CN106919909B - The metric learning method and system that a kind of pedestrian identifies again - Google Patents

The metric learning method and system that a kind of pedestrian identifies again Download PDF

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CN106919909B
CN106919909B CN201710073645.1A CN201710073645A CN106919909B CN 106919909 B CN106919909 B CN 106919909B CN 201710073645 A CN201710073645 A CN 201710073645A CN 106919909 B CN106919909 B CN 106919909B
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CN106919909A (en
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贺波涛
余少华
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Huazhong University of Science and Technology
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    • G06V40/10Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
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Abstract

The invention discloses the metric learning method and system that a kind of pedestrian identifies again, the realization of wherein method includes:Collect pedestrian's clarification of objective vector under two cameras, positive sample is established to characteristic vector set and negative sample to characteristic vector set, calculate just, distance of the negative sample to characteristic vector, single threshold constraint is carried out to characteristic vector to positive sample, row constraint is entered using dual threshold to characteristic vector to negative sample, just, negative sample is to establishing the loss function based on metric matrix under the distance constraints of characteristic vector, with the minimum target iteration renewal metric matrix of loss function value, this method can effectively mitigate image background, the irrelevant variables such as noise learn to produce large effect to matrix, so as to avoid over-fitting, obtained metric matrix generalization ability is strong.

Description

The metric learning method and system that a kind of pedestrian identifies again
Technical field
The invention belongs to mode identification technology, more particularly, to a kind of metric learning identified for pedestrian again Method and system.
Background technology
The heavy recognizer of pedestrian is one of image procossing and the key areas of pattern identification research, is conceived to without public The identification work of specific objective pedestrian under the camera of the ken.Because video definition etc. limits, it is difficult to pass through intuitively face Deng the same target of information searching, but it is conceived to the feature representation based on pedestrian's appearance, mainly includes the face comprising pedestrian image The information such as color and texture, then find a kind of suitable measure and make it that across the camera feature of same pedestrian target is as far as possible similar, Heterogeneous destinations characteristic difference is as far as possible notable.Because same target the factor such as is blocked under different cameras by visual angle, illumination, object Influence, the expression of its feature under different visual angles often has deviation, so it is solution to find a kind of suitable measure With the very corn of a subject part.At present, for the special scenes of a certain database, one is produced more by training set sample learning Suitable metric space carries out characteristic similarity calculating, and this method is referred to as metric learning.In existing metric learning method, Constraints often excessively pursues inter- object distance minimum and between class distance maximizes, and ignores in complex scene in target signature Also in training often there is over-fitting in being extended, the metric space finally given to the information such as image background, noise simultaneously Risk, in testing less effective.
The content of the invention
The present invention propose a kind of metric learning method that pedestrian identifies again, and it is an object of the present invention to provide it is a kind of to positive sample to feature Vector carries out single threshold constraint, the metric learning method constrained for negative sample characteristic vector dual threshold, solves existing measurement Learning art existing over-fitting problem under complex scene.
To achieve the above object, according to one aspect of the present invention again, there is provided the metric learning side that a kind of pedestrian identifies Method, it the described method comprises the following steps:
(1) pedestrian's clarification of objective vector under two cameras is collected, establishes positive sample to characteristic vector set and negative sample This is to characteristic vector set;
(2) distance of the positive sample to characteristic vector and negative sample to characteristic vector is calculated;
(3) it is μ positive sample to be constrained to a radius to the distance of characteristic vector in metric space1Circle, by negative sample This distance to characteristic vector is constrained to one with μ in metric space2For inside radius, μ3For the annulus of outer radius, 0 < μ1< μ2< μ3
(4) loss function based on metric matrix is established under distance constraints of the positive and negative samples to characteristic vector;
(5) with the minimum target iteration renewal metric matrix of loss function value.
Further, the specific implementation of the step (1) is:
Pedestrian's clarification of objective vector under two cameras is collected, establishes set X and set Z, x respectivelyiIn gathering for X Element, represent the characteristic vector that i-th of pedestrian target is collected in a camera, 0 < i≤N;zjElement in gathering for Z, table Show the characteristic vector that j-th of pedestrian target is collected in another camera, 0 < j≤N;I=j, xiAnd ziFor same pedestrian's mesh The characteristic vector being marked under two different cameras, (xi,zi) represent that positive sample to characteristic vector, shares N pairs;I ≠ j, xiAnd zj For characteristic vector of the different pedestrian targets under two different cameras, (xi,zj) represent negative sample to characteristic vector.
