data set[1]Comprising from SUN data sets[17]2,222 images, the memory score of image
Obtained by Amazon Mechanical Turk Visual Memory Game；The recurrence instruction of combining adaptive transfer learning
Practice, the feature database of extraction is trained using the method for linear regression.In terms of the Score on Prediction of iconic memory degree is divided into two, one
Aspect is to obtain every a kind of characteristics of image to the mapping square of iconic memory degree directly using character representation come prognostic chart picture memory degree
Battle array wi, learn with reference to low-rank, obtain the relation of every class image attributes and iconic memory degree；According to initial pictures set of eigenvectors X
∈RN×D, the target of JLRSR models is to combine low-rank representation and sparse regression on the basis of the visual cues of extraction to strengthen Shandong
Rod character representation, establish accurate regression model.
Each part is specifically introduced：
Because low-rank constraint can remove noise or redundancy to help to disclose the essential structure of data.Therefore, these
Low-rank attribute can be integrated into feature learning to handle these problems.LRR assumes that primitive character matrix includes all samples
Shared potential lowest rank structure components and its unique error matrix,
Wherein A ∈ RD×DIt is the low-rank projection matrix of N number of sample, E ∈ RN×DIt is to useUnique sparse error of norm constraint
Part, to handle random error, λ ＞ 0 are balance parameters, and X is the feature of input；D is the intrinsic dimensionality after low-rank constraint；
The low-rank representation method that rank is characterized.
Because above-mentioned equation is difficult optimization, therefore use nuclear norm | | A | |*(*Represent that nuclear norm refers to singular values of a matrix
With) approach A order, therefore L (A, E) formula can be defined as foloows
In the framework that the embodiment of the present invention proposes, the problem of iconic memory is predicted, is as standard regression problem.It is proposed
Lasso[5]Homing method, by the linear relationship v for establishing input feature vector matrix X and can be between degree of memory scores vector y, most
Smallization minimum mean-square errorTo solve forecasting problem.After adding ridge regularization in minimum mean-square error part, obtain
With ridge regression[6]Typical least square problem.
Wherein, α is to predict the balance parameters between error component and regularization part.
From the perspective of matrix decomposition, conversion vector v can be broken down into the product of two components, i.e., thrown using low-rank
Coefficient vector w is applied to the sample after conversion with theirs by shadow matrix A to capture the low-rank structure shared between sample
Memory score is associated.Introduce v=Aw and be defined as loss function F (A, w)
Thought based on Diverse study, the uniformity of geometry is kept to be asked to solve this using figure regularization
Topic.The core concept of figure regularization is that sample in character representation is close in form, then their memory score is also
Close, vice versa.By minimizing figure regularizer G (A), the geometry between feature and memory degree score is realized
Uniformity：
Wherein, L=B-S is Laplace operator, and B is angular moment battle array, Bii=∑jSij, s is that Gauss similarity function is calculated
The weight matrix gone out, its calculating are obtained by Gauss similarity function,
Wherein, yiAnd yjIt is the popularity score of i-th of sample and j-th of sample, NKRepresent xiIt is xjK close on data, σ
It is a radius parameter, it is simply set as intermediate value of all pictures to upper Euclidean distance.
Therefore defining JLRSR models is：
Wherein：
A∈RD×DIt is that the low-rank projection matrix of N number of sample captures the bottom low-rank structure shared between sample,
E∈RN×DIt is to utilize L1Norm solves random error；X is characterized；The low-rank representation and output that w is characterized are remembered
The linear dependence spent between fraction, y are the label of training sample.
It is to ensure sample memory fraction similar in feature
It is and close.
α, β, λ and φ in JLRSR model objective functions is initialized；A, E, w and Q and derivation, constantly weight are fixed respectively
Multiple derivation process reaches the minimum value of setting until error.
Lower mask body introduces solution procedure, and (MAR) algorithm is returned using more vision self-adaptings[7]To solve automatic Prediction figure
The problem of mnemonic of picture, to solve optimization problem.First, a slack variable Q is introduced to change the problem of above-mentioned of equal value：
S.t.X=XA+E, Q=Aw
Then, two slack variable Y are introduced1And Y2To obtain the Lagrangian of augmentation：
Wherein ＜, ＞ represent the inner product operation of matrix, Y1And Y2Lagrangian matrix is represented, μ ＞ 0 are positive punishment ginsengs
Number, the above method is merged into：
Wherein
This method is solved using the method for alternating iteration.By by quadratic term h (A, Q, E, w, Y1,Y2, μ) and it is approximately two
Rank Taylor expansion handles each subproblem respectively.In order to more fully understand and understand this process, a variable t is introduced,
And define, At,Et,Qt,wt,Y1,t,Y2,tWith results of the μ as the t times iteration of variable, therefore the t+1 times iteration knot is obtained
Fruit is as follows.
A iteration result：
Then w is fixed, the optimization that A, Q obtain E is as follows：
Then w is optimized by fixed E, A, Q, it is as a result as follows：
Above mentioned problem is actually well-known ridge regression problem, and its optimal solution is
E is finally fixed, w, A optimization Q, can be obtained：
Wherein,
In addition, Lagrange's multiplier Y1And Y2Updated by following scheme：
Y1,t+1=Y1,t+μt(X-XAt+1-Et+1)
Y2,t+1=Y2,t+μt(Qt+1-At+1wt+1)
Wherein, ▽ is the symbol for seeking local derviation.
The relation between the fraction of prediction and true score is studied under selected evaluation criterion, obtains algorithm performance result.
