CN104574555A - Remote checking-in method adopting face classification algorithm based on sparse representation - Google Patents

Abstract

The invention discloses a remote checking-in method adopting a face classification algorithm based on sparse representation, belongs to the field of checking-in and aims to solve the problem that the existing checking-in cannot be identified remotely. The method comprises the following step: (1) acquiring face information of each checked person as a training sample data set; (2) re-acquiring the face information of each checked person as a test sample, and performing sparse representation on the test sample in the training sample set by adopting a face classification algorithm based on sparse representation to obtain a most-spare solution; (3) realizing remote person identify information identification based on an active RFID of a ZigBee technology according to the most-spare solution, and accurately judging the passing direction of each person by adopting a double-base-station model and utilizing an RSSI location technology so as to identify whether the person enters a checking-in area or leaves away from the checking-in area. The method disclosed by the invention can be used for remotely tracking and recording the detailed entrance and exit conditions of each person in real time.

Description

Based on the remote Work attendance method of the face classification algorithm of rarefaction representation

Technical field

Based on the remote Work attendance method of the face classification algorithm of rarefaction representation, realize the details of remote real-time follow-up and record's discrepancy, belong to work attendance technical field.

Background technology

Attendance management is the important component part of human resource management, is the important means ensureing that colleges and universities and enterprises and institutions run well, is related to the vital interests of employee.Work attendance management system is an interdiscipline, high-tech integrated technology set, be mainly concerned with the technology-oriented disciplines such as psychology, infotech, Database Systems, computer network and Internet of Things application, have and work attendance, data analysis, the automatically several functions such as emolument calculating and examination are carried out to enterprises and institutions employee.

Work attendance management system mainly contains identification module, authentication module and information management module three parts composition.First need to identify the identity of personnel and confirm, then by network, personnel identity information is uploaded to central server and carry out analysis and treament.Usually needing the doorway of work attendance that Time Attendance Device is installed, as IC (ID) card reader, fingerprint machine, iris scan machine, make a video recording first-class, after personnel identity information is caught by these equipment, by computer network, data transferred back to central server, data are confirmed, record and analyze.The development of rational attendance management to an enterprise or colleges and universities has very important effect.

In recent years, various types of Work attendance management system is widely used in colleges and universities, enterprises and institutions.The many employings of early stage Work attendance management system are manually registered, closely the active mode such as to swipe the card carry out attendance management, need initiatively to be stopped in face of Time Attendance Device by work attendance personnel to carry out attendance management, waste time and energy, easily occur that card is lost, wear and tear, be replicated and other people replace the problem such as to swipe the card, and when numerous by work attendance personnel amount, need queuing work attendance, Consumer's Experience is very poor, emphasizing today that hommization is experienced, so that the demand of various application scenario can not be met.

Beat fingerprint, be faced with these problems by palmmprint, scanning iris etc. equally based on the attendance management mode of biological information of human body identification, need in face of Time Attendance Device, stop the several seconds and carry out work attendance, characteristics such as although the biological information of human body such as fingerprint, iris have permanency, carry with, the demand of modern Intelligent Checking on Work Attendance management still can not be met.

Non-contact attendance management based on RFID technique avoids the shortcoming needing to stop work attendance, can make to be carried with card by work attendance personnel and freely come in and go out, and can not miss attendance management data, obtain increasing application in recent years.But traditional RFID exists, and decipherment distance is short, security is low, easily by human body and the problem such as metal screening and location difficulty.For these problems, remote active RFID recognition method based on ZigBee technology is passed through in tag card, add low-power consumption microcontroller and ZigBee communication module, and adopt sleeping/waking pattern, remote (50-80 rice) identification automatically can be realized.Radio-frequency recognition system based on ZigBee technology not only can support the light reading within the scope of 50 meters, also support to read up to while 200 tag cards, more can overcome remote passive discerning mode easily by problem that human body, metal etc. block, can ensure the correct reading that up to a hundred employees pass in and out simultaneously, be a kind of recognition method that application is maximum, pouplarity is maximum at present.The method can also be followed the tracks of and record the details of employee's turnover in real time, but still easily occurs that other people replace swiping the card and card is lost, the problem such as to be replicated.

Summary of the invention

The present invention is directed to the remote Work attendance method that the deficiencies in the prior art part provides a kind of face classification algorithm based on rarefaction representation, realize the details of remote real-time follow-up and record's discrepancy, and the security of management or gate control system before examination can be improved, avoid the safety issue occurring that some are artificial.

To achieve these goals, the technical solution used in the present invention is:

Based on a remote Work attendance method for the face classification algorithm of rarefaction representation, it is characterized in that, following steps:

(1) gather all by the face information of work attendance personnel as training sample data collection;

(2) Resurvey by the face information of work attendance personnel as test sample book, test sample book is concentrated rarefaction representation at training sample by the face classification algorithm based on rarefaction representation, rarefaction representation finds out system of linear equations: the solution that Ax=b is the most sparse, and A is the matrix of a m × n be a vector, x is this solution of equations, adopts a valuation functions J (x) to find the most sparse unique solution, defines a conventional optimization problem P _j, PJ:minxJ (x), makes Ax=b, wherein J (x) adopt two norms square || x|| ₂ ², obtain the most sparse solution;

(3) the most sparse solution will obtained, active RFID based on ZigBee technology realizes the identification of remote personnel identity information, adopt Dual base stations model, and utilizing RSSI location technology to differentiate accurately the direction that personnel pass through, the personnel of identifying enter work attendance region or leave work attendance region.

As preferably, in described step (2), the step of the described face classification algorithm based on rarefaction representation is as follows:

(21) the dictionary data collection be made up of k class training sample is inputted and test sample book

(22) with all row of unit two norm standardization dictionary Α;

(23) l is solved ₁minimization problem, x1:min ‖ x ‖ ₁st. ‖ Ax-y ‖ ₂≤ ε, ε are two norm constants of given tolerable noise items;

(24) residual error for i=1:k is calculated; Ri (y)=‖ y-A δ i (x ₁) ‖ ₂, wherein truncation funcation δ i: δ _i(x ₁) in order to retain x ₁in the coefficient corresponding with the i-th class, all the other positions are all set to 0;

(25) export the category IDs of test sample y, namely test sample y belongs to the i-th class in dictionary.

As preferably, in described step (21), judge whether face test sample book is legal sample, and step is as follows:

(211) by sparse coefficient of concentration, compute sparse coefficient on training sample, judges in rarefaction representation x, whether non-zero entry concentrates in some classifications of training sample, sparse coefficient of concentration $\mathrm{SCI}\left(x\right)=\frac{k\·{\max }_{i}P{\mathrm{\δ}}_i\left(x\right)P_1/\mathrm{Px}{P}_1-1}{k-1}\∈\left[\mathrm{0,1}\right],$ Coefficient vector if SCI (x)=1, then show that test sample book is only represented by the some classes in training sample, and if SCI (x)=0, then show that the non-zero entry of sparse coefficient is almost dispersed in all classifications;

(212) a fixed τ ∈ [0,1] is got, if SCI is (x ₁) < τ, then refuse this test sample book.