Further, the specific implementation of the step (2) is:
Metric learning method based on mahalanobis distance, calculate positive sample is to the distance of characteristic vector:Calculate negative sample is to the distance of characteristic vector:Wherein M is metric matrix.
Further, the specific implementation of the step (4) is:
In step (3) under distance constraints of the positive and negative samples to characteristic vector, the loss based on metric matrix is established Function:
Wherein, loss function of the positive sample to characteristic vector:
Loss function of the negative sample to characteristic vector:
β is smoothing parameter in formula.
Further, the specific implementation of the step (5) is:
(5-1) makes MKMetric matrix during iteration secondary for kth,Positive sample is to feature when being kth time iteration The space length of vector,Negative sample is to the space length of characteristic vector, counting loss letter when being kth time iteration Number gradient:
Wherein, the positive sample coefficient related to constraints to characteristic vector is:The negative sample coefficient related to constraints to characteristic vector be:
(5-2) in kth time iterative process, to MK according to αkStep-length update to obtain along the direction that gradient declines:Wherein αkIt is the renewal step-length of iteration;
(5-3) judgesWhether meet the constraints of positive semidefinite matrix, directly made if meetingIf not satisfied, need to then be found in positive semidefinite matrix space one withMost like matrix conduct Mk+1Value;
(5-4) judges whether to meet termination conditionε is preset value, if being unsatisfactory for terminating Condition, then k=k+1 is made, continue executing with step (5-1), if meeting to terminate iterated conditional, output metric matrix, current iteration obtains The M arrivedk+1The final metric matrix that the metric learning method exactly identified again using pedestrian is obtained.
Further, the specific implementation of the step (5-3) is:
(5-3-1) uses formula:Wherein, S is half The set of positive definite matrix, F represent F norms;
(5-3-2) willSingular value decompositionWhereinAnd Λk+1Be byThe diagonal matrix of singular value composition;
(5-3-3) makesThenObtain in positive semidefinite space with Most like matrix Mk+1
Further, the characteristic vector in the step (1) includes colouring information and texture information.
It is another aspect of this invention to provide that provide the metric learning system that a kind of pedestrian identifies again, the system includes With lower module:
Feature vector module, for collecting pedestrian's clarification of objective vector under two cameras, positive sample is established to feature Vector sum negative sample is to characteristic vector set;
Metric learning method module, the metric learning method based on mahalanobis distance, for calculating positive sample to characteristic vector Distance and negative sample to the distance of characteristic vector;
Constraints module, it is for positive sample to be constrained to a radius to the distance of characteristic vector in metric space μ1Circle, negative sample is constrained to one with μ to the distance of characteristic vector in metric space2For inside radius, μ3For outer radius Annulus, 0 < μ1< μ2< μ3
Loss function module, for being based on measuring under the constraints of the distance of characteristic vector, establishing in positive and negative samples The loss function of matrix;
Projected descent method module, for loss function value minimum target iteration renewal metric matrix, including with Lower submodule:Loss function gradient submodule, iteration submodule, judging submodule and end submodule.
Further, the judging submodule includes the first judge module, the second judge module and the 3rd judge module.
Further, the characteristic vector in the feature vector module includes colouring information and texture information.
In general, by the contemplated above technical scheme of the present invention compared with prior art, mainly possesses following skill Art advantage:
1st, the present invention is different from the constraints of the metric learning of generally use, it is proposed that more superior based on dual threshold pair The metric learning method that negative sample is constrained characteristic vector, its feature essentially consist in, and ensure distance of the positive sample to characteristic vector Meanwhile also negative sample is limited apart from size characteristic vector, with the form of dual threshold cause negative sample to feature to Amount apart from size in a controllable scope, rather than allow positive sample to feature under generally selected binary constraints The distance of vector is more than a constant with negative sample to the range difference of characteristic vector, or sets one respectively under ternary constraints The method of individual threshold value, it is actually a kind of thought of regularization so to do theoretical foundation, and this method can effectively mitigate figure The irrelevant variables such as picture background, noise learn to produce large effect to matrix, so as to avoid over-fitting;
2nd, the metric matrix generalization ability that the algorithm obtains is strong, special for well adapting to property of various features vector It is not that pedestrian under the complex scene for containing more noise for some identifies with good effect again.