Wherein, database is randomly divided into 10 groups by the embodiment of the present invention, and all carrying out above-mentioned steps to each group obtains 10 groups
Coefficient correlation, evaluation algorithms performance of averaging.The evaluation criterion of this method selection has sequence correlation (Ranking
Correlation) and R-value, also have in embodiment 3 and be discussed in detail.
Embodiment 3
With reference to specific experimental data, Fig. 3 to Fig. 4 carries out feasibility checking to the scheme in Examples 1 and 2, in detail
See below description：
Image mnemonic data set includes 2,222 images from SUN data sets.The memory score of image passes through
Amazon Mechanical Turk Visual Memory Game are obtained, and image mnemonic is the successive value from 0 to 1.
Value is higher, and image is more difficult to remember, and has the sample image of various memory scores as shown in Figure 2.
This method takes two kinds of appraisal procedures：
The dependent evaluation method that sorts (Ranking Correlation, RC)：Obtain the sequence of real memory degree and prediction memory
Fraction ordering relation is spent, the phase relation between two kinds of sequences is weighed using the standard of the related Spearman coefficient correlations of sequence
Number.Its span is [- 1,1], and value is higher, and to represent two kinds of sequences closer：
Wherein, N is test set image number, r1In element r1iIt is the position that the i-th pictures sort in legitimate reading,
r2In element r2iIt is the position that the i-th pictures sort in prediction result.
R-value：Compared with assessment prediction fraction is easy to regression model with the coefficient correlation between true score.R-value takes
Value scope is [- 1,1], and 1 represents positive correlation, and -1 represents negative correlation：
Wherein, N is test set image number, siIt is image real memory degree scores vector,It is all image real memories
Spend the average of fraction；viIt is image prediction memory degree scores vector,It is the average of all image prediction memory degree fractions.
This method and following four method are contrasted in experiment：
LR(Liner Regression)：The pass between low-level image feature and memory degree fraction is trained using linear prediction function
System；
SVR(Support Vector Regression)：Support vector regression, by low-level image feature string together, with reference to
RBF kernel function learning of nonlinear functions prognostic chart picture memory degree；
MRR[9](Multiple Rank Regression)：Established back using multistage left projection vector and right projection vector
Return model；
MLHR[10](Multi-Level via Hierarchical Regression)：Multimedia based on hierarchical multiple regression
Information analysis.
Fig. 3 demonstrates convergence；Fig. 4 illustrates this method and other method performance comparison result, it can be seen that
This method is better than other method.Low-level image feature and the relation of memory degree prediction have only been probed into control methods.This method is special by bottom
Sign is incorporated under same framework with image attributes feature to be predicted to iconic memory degree.This method also uses transfer learning simultaneously
Train to obtain image attributes detector from external data base, obtain a relatively stable model.Experiment show we
The feasibility and superiority of method.
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It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Sequence number is for illustration only, does not represent the quality of embodiment.
The foregoing is only presently preferred embodiments of the present invention, be not intended to limit the invention, it is all the present invention spirit and
Within principle, any modification, equivalent substitution and improvements made etc., it should be included in the scope of the protection.
Claims (4)
1. a kind of combine low-rank representation and the learning method of sparse regression, it is characterised in that the described method comprises the following steps：
Feature extraction is carried out to the SUN data sets with iconic memory degree fraction label；
One entirety of composition under same framework is placed on by low-rank representation and with reference to sparse regression model two parts, structure joint is low
The model of sum of ranks sparse regression；
Solve the problems, such as the mnemonic of automatic Prediction image using more vision self-adapting regression algorithms, obtained under optimized parameter
The relation of characteristics of image and iconic memory degree；
The feature that combination image proposes, utilize the relational result obtained under optimized parameter, forecast database test set image note
Degree of recalling, and verify prediction result with relevant evaluation standard.
2. the learning method of a kind of joint low-rank representation according to claim 1 and sparse regression, it is characterised in that described
Method also includes：Obtain image mnemonic data set.
3. the learning method of a kind of joint low-rank representation according to claim 1 and sparse regression, it is characterised in that described
Feature includes：Scale invariant features transform feature, search tree feature, histograms of oriented gradients feature and structural similarity are special
Sign.
4. the learning method of a kind of joint low-rank representation according to claim 1 and sparse regression, it is characterised in that described
The model of joint low-rank and sparse regression is specially：
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Wherein：
X be input feature, A ∈ RD×DIt is that the low-rank projection matrix of N number of sample captures the bottom low-rank knot shared between sample
Structure, E ∈ RN×DIt is to utilize L1Norm solves random error；w∈RD×1It is transformation matrix, by the sample after conversion and their note
Recalling score is associated, and y is the label of training sample；It is the error function of definition；λ ＞ 0 are balance ginsengs
Number.
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| CN109558882B (en) * | 2018-11-30 | 2023-05-05 | 苏州大学 | Image classification method and device based on robust local low-rank sparse CNN features |
| CN109885728A (en) * | 2019-01-16 | 2019-06-14 | 西北工业大学 | Video summarization method based on meta learning |
| CN109885728B (en) * | 2019-01-16 | 2022-06-07 | 西北工业大学 | Video abstraction method based on meta-learning |
| CN109858543A (en) * | 2019-01-25 | 2019-06-07 | 天津大学 | The image inferred based on low-rank sparse characterization and relationship can degree of memory prediction technique |
| CN109858543B (en) * | 2019-01-25 | 2023-03-21 | 天津大学 | Image memorability prediction method based on low-rank sparse representation and relationship inference |
| CN110457672A (en) * | 2019-06-25 | 2019-11-15 | 平安科技（深圳）有限公司 | Keyword determines method, apparatus, electronic equipment and storage medium |
| CN112990242A (en) * | 2019-12-16 | 2021-06-18 | 京东数字科技控股有限公司 | Training method and training device for image classification model |
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