Compared with prior art, the invention has the advantages that:

One, realize the identification of remote personnel identity information and RSSI location based on the face classification algorithm of rarefaction representation, the active RFID of ZigBee technology, realize the details of remote real-time follow-up and record's discrepancy;

Two, according to the non-zero entry of sparse solution distribution carry out Classification and Identification, and this distribution can be utilized to carry out the validation verification of test sample book, refusal invalid data, the performance of boosting algorithm.

Accompanying drawing explanation

Fig. 1 is the automatic attendance management process flow diagram of the present invention;

Fig. 2 is the b=Ax after the present invention rearranges;

Fig. 3 is non-zero sparse coefficient of the present invention classification schematic diagram;

Fig. 4 is the distribution of the illegal test sample book coefficient of the present invention;

Fig. 5 is the distribution of the illegal test sample book residual error of the present invention;

Fig. 6 is the present invention is the legal test sample book coefficient distribution of the present invention;

Fig. 7 is the distribution of the legal test sample book residual error of the present invention;

Fig. 8 is present system integrated stand composition;

Fig. 9 identifies schematic diagram automatically for the present invention staff's identity information;

Figure 10 is the structural drawing of the present invention staff's card structure figure and work attendance base station;

Figure 11 is backbone network network topology structure figure of the present invention;

Figure 12 is the circuit structure sketch of backbone network base station of the present invention;

Figure 13 is that the present invention is from base station one to the RSSI value of base station two change schematic diagram;

Figure 14 is attendance data treatment scheme of the present invention;

Figure 15 is the impact that λ of the present invention changes on SRC face identification rate;

Figure 16 is that dimension that the present invention is different is on the impact of discrimination;

Figure 17 is that PCA of the present invention compares with random face characteristic extracting method discrimination;

Figure 18 is SRC and NN of the present invention, NS discrimination compares.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further illustrated.

For a non-singular matrix as m<n, owing constant linear system of equations Ax=b will have infinite multiple solution.Rarefaction representation is intended to find out system of linear equations: the solution that Ax=b is the most sparse, and wherein, A is the matrix of a m × n, be a vector, x is this solution of equations.In order to avoid system of equations may not separated, if m < < is n, to ensure that equation is with or without poor multiple solution.In all solutions, most interested surely belongs to that the most sparse solution, namely comprises the solution of minimum nonzero element.Find the problem of the most sparse solution, be called rarefaction representation.Want in infinite multiple solution, find that the most sparse solution, need to adopt additional strategy.Introduce validity function J (x) and assess a possible solution, the value of J (x) is the smaller the better.The optimization problem P that first definition one is conventional _j, P _j: min _xj (x) makes Ax=b, selects a strict convex function to ensure uniqueness of solution, J (x) adopt two norms square || x|| ₂ ², two norm problem P ₂unique solution will be only had.

In the field of rarefaction representation, openness (Sparsity) can also be adopted to assess.Simply and intuitively assess the openness of a vector x, by judging the number of nonzero element in x, when in x, the number of nonzero element is fewer, vector x is more sparse, introduces zero norm l ₀optimization problem: || x|| ₀=#{i:x _i=0}, if || x|| ₀< < n, then x is sparse.The zero norm problem P drawn above ₀, have J (x)=J ₀(x)=|| x|| ₀, obviously: (P ₀): min _x|| x|| ₀make Ax=b, make a _i(1≤i < < n) is the row of matrix A, then the equation above can be expressed as again: b=x ₁a ₁+ ... + x _na _n.

Sparse optimization problem and minimize two norm (l ₂) problem is very similar, but they make a big difference in itself.L ₂problem always has unique solution and ripe linear algebra instrument can be utilized to solve, and l ₀problem is NP-hard.Need to verify l ₀problem has unique solution.Concrete checking the following is:

Based on the uniqueness of spark, Spark is for Arbitrary Matrix the minimal linear that Spark (A) is A is correlated with columns.The columns of the Maximal linearly independent group that the order (Rank) of matrix A is A, obvious similarity is had between rank of matrix and Spark, relative to asking rank of matrix, the solution procedure of the Spark of matrix the subset possible to all row of matrix A will carry out Combinatorial Optimization search.The Spark of matrix is that sparse uniqueness of solution gives a simple standard, the kernel of equation y=Ax and matrix A is connected, from the kernel of matrix, on the kernel Ax=0 of matrix, the distribution of the nonzero element of x is more uniform, be not concentrated on some elements, this does not conform to the result expected, at this moment it is desirable that throw the solution in Ax=0.The x solved in Ax=0 picks out some row in fact from A, and these row are linear correlations, and this is not desired situation, so need the generation trying every possible means to avoid this situation.Found by equation, the solution vector of kernel is exactly the row of the linear correlation selected, the row of these linear correlations inherently exist a boundary, have exceeded this boundary, and the column vector in A is exactly linear correlation, is namely that the equation on kernel has solution.Be exactly linear independence in the column vector of this boundary and so on, the equation on kernel is without solution.By analyze can specify we need be exactly this boundary, this boundary is exactly spark (A).For Arbitrary Matrix the minimal linear that Spark (A) is A is correlated with columns, and all solution x for its kernel are satisfied || x|| ₀> spark (A).If by Spark, can to obtain conclusion be x is the P of a system of linear equations y=Ax ₀separate, and x meets ‖ x ‖ ₀<Spark (A)/2, then this separates the most sparse unique solution that x is system of linear equations.

Concrete proves: suppose P ₀there is another one solution y to satisfy condition, then ‖ x ‖ ₀=‖ y ‖ ₀, and A (x-y)=0, row and the element x-y linear correlation of matrix A are described.According to the definition of Spark, ‖ x-y ‖ ₀>=Spark (A).

Due to ‖ x ‖ ₀+ ‖ y ‖ ₀>=‖ x-y ‖ ₀, can draw || y|| ₀>=spark (A)-|| x|| ₀> spark (A)/2 > || x|| ₀, this and contradicting above, therefore x must be unique.This proof procedure provides clearly and when just can obtain unique most sparse solution, but the solution procedure of spark (A) is very complicated, therefore can consider to utilize Lindsey Graham (Gram) matrix very relevant to spark to solve.

If the row of matrix A are typically canonicalized, order matrix for the p of matrix A arranges the matrix formed, then Gram matrix A _pcan be defined as: when Gram determinant of a matrix is nonzero value (when Gram matrix is nonsingular), matrix A _prow be only linear independence.

Based on the uniqueness of related coefficient, solve the complexity of spark and solve P ₀the complexity of problem is suitable, and a kind of method adopting related coefficient (Mutual Coherence) is the straightforward procedure solving sparse uniqueness of solution, and related coefficient is defined as: for Arbitrary Matrix its related coefficient is: a _i, a _jbe respectively A ^{m × n}i-th, j row.Can show that the related coefficient of a matrix is inner product between this matrix different lines maximum value after standardization, be Description Matrix row between a kind of method of correlativity.For a unit matrix, mutually orthogonal between its all row, therefore, related coefficient is zero.A columns is greater than to the ordinary channel of line number, m>n, related coefficient is certainly for just, and we need to obtain a value little as far as possible, to obtain the characteristic similar in appearance to unit matrix as far as possible.