3rd, the algorithm construction is simple in construction, and using the computational methods of Projected descent method, speed, efficiency are higher, And effect excellent performance is tested on each database (such as VIPer, CUHK03, CUHK01 storehouse) for being usually used in pedestrian and identifying again.
Brief description of the drawings
Fig. 1 is the flow chart for the metric learning method that a kind of pedestrian proposed by the invention identifies again;
Fig. 2 is the graphical schematic diagram of constraints of the present invention;
Fig. 3 is the structural representation for the metric learning system that a kind of pedestrian proposed by the invention identifies again.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below Conflict can is not formed each other to be mutually combined.
In order to facilitate narration, we set our data set and come from two cameras, and each of which pedestrian is at one There was only an image under camera (this algorithm can extremely be easily extended to multiple cameras and multiple images)
As shown in figure 1, the metric learning method that a kind of pedestrian proposed by the invention identifies again, comprises the following steps:
Step (1) collects characteristic vector, establishes positive sample to characteristic vector and negative sample to characteristic vector:Two are collected to take the photograph As pedestrian's clarification of objective vector under head, set X and set Z, x are established respectivelyiElement in gathering for X, represent i-th of pedestrian The characteristic vector that target is collected in a camera, 0 < i≤N;zjElement in gathering for Z, represent that j-th of pedestrian target exists The characteristic vector collected in another camera, 0 < j≤N;I=j, xiAnd ziIt is same pedestrian target in two different cameras Under characteristic vector, (xi,zi) represent that positive sample to characteristic vector, shares N pairs;i≠j,xiAnd zjIt is different pedestrian targets two Characteristic vector under individual different cameras, (xi,zj) represent that to characteristic vector, it is right to share N × (N-1) for negative sample.
Metric learning method of the step (2) based on mahalanobis distance calculates distance of the positive and negative samples to characteristic vector:Positive sample Distance to characteristic vector is:Negative sample to characteristic vector away from From for:Wherein M is metric matrix, and M is initialized as unit square Battle array, constraints is a positive semidefinite matrix.
Step (3) provides constraints of the positive and negative samples to the distance of characteristic vector:Wherein, 0 < μ1< μ2< μ3, positive sample measuring to the distance of characteristic vector It is μ that a radius is constrained in space1Circle;Row constraint is entered using dual threshold to characteristic vector to negative sample, negative sample is to spy The distance of sign vector is constrained to one with μ in metric space2For inside radius, μ3For the annulus of outer radius.
Step (4) in step (3) positive and negative samples under the constraints of the distance of characteristic vector, establishing loss function:Wherein, loss letter of the positive sample to characteristic vector Number:Loss function of the negative sample to characteristic vector:
In formula β be one rise smoothing effect parameter, β=1;
The value of metric matrix when step (5) tries to achieve loss function minimum using Projected descent method, including following sub-step Suddenly:
Step (5-1) counting loss functional gradient, MKMetric matrix during iteration secondary for kth,It is kth time Positive sample is to the space length of characteristic vector during iteration,Sky of the negative sample to characteristic vector when being kth time iteration Between distance:
Wherein, the positive sample coefficient related to constraints to characteristic vector is:The negative sample coefficient related to constraints to characteristic vector be:
Loss function is to M when step (5-2) makes kth time iterationkDerivation is to function ▽ L (Mk), in kth time iterative process, To MKAccording to αkStep-length update it along the direction that gradient declines and be worth to: Wherein αkIt is the renewal step-length of iteration, αk=1;
Step (5-3) judgesWhether meet the constraints of positive semidefinite matrix, directly made if meetingIf not satisfied, need to then be found in positive semidefinite matrix space one withMost like matrix conduct Mk+1Value;
Step (5-4) judges whether to meet iteration termination conditionε=1 × 10-4If not Meet to terminate iterated conditional, then make k=k+1, continue executing with step (5-1), if meeting to terminate iterated conditional, iteration terminates, Output metric matrix, the M that current iteration obtainsk+1It is exactly final optimization metric matrix.
The specific implementation of the step (5-3) is:
Step (5-3-1) uses formula:Wherein, S It is the set of positive semidefinite matrix, F represents F norms;
Step (5-3-2) willSingular value decompositionWhereinAnd Λk+1It is ByThe diagonal matrix of singular value composition;
Step (5-3-3) makesThenObtain in positive semidefinite space withMost like matrix Mk+1
Further, the characteristic vector in the step (1) includes colouring information and texture information.
As shown in Fig. 2 the graphical schematic diagram of constraints of the present invention, the pattern of each shape correspond to same mesh The characteristic vector being marked under different cameras, different patterns are different clarification of objective vectors, and positive sample is to characteristic vector Distance a radius is constrained in metric space is μ1Circle;Negative sample is carried out about to characteristic vector using dual threshold Beam, negative sample are constrained to one to the distance of characteristic vector with μ in metric space2For inside radius, μ3For the annulus of outer radius; Specific constraints is 0 < μ1< μ2< μ3, wherein μ1For 0.2, μ2For 1.8, μ3For 2.2.
As shown in figure 3, the metric learning system that a kind of pedestrian proposed by the invention identifies again, including with lower module:
Feature vector module, for collecting pedestrian's clarification of objective vector under two cameras, set X and collection are established respectively Close Z, xiElement in gathering for X, represent the characteristic vector that i-th of pedestrian target is collected in a camera, 0 < i≤N;zjFor Element in Z set, represent the characteristic vector that j-th of pedestrian target is collected in another camera, 0 < j≤N;I=j, xiWith ziFor characteristic vector of the same pedestrian target under two different cameras, (xi,zi) positive sample is represented to characteristic vector, it is common There is N pairs;i≠j,xiAnd zjFor characteristic vector of the different pedestrian targets under two different cameras, (xi,zj) represent negative sample pair Characteristic vector, it is right to share N × (N-1);
Metric learning method module, for calculating distance of the positive and negative samples to characteristic vector, the measurement based on mahalanobis distance Learning method, positive sample are to the distance of characteristic vector:Negative sample Distance to characteristic vector is:Wherein M is metric matrix;
Constraints module, for entering row constraint to the distance of characteristic vector to positive and negative samples, positive and negative samples are to feature The constraints of the distance of vector:Wherein, 0 < μ1< μ2< μ3, wherein μ1For 0.2, μ2For 1.8, μ3For 2.2, it is μ that positive sample is constrained to a radius to the distance of characteristic vector in metric space1Circle; Row constraint is entered using dual threshold to characteristic vector to negative sample, negative sample is constrained to the distance of characteristic vector in metric space One with μ2For inside radius, μ3For the annulus of outer radius;
Loss function module, under the constraints of the distance of characteristic vector, establishing loss letter in positive and negative samples Number:Wherein, damage of the positive sample to characteristic vector Lose function:Loss function of the negative sample to characteristic vector:
In formula β be one rise smoothing effect parameter, β=1;
Projected descent method module, the value of metric matrix during for counting loss function minimum, including following submodule:
Loss function gradient submodule:
Wherein, MKMetric matrix during iteration secondary for kth,When being kth time iteration positive sample to feature to The space length of amount,Negative sample is to the space length of characteristic vector when being kth time iteration, and positive sample is to feature The vector coefficient related to constraints be:Negative sample to characteristic vector with The related coefficient of constraints is:
Iteration submodule, loss function is to M during for calculating kth time iterationkDerivation is to function ▽ L (Mk), in kth time repeatedly During generation, to MK according to αkStep-length update it along the direction that gradient declines and be worth to:Wherein αkIt is the renewal step-length of iteration, αk=1;
Judging submodule, for judgingWhether meet the constraints of positive semidefinite matrix, directly made if meetingIf not satisfied, need to then be found in positive semidefinite matrix space one withMost like matrix conduct Mk+1Value;
Terminate submodule, for judging whether to meet iteration termination conditionε=1 × 10-4If being unsatisfactory for terminating iterated conditional, k=k+1 is made, continues executing with loss function gradient submodule, if meeting to terminate iteration bar Part, then iteration terminate, output metric matrix, the M that current iteration obtainsk+1It is exactly final optimization metric matrix.