For the matrix of, allow A ^tbe multiplied with A, just can obtain a matrix A relevant with A itself ^ta, because the data collected are not very clean data usually, in order to avoid the unnecessary problem that data skew brings, first standardize matrix A by row, then, just can obtain the expression of any one inside this matrix, namely formula has just had each expression, and the result can calculated by this formula is a lot, needs matrix A ^tthe result of A is expressed by simpler and clearer mode.A kind of method be more intuitively with the maximal term in whole matrix come alternative other.For expression formula maximal term, exactly when the element on whole diagonal line is all 1, if whole matrix all replaces to 1, just becoming unit matrix, is not required result.In order to avoid this result, needing the element avoided on diagonal line, going to replace all these elements by the maximal value in other all elements, after replacing it, obtaining Arbitrary Matrix related coefficient μ (A) with the pass of spark (A) is: the spark (A) being difficult to calculate and the related coefficient μ (A) relatively easily calculated contacted together with, solve the problem that spark (A) is difficult to calculating, below to issuing a certificate.

Given arbitrary p > 0, selects p to arrange composition A from matrix A _pand the Gram matrix of correspondence, Gram matrix G (Ap) is non-diagonally dominant matrix, if 1-(p-1) μ (A)≤0, namely matrix A is described _pp row may linear correlation, according to the definition of spark, it is the effective criterion judging sparse solution uniqueness.According to this condition, continue to explore the relation between 0 norm of x and related coefficient.

When the most sparse solution of equation is unique, there is ‖ x ‖ ₀<spark (A)/2, namely for meeting arbitrarily ‖ x ‖ ₀the x of <spark (A)/2, x must be had to be less than a minimum spark (A), pass through formula, obtain the value of minimum spark (A), if directly replace spark (A) by the minimum value of spark (A), just one has unique sparse solution assessment expression formula for accounting equation is obtained, namely obtain assessing linear equation based on the method for related coefficient and whether there is unique most sparse solution, if system of linear equations y=Ax has one to separate x ₀meet: then this solution is the solution that this system of linear equations is the most sparse.

When what condition understanding meet, just getable most sparse solution is only unique.Simple directly method is difficult to P ₀problem solves, and needing first to find can under given conditions to P ₀problem carries out the method solved.For P ₀problem, namely

(P ₀):minx‖x‖ ₀s.t. b＝Ax,

Unknown number x is made up of two effective parts, and a part of demand fulfillment system of equations makes equation set up, and another part will make non-zero entry number minimum.Therefore, feasible method is exactly the efficient solution from meeting equation, then the nonzero value in x will be tried to achieve easily via least square method.Solve P ₀the algorithm of problem is discrete, and greedy algorithm will be optimal selection.

Greedy algorithm solves l ₀problem is as follows:

If a matrix A, its spark (A) >2, the solution (optimum solution) of optimization 0 norm problem is val (P ₀)=1, and this optimum solution is unique, and therefore vectorial b is some row of matrix A and the product of a scalar.Find these to arrange by carrying out test to each row of matrix A, jth plows test and can be undertaken by minimizing ∈ (j), and the expression formula obtaining residual error is:

$\begin{array}{c}\&Element;\left(j\right)=\underset{z_j}{\min }{\left|\right|a_j{z}_j-b\left|\right|}_2^2={\left|\right|\frac{a_j^{T}b}{{\left|\right|a_j\left|\right|}_2^2}{a}_j-b\left|\right|}_2^2\\ ={\left|\right|b\left|\right|}_2^2-2\frac{{\left(a_j^{T}b\right)}^2}{{\left|\right|a_j\left|\right|}_2^2}+\frac{{\left(a_j^{T}b\right)}^2}{{\left|\right|a_j\left|\right|}_2^2}\\ ={\left|\right|b\left|\right|}_2^2-\frac{{\left(a_j^{T}b\right)}^2}{{\left|\right|a_j\left|\right|}_2^2}\end{array}$

If residual error is zero, just obtain desired solution.As can be seen from formula above, this test only needs to calculate and b and a _jparallel.The time complexity of whole process is O (mn), is common PC acceptable.

Same principle, if a matrix A, its spark (A) >2k ₀, the solution of optimization 0 norm problem is val (P ₀)=k ₀, then vectorial b is maximum k in matrix A ₀the linear combination of row.Owning A individual by k ₀the subset of row composition carries out enumeration test, utilizes the time complexity of enumeration test to be calculated amount exponentially level increases, and is difficult to allow common PC accept.

Greedy strategy has abandoned exhaustive search, in each step computation process, carrys out more new explanation by solving local optimum.Algorithm is from x ₀=0 starts, by the set x of k iteration maintenance activity row ^k, in iterative process each time, add row in this set.The object of iteration reduces the residual error with the approximate b of current active row as much as possible each time, and after new row add, reappraise to residual error, if residual error is less than certain given threshold value, algorithm terminates.

OMP algorithm approximate solution l ₀problem is as follows:

OMP (Orthogonal-Matching-Pursuit) algorithm is a member of greedy algorithm family, adds new row, solve 0 norm minimum problem by each iteration.OMP algorithm selects an atom to build the set A of optimum atom at every turn from training sample dictionary A _opt, and in each step, orthogonalization process is carried out to selected atom.The initiation parameter of OMP algorithm is: k=0, r ₀=b kth step iteration time, from dictionary A by following formula selection an atom wherein, $r_k=b-\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{a}_{{\mathrm{\&lambda;}}_i}{x}_i=b-A_k{x}_k,$ And $x_k\text{=arg}\underset{x\&Element;R^k}{\min }{\left|\right|b-A_{k}x\left|\right|}_2\&Element;R^k,$ Then can define oMP algorithm will not select same atom twice, and namely OMP algorithm is certain to restrain being no more than in m iterative process.Concrete proof is as follows:

To arbitrary k >=0, due to $x_k\text{=arg}\underset{x}{\min }{\left|\right|b-A_{k}x\left|\right|}_2,$ Then $(b-A_k{x}_k)A_k^T=0,$ Namely $a_{{\mathrm{\&lambda;}}_i}^T\&CenterDot;r_k=0,(i=1,...,k),$ Can draw $a_{{\mathrm{\&lambda;}}_{k+1}}=\arg \underset{a\&Element;A}{\max }\left|a^T{r}_k\right|=\arg \underset{a\&Element;A\backslash A_k}{\max }\left|a^T{r}_k\right|\&NotElement;A_k,$ The new atom that each iterative process is selected, belong to the set having selected atomic building scarcely, namely OMP algorithm is in different iterative steps, can not select same atom, so OMP algorithm is inherently restrained after limited iterative step, and iterations can not more than m time.