Further, the judging submodule includes:
First judge module, calculated for formula:
Wherein, S is the set of positive semidefinite matrix, F Represent F norms;
Second judge module, for inciting somebody to actionSingular value decompositionWhereinAnd Λk+1Be byThe diagonal matrix of singular value composition;
3rd judge module, for makingThenObtain positive semidefinite space In withMost like matrix Mk+1
Further, the characteristic vector in the feature vector module includes colouring information and texture information.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles of the invention etc., all should be included Within protection scope of the present invention.

Claims (2)

1. a kind of metric learning method that pedestrian identifies again, it is characterised in that the described method comprises the following steps:
(1) pedestrian's clarification of objective vector under two cameras is collected, establishes positive sample to characteristic vector set and negative sample pair Characteristic vector set;
(2) distance of the positive sample to characteristic vector and negative sample to characteristic vector is calculated;
(3) it is μ positive sample to be constrained to a radius to the distance of characteristic vector in metric space1Circle, by negative sample to spy The distance of sign vector is constrained to one with μ in metric space2For inside radius, μ3For the annulus of outer radius, 0 < μ1< μ2< μ3
(4) loss function based on metric matrix is established under distance constraints of the positive and negative samples to characteristic vector;
(5) with the minimum target iteration renewal metric matrix of loss function value;
The specific implementation of the step (1) is:
Pedestrian's clarification of objective vector under two cameras is collected, establishes set X and set Z, x respectivelyiElement in gathering for X, Represent the characteristic vector that i-th of pedestrian target is collected in a camera, 0 < i≤N;zjElement in gathering for Z, represent jth The characteristic vector that individual pedestrian target is collected in another camera, 0 < j≤N;I=j, xiAnd ziIt is same pedestrian target two Characteristic vector under individual different cameras, (xi,zi) represent that positive sample to characteristic vector, shares N pairs;I ≠ j, xiAnd zjFor difference Characteristic vector of the pedestrian target under two different cameras, (xi,zj) represent negative sample to characteristic vector;
The specific implementation of the step (2) is:
Metric learning method based on mahalanobis distance, calculate positive sample is to the distance of characteristic vector:Calculate negative sample is to the distance of characteristic vector:Wherein M is metric matrix;
The specific implementation of the step (4) is:
In step (3) under distance constraints of the positive and negative samples to characteristic vector, the loss letter based on metric matrix is established Number:
Wherein, loss function of the positive sample to characteristic vector:
Loss function of the negative sample to characteristic vector:
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β is smoothing parameter in formula;
The specific implementation of the step (5) is:
(5-1) makes MkMetric matrix during iteration secondary for kth,Positive sample is to characteristic vector when being kth time iteration Space length,Negative sample is to the space length of characteristic vector, counting loss function ladder when being kth time iteration Degree:
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Wherein, the positive sample coefficient related to constraints to characteristic vector is:The negative sample coefficient related to constraints to characteristic vector be:
<mrow> <mi>w</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;mu;</mi> <mn>3</mn> </msub> <mo>-</mo> <msubsup> <mi>D</mi> <msub> <mi>M</mi> <mi>k</mi> </msub> <mn>2</mn> </msubsup> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <msub> <mi>M</mi> <mi>k</mi> </msub> <mn>2</mn> </msubsup> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo>;</mo> </mrow>
(5-2) in kth time iterative process, to MkAccording to αkStep-length update to obtain along the direction that gradient declines:Wherein αkIt is the renewal step-length of iteration;
(5-3) judgesWhether meet the constraints of positive semidefinite matrix, directly made if meetingIf Be unsatisfactory for, then need to be found in positive semidefinite matrix space one withMost like matrix is as Mk+1Value;
(5-4) judges whether to meet to terminate iterated conditionalε is preset value, if being unsatisfactory for terminating Condition, then k=k+1 is made, continue executing with step (5-1), if meeting to terminate iterated conditional, output metric matrix, current iteration obtains The M arrivedk+1The final metric matrix that the metric learning method exactly identified again using pedestrian is obtained;
The specific implementation of the step (5-3) is:
(5-3-1) uses formula:Wherein, S is positive semidefinite The set of matrix, F represent F norms;
(5-3-2) willSingular value decompositionWhereinAnd Λk+1Be byIt is unusual It is worth the diagonal matrix of composition;