If sample b just can by K atom Linearly Representation, then b can be expressed as by these former molecular set expressions be $A_{\mathrm{opt}}=\{a_{{\mathrm{\&lambda;}}_1},a_{{\mathrm{\&lambda;}}_2},...,a_{{\mathrm{\&lambda;}}_k}\}.$

By rearranging matrix A and x, as shown in Figure 2, need to prove that OMP algorithm often walks the atom of iterative process selection in set A _optin, namely every single-step iteration of OMP algorithm all can select optimum atom.What demonstrate that optimum solution that OMP algorithm tries to achieve can ensure to separate is openness, can obtain each iteration of OMP algorithm and all can select correct atom, and can not repeat to select by the atom selected, namely OMP algorithm often walk the atom that iterative process selects must in set A _optin, through k ₀after secondary iterative process, calculate residual error and will become 0, algorithm termination, ensure that whole algorithm can successful reconstructed sample.

Because 0 norm problem is NP-hard problem, therefore wish by carrying out some conversions of equal value to 0 norm problem, thus feasible solution to be found.Specific as follows:

When solution is enough sparse, the 0 norm problem that minimizes can change into and minimize 1 norm problem, and the 1 norm problem that minimizes can solve by ripe linear programming (linear programming) method.By 0 norm question variation will be minimized for minimizing 1 norm problem, by linear programming method, former problem is solved, and the solution of trying to achieve can ensure the characteristic of solution.Shown below is the equivalence proof minimizing 0 norm problem He minimize 1 norm problem.

First define l ₁(P ₁) problem: (P ₁) min||Wx|| ₂s.t. b=Ax, wherein W is diagonal angle positive definite matrix, W _i=|| ai|| ₂, a _ifor the i-th row of matrix A.Separate x for one of system of linear equations b=Ax ₀meet the most sparse condition then x ₀be all P ₀problem and P ₁the unique solution of problem, wherein and rank (A)=m, m<n, obtain (P ₀) x _l0: min ‖ x ‖ ₀s.t. b=Ax, (P ₁) x _l1: min ‖ Wx ‖ ₁s.t. b=Ax, concrete proof is as follows:

First define the set Γ of other feasible solutions, Γ=y|y ≠ x, A (y-x)=0, || Wy|| ₁≤ || Wx|| ₁, || y|| ₀> || x|| ₀, if Γ non-NULL, illustrate that there is other feasible solutions being different from x exists; If set Γ is empty set, illustrate that it is unique for separating x.X is the most sparse solution of system of equations, and other solution does not all have x sparse, therefore, if e=y-x, then and Γ=y|y ≠ x, A (y-x)=0, || Wy|| ₁≤ || Wx|| ₁, || y|| ₀> || x|| ₀formula can be expressed as again: Γ _e=e|e ≠ 0, Ae=0, || W (x+e) || ₁≤ || Wx|| ₁, || x+e|| ₀> || x|| ₀, this set is amplified, even and prove that this set is still empty set after zooming.

First from || W (x+e) || ₁≤ || Wx|| ₁set out, the k of Assumption set x ₀individual nonzero element all concentrates on the foremost of vector, then ${\left|\right|W(x+e)\left|\right|}_1-{\left|\right|\mathrm{Wx}\left|\right|}_1={\mathrm{\&Sigma;}}_{i=1}^{k_0}{W}_{\mathrm{ii}}\&CenterDot;\left(\right|(x_i+e_i)|-x_i)+{\mathrm{\&Sigma;}}_{i>k_0}{W}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|\&le;0,$ According to character and the W of inequality _ii> 0, with to formula ${\left|\right|W(x+e)\left|\right|}_1-{\left|\right|\mathrm{Wx}\left|\right|}_1={\mathrm{\&Sigma;}}_{i=1}^{k_0}{W}_{\mathrm{ii}}\&CenterDot;\left(\right|(x_i+e_i)|-x_i)+{\mathrm{\&Sigma;}}_{i>k_0}{W}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|\&le;0$ Carry out convergent-divergent: ${\mathrm{\&Sigma;}}_{i=1}^{k_0}{w}_{\mathrm{ii}}\&CenterDot;\left(\right|(x_i+e_i)|-x_i)+{\mathrm{\&Sigma;}}_{i>k_0}{w}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|\&GreaterEqual;-{\mathrm{\&Sigma;}}_{i=1}^{k_0}{W}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|+{\mathrm{\&Sigma;}}_{i>k_0}{W}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|,$ Will be designated as represent vector | the front k of We| ₀individual element and, then ${\mathrm{\&Sigma;}}_{i=1}^{k_0}{w}_{\mathrm{ii}}\&CenterDot;\left(\right|(x_i+e_i)|-x_i)+{\mathrm{\&Sigma;}}_{i>k_0}{w}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|\&GreaterEqual;-{\mathrm{\&Sigma;}}_{i=1}^{k_0}{W}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|+{\mathrm{\&Sigma;}}_{i>k_0}{W}_{\mathrm{ii}}\&CenterDot;\left|e_i\right|$ Can be expressed as: ${\left|\right|\mathrm{We}\left|\right|}_1-{21}_{k_0}^T\&CenterDot;\left|\mathrm{We}\right|\&le;0.$ Analysis condition Ae=0,

0=Ae=A ^tae=A ^taW ^-1we=W ^-1a ^taW ^-1we, is namely multiplied by an A on the left side of Ae ^t, result is constant, obtains W ^-1a ^taW ^-1we=0, and have-We=(W ^-1a ^taW ^-1-I) We, both sides are taken absolute value, and carries out scaling, obtain | we|=| (W ^-1a ^taW ^-1-I) We|≤| W ^-1a ^taW ^-1-I||We|, analyzes W ^-1a ^taW ^-1the structure of-I, if A=is [a ₁, a ₂..., a _n], wherein a _jfor the jth of matrix arranges, namely

Wherein, for order is the n rank square formation that 1 all elements is 1, and use related coefficient. can draw definition f=We, then Γ _e=e|e ≠ 0, Ae=0, || W (x+e) || ₁≤ || Wx|| ₁, || x+e|| ₀> || x|| ₀can again be expressed as: set Γ _f ¹unbounded, because if f ∈ is Γ _f ¹, then α f ∈ Γ _f ¹set up all α ≠ 0, in order to further prove its characteristic, constraint f is normalization vector, namely then can define new set ${\mathrm{\&Gamma;}}_f^2=\left\{f\right|{\left|\right|f\left|\right|}_1=1,\left|f\right|\&le;\frac{\mathrm{\&mu;}\left(A\right)}{1+\mathrm{\&mu;}\left(A\right)}\mathrm{1,1}-{21}_{k_0}^T\left|f\right|\&le;0\},$ By again because || f|| ₁=1, so $1-{21}_{k_0}^T\left|f\right|=1-2{\mathrm{\&Sigma;}}_{i=1}^{k_0}\left|f_i\right|\&GreaterEqual;1-2k\max \left|f_i\right|=1-2k_0\frac{\mathrm{\&mu;}\left(A\right)}{1+\mathrm{\&mu;}\left(A\right)},$ If $k_0<(\frac{1}{\mathrm{\&mu;}\left(A\right)}+1)/2,$ Then have $1-2k_0\frac{\mathrm{\&mu;}\left(A\right)}{1+\mathrm{\&mu;}\left(A\right)}>0,$ Namely $1-{21}_{k_0}^T\left|f\right|>0,$ This and Γ _f ²in $1-{21}_{k_0}^T\left|f\right|\&le;0,$ Contradiction, namely there are not other feasible solutions, separate x for one of system of linear equations b=Ax ₀meet the most sparse condition then x ₀be all P ₀problem and P ₁the unique solution of problem, wherein and rank (A)=m, m<n, obtain (P ₀) x _l0: min ‖ x ‖ ₀s.t. b=Ax, (P ₁) x _l1: min ‖ Wx ‖ ₁s.t. b=Ax must demonstrate,prove.

By above-mentioned known, for the 0 norm minimum problem being difficult to solve, the 1 norm minimum problem that can be converted into solves, and can ensure the openness and uniqueness of solution.And 1 Norm minimum problem can utilize ripe linear programming method to solve, such as BP (BasisPursuit) algorithm.Usual employing minimizes the sparse solution that 1 norm problem carrys out solving equation group, and rarefaction representation problem can be solved on common PC.

In field of face identification, rarefaction representation algorithm is intended to solve the rarefaction representation that test sample book is concentrated at training sample, how according to the non-zero entry of sparse solution distribution carry out Classification and Identification, and this distribution can be utilized to carry out the validation verification of test sample book, refusal invalid data, the performance of boosting algorithm.The concrete face classification algorithm based on rarefaction representation (ClassificationBased On Sparse Representation, SRC) is as follows:

Face classification refers to and is divided in a certain class of the training sample belonging to this sample by a given face sample, i.e. a given test sample book, algorithm needs to determine this test sample book and belongs to which class.From training sample, select a face y as test sample book, ideally, the non-zero entry of the sparse solution of being tried to achieve by sparse 1 norm minimum problem all be arranged in that class corresponding to test sample y, just can directly be classified by the non-zero entry of sparse solution.As shown in Figure 3, the sparse solution of 1 norm minimum problem of test sample y only has the element of corresponding i-th class non-vanishing, therefore can think that y belongs to the i-th class.

In actual applications, due to the impact of noise and model error, the non-zero entry of sparse solution may be distributed in multiple classifications of training sample, makes us directly not utilize the non-zero entry of sparse solution to classify.In this case, overall rarefaction representation can be utilized to design multiple possible sorting technique.Such as, simply y can be divided into the class corresponding to element maximum in all non-zero entry.But this method does not well utilize the closure of the subspace computing of image in recognition of face problem, in order to better utilize this linear structure, we utilize the quality corresponding to different classes of coefficient reconstruct facial image to classify, namely reconstructed error is less, and test sample book more likely belongs to this class.

For each class i, we introduce truncation funcation

Wherein, be one and comprise n _i× n _iunit submatrix, for selecting for the element with the i-th class in x, and then utilize these yuan usually to reconstruct test sample y.For given test specimens y, Y _i=A δ _i(x ₁).The difference r of the expression of foundation test sample y and face subspace _i(y)=‖ y-Yi ‖ ₂the minimum classification dividing y, namely sample belongs to kth class, if r _k(y)=min _ir _i(y)=min _,|| y-Y _i|| ₂=min _i|| y-A δ _i(x ₁) || ₂,

Wherein, x ₁=arg min||x|| ₁s.t Ax=y.

Face classification algorithm concrete steps based on rarefaction representation are as follows:

Step 1: input the dictionary data collection be made up of k class training sample and test sample book

Step 2: with all row of unit two norm standardization dictionary Α;

Step 3: solve l ₁minimization problem, x1:min ‖ x ‖ ₁st. ‖ Ax-y ‖ ₂≤ ε, ε are two norm constants of given tolerable noise items;

Step 4: calculate residual error for i=1:k; Ri (y)=‖ y-A δ i (x ₁) ‖ ₂, wherein truncation funcation δ _i(x ₁) in order to retain x ₁in the coefficient corresponding with the i-th class, all the other positions are all set to 0;

Step 6: the category IDs exporting test sample y, namely test sample y belongs to the i-th class in dictionary.

Facial image validation verification: sorting algorithm be intended to a given test sample book to be divided into Sample Maximal may belonging to classification in, if but a given sample not belonging to any classification, the sorting algorithm of foregoing description can show that this sample belongs to some classifications equally, in order to avoid this situation, be necessary before test sample y is classified, first judge whether it is effective sample data, namely whether training data is concentrated to contain and is belonged to of a sort sample data with test sample y, and refusal is classified for not belonging to any class testing sample in training sample.If do not carry out judging just directly to classify, do not belong to the test sample book of any classification of training sample, can be divided in the middle of that minimum classification of residual error according to above sorting algorithm yet.

The incoherent image of Stochastic choice one is used for test, and by down-sampled for this picture to 12 × 10, and on Extended Yale B training sample compute sparse coefficient, Fig. 4 gives the schematic diagram of sparse coefficient, and Fig. 5 gives the schematic diagram of residual error.And Fig. 6 and Fig. 7 is sparse coefficient and the residual error schematic diagram of legal test sample book respectively, contrast can find, the sparse coefficient of the sample of Stochastic choice does not concentrate in any one classification, but is dispersed on all categories, and the sparse coefficient of legal sample is concentrated in some classifications.Therefore, the authentication mask being distributed in test sample book of sparse coefficient has very large quantity of information: for a legal test sample book, the non-zero entry of its sparse coefficient is concentrated in some classifications; And for illegal test sample book, the non-zero entry of its sparse coefficient can be dispersed on all categories.

Effective test sample book concentrates in a certain classification in the non-zero entry of the rarefaction representation of data centralization mostly, so can by the non-zero entry of observing x coefficient whether integrated distribution in certain class, judge the validity of test sample book, thus avoid the situation occurring invalid data mis-classification, and then can verify whether current face is legal user.

Sparse coefficient of concentration can be passed through $\mathrm{SCI}\left(x\right)=\frac{k\&CenterDot;{\max }_{i}P{\mathrm{\&delta;}}_i\left(x\right)P_1/\mathrm{Px}{P}_1-1}{k-1}\&Element;\left[\mathrm{0,1}\right],$ Coefficient vector judge in rarefaction representation x, whether non-zero entry concentrates in some classifications of training sample.

Utilize the solution x that 1 norm minimum problem of rarefaction representation is tried to achieve, if SCI (x)=1, then show that test sample book is only represented by the some classes in training sample; If SCI (x)=0, then show that the non-zero entry of sparse coefficient is almost dispersed in all classifications.Namely SCI more more concentrates on a certain class close to the non-zero entry in 1, x, otherwise the non-zero entry of SCI more close to 0, x is overstepping the bounds of propriety loose.Therefore, we can choose a lower limit τ, by the standard of SCI (x) >=τ as validity.If SCI (x) >=τ, then we accept this test sample book, otherwise we think that this test sample book is illegal.