(5-3-3) makesThenObtain in positive semidefinite space withIt is most like Matrix Mk+1
2. the metric learning system that a kind of pedestrian identifies again, it is characterised in that the system is included with lower module:
Feature vector module, for collecting pedestrian's clarification of objective vector under two cameras, set X and set Z is established respectively, xiElement in gathering for X, represent the characteristic vector that i-th of pedestrian target is collected in a camera, 0 < i≤N;zjFor Z collection Element in conjunction, represent the characteristic vector that j-th of pedestrian target is collected in another camera, 0 < j≤N;I=j, xiAnd ziFor Characteristic vector of the same pedestrian target under two different cameras, (xi,zi) represent that positive sample to characteristic vector, shares N It is right;I ≠ j, xiAnd zjFor characteristic vector of the different pedestrian targets under two different cameras, (xi,zj) represent negative sample to spy Sign vector;
Metric learning method module,
Metric learning method based on mahalanobis distance, calculate positive sample is to the distance of characteristic vector:Calculate negative sample is to the distance of characteristic vector:Wherein M is metric matrix;
Constraints module, it is μ for positive sample to be constrained to a radius to the distance of characteristic vector in metric space1's Circle, one is constrained to μ by negative sample to the distance of characteristic vector in metric space2For inside radius, μ3For the circle of outer radius Ring, 0 < μ1< μ2< μ3
Loss function module, is used for
Under distance constraints of the positive and negative samples to characteristic vector, the loss function based on metric matrix is established:
Wherein, loss function of the positive sample to characteristic vector:
Loss function of the negative sample to characteristic vector:
<mrow> <msub> <mi>l</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>&amp;beta;</mi> </mfrac> <mrow> <mo>(</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mi>M</mi> <mn>2</mn> </msubsup> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> </mrow> <mo>)</mo> <mo>+</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;mu;</mi> <mn>2</mn> </msub> <mo>-</mo> <msubsup> <mi>D</mi> <mi>M</mi> <mn>2</mn> </msubsup> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
β is smoothing parameter in formula;
Projected descent method module, for the minimum target iteration renewal metric matrix of loss function value, including following son Module:Loss function gradient submodule, iteration submodule, judging submodule and end submodule;
The loss function gradient submodule, for making MkMetric matrix during iteration secondary for kth,It is kth time Positive sample is to the space length of characteristic vector during iteration,Sky of the negative sample to characteristic vector when being kth time iteration Between distance, counting loss functional gradient:
<mrow> <mo>&amp;dtri;</mo> <mi>L</mi> <mrow> <mo>(</mo> <msub> <mi>M</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>w</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;NotEqual;</mo> <mi>j</mi> </mrow> </munder> <mi>w</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mrow>
Wherein, the positive sample coefficient related to constraints to characteristic vector is:The negative sample coefficient related to constraints to characteristic vector be:
<mrow> <mi>w</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;mu;</mi> <mn>3</mn> </msub> <mo>-</mo> <msubsup> <mi>D</mi> <msub> <mi>M</mi> <mi>k</mi> </msub> <mn>2</mn> </msubsup> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <msub> <mi>M</mi> <mi>k</mi> </msub> <mn>2</mn> </msubsup> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo>;</mo> </mrow>
The iteration submodule, in kth time iterative process, to MkAccording to αkThe direction that declines along gradient of step-length update Obtain:Wherein αkIt is the renewal step-length of iteration;
The judging submodule, for judgingWhether meet the constraints of positive semidefinite matrix, directly made if meetingIf not satisfied, need to then be found in positive semidefinite matrix space one withMost like matrix conduct Mk+1Value;
The end submodule, for judging whether to meet to terminate iterated conditionalε is default Value, if being unsatisfactory for termination condition, makes k=k+1, continues executing with loss function gradient submodule, if meeting to terminate iterated conditional, Output metric matrix, the M that current iteration obtainsk+1The final degree that the metric learning method exactly identified again using pedestrian is obtained Moment matrix;The judging submodule includes:First judge module, the second judge module and the 3rd judge module;
First judge module, for using formula: Wherein, S is the set of positive semidefinite matrix, and F represents F norms;
Second judge module, for inciting somebody to actionSingular value decompositionWhereinAnd Λk+1Be byThe diagonal matrix of singular value composition;
3rd judge module, for makingThenObtain positive semidefinite space In withMost like matrix Mk+1
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