Different from NN and NS, carrying out validation test sample by SCI does not need to calculate residual error.As can be seen from Fig. 6 and 7, even to a non-face image, the least residual of illegal sample is still smaller in a large training set.From rely on single statistical information to carry out to verify and identify different, based on SCI checking by checking and the process that identifies separately, utilize sparse coefficient to verify, and utilize residual error to identify.By comparing the size of SCI coefficient, differentiate that the validity whether acceptance test image carries out identifying experimentally have also been obtained checking.In the invalid image of correct refusal, improve 10 ~ 20 percentage points than NN and NS.If SCI being carried out test sample book checking joins in the algorithm of face classification, in order to improve the checking rate of algorithm to invalid data, namely before carrying out residual computations, first by the comparison of SCI system, judge whether current test sample book is legal sample, if be illegal sample, then refuses.To the method that test sample book is verified be: get a fixed τ ∈ [0,1], if SCI is (x ₁) < τ, then refuse this test sample book.

Before calculating residual error, first utilize SCI to judge whether this test sample book is legal sample, if not, then refuse Classification and Identification.Sorting algorithm after improvement can similar with multiple class to some test sample book when boosting algorithm performance.

Entire system Organization Chart: personnel identity identifies it is the main task of Work attendance management system automatically, is record the detailed turnover situation of competent person and analyze, can improves Consumer's Experience by the mode of automatic identification.Want the automatic identification realizing personnel identity information, RFID technique is excellent selection.Rfid system can have decipherment distance far away, higher accuracy of identification, be not easy blocked by the object such as human body and metal and have higher adaptive faculty to rugged surroundings.The present invention adopts a kind of novel RFID recognition method---based on the active RFID system of ZigBee technology.Because system adopts active electronic label, in order to ensure the serviceable life of active card, card adopts sleep-awake mode of operation, after card enters work attendance region, by low frequency signal, card is waken up, enter duty, in turn ensure that the serviceable life of card when realizing attendance management, the structure diagram of personnel's card as shown in Figure 10.During dormancy, the power consumption of card is only the per mille of duty, and namely this mode ensure that card has powerful function.In attendance management process, every personnel have an attendance card, at gate inhibition's passage, work attendance base station is housed, in order to the direction that the definite personnel that identify pass through, adopt Dual base stations model, i.e. two base stations, and sharp RSSI location technology differentiates accurately to the direction that personnel pass through, the personnel of identifying enter work attendance region or leave work attendance region, and as shown in Figure 8, Fig. 9 identifies schematic diagram for personnel's identity information to the Organization Chart of system automatically.

As shown in Figure 10, antenna adopts special antenna array to the structure diagram of work attendance base station, and the passage that may pass through personnel forms complete closed radiation space, and the personnel of realization are stuck in any position of passage, can be read fast and accurately.Low-frequency wakening module can regulate and wake distance up, makes to realize best Intelligent Recognition in concrete applied environment.Based on the radio sensing network of ZigBee---backbone network, be responsible for the two-way communication of perception data in the entire system.Backbone network, based on ZigBee wireless communication protocol, is the bidirectional wireless network technology of a kind of short distance, low complex degree, low-power consumption, low data rate, low cost.Backbone network is made up of the backbone network base station being deployed in diverse location, and whole network adopts website ZigBee topological structure, and utilize the automatic network-building function of ZigBee, these base stations MANET can add network, and have routing function.As shown in figure 11, the structure diagram of backbone network base station as shown in figure 12 for the topological structure of backbone network.

Radio-frequency module adopts CC2530, support 2.4GHz working frequency range, and inside is integrated with RF transceiver, enhancement mode 8051CPU, flash memory able to programme, has very powerful function.

Automatic attendance management process flow diagram as shown in Figure 1.Comprise data receiver, parsing, distribution, analysis, propelling movement and inquiry and store; Data receiver is the data passed back from functional gateway reception backbone network; After the data received are resolved, be distributed to respective platform.In different subsystem processes data, and carry out pushing, inquire about and storing according to data type.The core of data processing is exactly analyzed RSSI value and the card number of the data that two base stations are passed back by two, can be specified the identity information of current current personnel, and compare the direction that RSSI value can obtain current current personnel by card number.Card has four kinds of states, namely enters, enters, leaves, leaves.By the analysis to the conversion between these four kinds of states, the state of the personnel of holding can be learnt.

RSSI is the mark of signal power in ZigBee communication, and communication distance is nearer, and signal is stronger, distance far away, signal is more weak, compares the RSSI value of two packets, the personnel that just can determine current from that base station more close to.As shown in figure 13 for the personnel of holding to pass through from side, base station one the RSSI value change schematic diagram of side, base station two.

When personnel's card enters work attendance region, corresponding attendance data is uploaded onto the server through backbone network, when data processing, the RSSI value uploaded is blocked to same personnel and carries out record, when data volume reaches a certain amount of time, carrying out judging to receive the packet from two base stations and process simultaneously, just can utilize and once more just obtain a result, need not often secondary data arrival all compare.

The state of personnel's card is entering, is entering, is leaving, is leaving between four kinds of states and changed.When personnel block first time enter work attendance region time, its state is switched to and enters, when judgement personnel card enter into side, work attendance base station two from side, work attendance base station one, then by its State Transferring for enter.When after a timeslice, personnel's card enters work attendance region again, then personnel's card will leave state from getting the hang of to be switched to, and after arriving side, work attendance base station one, leave from leaving to be switched to.So just achieve and utilize two work attendance base stations, and realize personnel by RSSI value and to pass through the automatic identification in direction.

When determining that personnel have entered or left, need to record these information, i.e. the details of record's discrepancy, Figure 14 is attendance data treatment scheme.

In order to enable the client Real-time Obtaining checking-in result of registration, server end needs to push data into client while recording these information.System adopts WCF to realize the mutual of server and client, because client and server end belongs to different territories, want directly to send data by server end to client, need client to realize previously defined callback contracts, be i.e. SendAttData (string message).Callback contracts realizes by entrusting (Delegate), is namely called the method for client by delegated implementation.Attendance data is had to store in a database, to carry out attendance data analysis, inquiry.Such as, we can be turned out for work by the displaying of broken line graph close friend the attendance statistical graph of certain time period, as seen in figs. 5-6.

In based on the face verification of rarefaction representation feature extracting method selection and to process two major issues of blocking equal error.

The selection of feature extracting method: the feature extracting method of main flow is divided into two classes, one class extracts face global characteristics as Eigenfaces, Fisherfaces, Laplacianfaces, another kind of is extract the part face characteristic with stronger recognition capability, as eyes, nose, camber etc.

Because most of eigentransformation only relates to linear transformation, can be expressed as from facial image space to the transformation matrix in face characteristic space apply this transformation matrix to y=Ax both sides can obtain simultaneously: $\tilde{y}=\tilde{A}x=\mathrm{RAx},$ Wherein ${\tilde{y}}^{d\&times;1}=R^{d\&times;m}{y}^{m\&times;1},{\tilde{A}}^{d\&times;n}=R^{d\&times;m}{A}^{m\&times;n}.$ Due to d < < m, system of equations still has infinite multiresolution, if separate x ₀enough sparse, by l _r ¹problem solving: $\begin{array}{cccc}\left(l_R^1\right)& {\tilde{x}}_1:\min {\left|\right|x\left|\right|}_1& s.t.& {\left|\right|\mathrm{RAx}-\mathrm{Ry}\left|\right|}_2\&le;\mathrm{\&theta;}\end{array},$ Wherein will as training sample matrix, will as test sample book.The dimension d of R is larger, reduction degree is higher, and the accuracy rate of recognition of face is also higher.

For problem l _r ¹with l _ε ¹: $\begin{array}{cccc}\left(l_R^1\right)& {\tilde{x}}_1:\min {\left|\right|x\left|\right|}_1& st.& {\left|\right|\mathrm{RAx}-\mathrm{Ry}\left|\right|}_2\&le;\mathrm{\&theta;}\end{array},$ x ₁: min||x|| ₁st. || Ax-y|| ₂≤ ε, if separate x ₁enough sparse, then l _r ¹enough greatly have very large probability to recover l at dimension d _ε ¹in sparse signal x ₁.If x ₁in containing k nonzero element, and k < < n, as long as R ^{d × m}in d>=2tlog (n/d) time, l _r ¹just l can be recovered _ε ¹in sparse signal x1.

The feature utilizing gaussian random matrix linear mapping to generate is called random face (Randomfaces), the advantage of random face is that his production process compares more efficient, and transformation matrix R also has nothing to do with the facial image of data centralization, even if human face data changes, R does not need to recalculate yet.

For transformation matrix R ^{d × m}in each row element separate and obey the normal distribution that average is 0, and each provisional capital is through unit two norm standardization, and Ry is called y ^{m × 1}random Maps, then Ry is just called random face.Every row element of R is all unit length, average is the Gaussian distribution of 0.As long as sparse solution x ₁can by correct recovery, then sorting algorithm just can obtain identical classification results, and concrete feature extraction algorithm has nothing to do.Therefore, as long as feature extraction matrix R ^{d × m}middle d meets dimension blessing theorem, then sorting algorithm is by Fast Convergent, and the selection of feature extraction is no longer that recognition of face problem is successfully crucial.

To blocking and the process of error: in practical application, partial occlusion or damage may appear in test pattern, cause the data of test sample y to have error to exist.Now, measured value y ^{m × 1}with actual value y ₀ ^{m × 1}between have difference e ₀ ^{m × 1}, i.e. y=y ₀+ e ₀=Ax ₀+ e ₀, wherein e ₀be arbitrary, the error of different test pattern is unknown.As error e ₀matrix can be expressed as , there is error, e owing to only having partial data point in the linear combination of middle column vector ₀sparse concerning whole sample set, e ₀=A _eu ₀, wherein u ₀be sparse, then test sample book can be expressed as: $y=\mathrm{Bw}=\left[\begin{array}{cc}A& A_e\end{array}\right]\left[\begin{array}{c}{x}_0\\ u_0\end{array}\right]A{x}_0+A_e{u}_0=y_0+e_0,$ Wherein due to x ₀and u ₀all sparse, so $w=\left[\begin{array}{c}{x}_0\\ u_0\end{array}\right]$ Also be sparse.For the ease of calculating and expressing, choose a kind of special circumstances n _e=m, i.e. e ₀sparse under natural coordinates.So, $y={\mathrm{Bw}}_0=\left[\begin{array}{cc}A& I\end{array}\right]\left[\begin{array}{c}{x}_0\\ e_0\end{array}\right],$ Wherein the most sparse solution of system of equations.Under certain constraint condition, the l of expansion _e ⁰problem still can change into l _e ¹problem solving.When image damaged condition remains in certain scope, be the sparse solution that can us be found accurately to need, need satisfy condition as n _i+ | support (e ₀) | < d/3, wherein, n _ibe the dimension of broken parts, d is the dimension of test sample book.As long as namely to block or error is no more than this scope, l _e ¹the sparse solution w tried to achieve ₁just w can be recovered ₀.By solving the l of expansion _e ¹problem recovers sparse solution w ₀, w ₁=argmin||w|| ₁st. y=Bw, wherein try to achieve sparse solution w ₁, thus obtain e ₁, utilize y ₀=y-e ₁, obtain y ₀for the test sample book after reduction distortion data.For the distortion sample having partial occlusion or damage, residual error r in amendment sorting algorithm _i(y) expression formula: as long as can be correct solve most sparse solution w1, then algorithm still can process these preferably and exists and block and the distortion sample such as damage.

λ on the impact of discrimination: LASSO for solving l ¹problem is stable.L ¹problem (l ¹) x _l1: min||x|| ₁s.t. the LASSO extend type of Ax=y is: min||y-Ax|| ₂+ λ || x|| ₁, wherein λ is the inverse of Lagrange multiplier in LASSO.In experiment, first PCA dimensionality reduction is carried out to all human face data, the dimension values d=30 of feature extraction.Experimental result is as shown in the table:

λ	0.005	0.02	0.1	0.5	1
						d	30	30	30	30	30
Discrimination	91.65％	91.65％	91.74％	83.85％	68.87％

As can be seen from the table in LASSO the change of λ on the impact of face recognition result.In order to analysis design mothod result more intuitively, provide graphical explanation.As in Figure 15, we can find out when λ value increases gradually from 0 intuitively,

The discrimination of algorithm is more and more lower.Adopt PCA as feature extracting method in experiment.

Get λ=0.005 in LASSO to fix, the dimension d change of feature extraction, the accuracy of the characteristic dimension human face identification that experimental data is as different in following table gives.

d	30	50	80	100	120
						λ	0.005	0.005	0.005	0.005	0.005
Discrimination	91.65％	94.1％	96.01％	96.37％	97.19％

Figure 16 is corresponding result, and as can be seen from Figure, when other conditions are constant, the dimension of feature is larger, and discrimination is higher, but when dimension reaches certain threshold value, promotes less along with dimension increases discrimination.Adopt PCA as feature extracting method in experiment.

Requirement to feature extracting method during in order to verify that SRC carries out recognition of face, we adopt random face and conventional feature extracting method---principal component analytical method is tested respectively, and contrast their recognition result.

The feature extracting method that principal component analysis (PCA) general introduction is generally used for recognition of face comprises PCA, Laplacianface and DownSampled face tri-kinds, they carry out dimensionality reduction by diverse ways to facial image, and extract different features, in order to good keeping characteristics information, the dimension of feature is 120 dimensions.The process of feature extraction carries out dimensionality reduction to data exactly, is mapped to the space of a new low-dimensional by original image, carries out classifying and verify so that more effective.Wherein PCA farthest can retain the feature of original image, and Downsampled face is then the poorest.In order to better obtain the effect of contrast test, selection PCA and random face method carry out contrast test.PCA (principal component analysis (PCA)) is generally used for carrying out feature extraction to high dimensional data, to simplify storage space and calculated amount, and retains the key character of data as far as possible.

Utilize PCA to data set A=[a ₁, a ₂..., a _n] carry out feature extraction, its dimension is m × n, first will obtain the covariance matrix S of matrix A; Then calculate the eigenwert of covariance matrix S, and the eigenwert calculated is arranged according to order from big to small, select maximum eigenwert; Finally, obtain the proper vector corresponding to maximum eigenwert, and whole all sample datas are projected to eigenvalue of maximum characteristic of correspondence vector in the middle of the space of opening.Above three steps just achieve carries out feature extraction and dimensionality reduction with PCA to data.

Random face compares with PCA feature extraction discrimination: in common three kinds of feature extracting methods, it is best that PCA carries out feature extraction effect, utilizes random face and PCA method to extract the feature of different dimensions respectively, and the dimension of selection is 30,50,80,100,120 dimensions, SRC algorithm is coordinated to carry out recognition of face respectively, classify to the test data in the test database introduced above, classification results is as shown in the table, and gives more intuitive expression in fig. 17.

d	305	08	0	100	120
						PCA91.6	5％	94.10％	96.01％	96.37％	97.19％
Random face	89.92％	92.37％	95.04％	95.69％	96.42％

In experiment, we do not carry out other process to facial image, directly utilize the data in database to carry out feature extraction, then utilize SRC algorithm to identify.λ value in experiment is set to 0.005, and characteristic dimension is from 30 to 120 dimension changes.From experimental result, we can find out intuitively, two kinds of feature extracting methods are equally matched on discrimination, PCA method is due to can the feature of reservation original image of maximum possible, discrimination is slightly high, and although random face method discrimination is a little less than PCA, but calculated amount is much smaller, needing the place of process in real time.The face recognition algorithms demonstrated based on rarefaction representation is no longer that traditional face identification method is so harsh to the requirement of feature extraction, even random face method, also can obtain gratifying recognition effect.In addition, also demonstrate the increase along with characteristic dimension, discrimination can increase gradually, but after arriving a threshold value, the amplitude of increase is more and more less.

In order to verify the validity of SRC algorithm further, different algorithms is adopted to carry out emulation experiment in identical data centralization.Adopt PCA to carry out dimensionality reduction to human face data, carry out Classification and Identification with SRC, NN and NS respectively.

Test sample book by calculating the Euclidean distance between test sample y and all training samples, and is divided into this apart from the classification belonging to minimum sample, namely to all training sample a of k class by NN (Nearest Neighbor) classification _ij, for i=1:k; For j=1:n _i, $\mathrm{identity}\left(y\right)=r_i^{\mathrm{NN}}\left(y\right)=\arg \min {\left|\right|y-\left|a_{\mathrm{ij}}\right||}_2,$ Finally test sample y is divided into i-th class at the minimum sample place of Euclidean distance.

NS (Nearest Subspace) sorting technique is classified different from NN, and it calculates test sample book and the distance of test sample book between the projection of the subspace at each classification place, and test sample book is divided into apart from that minimum classification.Definition training sample subspace Ai (belonging to whole test sample books of the i-th class) calculate the Euclidean distance of test sample book and each classification subspace: for i=1:k, finally test sample book is divided into the i-th class.

NN algorithm is by technical testing sample y and training sample a _ijbetween Euclidean distance divide classification, make use of the relation between certain test sample book, intuitively just can find out that such standard is a bit unilateral.And NS algorithm divides classification by the distance calculated between test sample book and training sample subspace, measured the relation between test sample book and a classification, closer to the thought of manifold learning, such criteria for classification is also more credible than NN.

We adopt PCA to carry out feature extraction in an experiment, then utilize SRC, NN and NS to carry out face recognition experiment respectively, and data set adopts Extended Yale B face database, and half is as training set, and remaining part is as test set.We choose dimension is respectively 30,50, and 80,100,120 dimensions, test.As following table and Figure 18 give experimental result data.

d	30	50	80	100	120
						PCA+SRC	91.65％	94.10％	96.01％	96.37％	97.19％
PCA+NN	53.27％	64.25％	69.24％	71.78％	72.96％
						PCA+NS	67.36％	71.49％	74.98％	79.94％	80.24％

As can be seen from Figure 18, SRC algorithm can reach the superelevation discrimination of 97.19% when characteristic dimension is 120 dimension, and under square one, NN is 72.96%, NS is 80.24%, and rarefaction representation algorithm has better performance.Particularly when low dimensional feature, the validity of SRC algorithm is more outstanding, still has the discrimination of 91.65% when 30 dimension, and NN and NS most significant digit 67.36%, in the application cannot be satisfactory.

Claims (3)

1., based on a remote Work attendance method for the face classification algorithm of rarefaction representation, it is characterized in that, following steps:

(1) gather all by the face information of work attendance personnel as training sample data collection;

(2) Resurvey by the face information of work attendance personnel as test sample book, test sample book is concentrated rarefaction representation at training sample by the face classification algorithm based on rarefaction representation, rarefaction representation finds out system of linear equations: the solution that Ax=b is the most sparse, and A is the matrix of a m × n be a vector, x is this solution of equations, adopts a valuation functions J (x) to find the most sparse unique solution, defines a conventional optimization problem P _j, P _j: minxJ (x), makes Ax=b, wherein J (x) adopt two norms square || x|| ₂ ², obtain the most sparse solution;

(3) the most sparse solution will obtained, active RFID based on ZigBee technology realizes the identification of remote personnel identity information, adopt Dual base stations model, and utilizing RSSI location technology to differentiate accurately the direction that personnel pass through, the personnel of identifying enter work attendance region or leave work attendance region.

2. the remote Work attendance method of a kind of face classification algorithm based on rarefaction representation according to claim 1, is characterized in that, in described step (2), the step of the described face classification algorithm based on rarefaction representation is as follows:

(21) the dictionary data collection be made up of k class training sample is inputted and test sample book

(22) with all row of unit two norm standardization dictionary Α;

(23) l is solved ₁minimization problem, x1:min ‖ x ‖ ₁st. ‖ Ax-y ‖ ₂≤ ε, ε are two norm constants of given tolerable noise items;

(24) residual error for i=1:k is calculated; Ri (y)=‖ y-A δ i (x ₁) ‖ ₂, wherein truncation funcation δ i: δ _i(x ₁) in order to retain x ₁in the coefficient corresponding with the i-th class, all the other positions are all set to 0;

(25) export the category IDs of test sample y, namely test sample y belongs to the i-th class in dictionary.

3. the remote Work attendance method of a kind of face classification algorithm based on rarefaction representation according to claim 2, is characterized in that, in described step (21), judges whether face test sample book is legal sample, and step is as follows:

(211) by sparse coefficient of concentration, compute sparse coefficient on training sample, judges in rarefaction representation x, whether non-zero entry concentrates in some classifications of training sample, sparse coefficient of concentration

$\mathrm{SCI}\left(x\right)=\frac{k\&CenterDot;{\max }_{i}P{\mathrm{\&delta;}}_i\left(x\right)P_1/{\mathrm{PxP}}_1-1}{k-1}\&Element;\left[\mathrm{0,1}\right],$ Coefficient vector if SCI (x)=1, then show that test sample book is only represented by the some classes in training sample, and if SCI (x)=0, then show that the non-zero entry of sparse coefficient is almost dispersed in all classifications;

(212) a fixed τ ∈ [0,1] is got, if SCI is (x ₁) < τ, then refuse this test sample book.