CN112434724A - NSET-based improved evaluation method, medium and application - Google Patents

NSET-based improved evaluation method, medium and application Download PDF

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CN112434724A
CN112434724A CN202011186823.XA CN202011186823A CN112434724A CN 112434724 A CN112434724 A CN 112434724A CN 202011186823 A CN202011186823 A CN 202011186823A CN 112434724 A CN112434724 A CN 112434724A
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nset
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徐华卿
洪晶瑾
游海涛
王琳
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Ylz Information Technology Co ltd
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Abstract

The invention provides an NSET-based improved evaluation method, a medium and application, wherein a Tikhonov-Phillips regular term is introduced to change the form of a final cognitive matrix when a residual minimum value is calculated, so that the cognitive matrix is accompanied by a regular term coefficient, and the regular term coefficient is adjusted near a small number to make the cognitive matrix reversible, so that the final form of an NSET model is directly changed, the form of the cognitive matrix is changed, the cognitive matrix is added with a product term of the regular term coefficient and a unit matrix, the problem that the cognitive matrix is not reversible can be solved, the cognitive matrix is directly solidified in a code, the problem that the cognitive matrix is not reversible is automatically solved, and the application can be widely obtained in evaluation of a nonlinear state estimation method.

Description

NSET-based improved evaluation method, medium and application
Technical Field
The invention relates to the field of pattern recognition, in particular to an improved evaluation method based on NSET, a medium and application.
Background
A Nonlinear State Estimation Technique (NSET) is a classical pattern recognition Technique, and is commonly used in the industry to solve the problem of anomaly detection. A memory matrix formed on the basis of massive historical high-dimensional sample vectors is calculated, a cognitive matrix is calculated, a certain nonlinear mode between every two historical sample vectors is contained in the cognitive matrix, and finally, the abnormal conditions of the samples can be evaluated by calculating the similarity between the input sample vectors and the output estimation vectors.
The conclusion formula of the nonlinear state estimation technology is as follows:
Figure BDA0002751611270000011
wherein
Figure BDA0002751611270000012
The cognitive matrix is called as a cognitive matrix, and the problem of evaluation by using a nonlinear state estimation method is caused by the problem of inversion of the cognitive matrix, but some cognitive matrices are irreversible in practical situations.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an improved assessment method based on NSET, which comprises the following steps:
s1: inputting historical observation vectors in the NSET model to form a memory matrix D, and generating a cognitive matrix according to the memory matrix D
Figure BDA0002751611270000013
And introduces a weight vector W to generate an estimate vector Yest；
S2: inputting an observation vector Y to be estimatedobs；
S3: according to the calculation of the observation vector Y to be estimatedobsAnd an estimated vector YestThe minimum value of the residual errors between the two groups of the data points obtains a W value; when the minimum value of the residual error is calculated, a Tikhonov-Phillips regular term is added into a residual error square sum function to constrain the weight W so as to make the value of W unique;
s4: substituting the W value into step S1, and finally outputting the estimated vector Yest；
S5: judging the input observation vector YobsAnd the estimated direction of the outputQuantity YestAnd used to assess sample abnormalities.
Further, the historical observation vector has n variables, and the historical observation vector is:
X＝[x1，x2，…，xn]T。
further, the memory matrix D is used to store historical observation vectors, and there are m historical observation vectors, the memory matrix D is n × m, and the memory matrix D is:
Figure BDA0002751611270000021
further, the weight vector W is:
W＝[w1，w2，…，wm]T
the estimation vector YestExpressed as:
Yest＝DW＝w1X(1)+w2X(2)+…+wmX(m)
namely, it is
Figure BDA0002751611270000022
Further, the residual between the observation vector and the estimation vector is:
Figure BDA0002751611270000031
further, adding a Tikhonov-Phillips regularization term to a residual sum-of-squares function G to constrain the weight W, where the residual sum-of-squares function G is:
Figure BDA0002751611270000032
wherein lambda is a regular term coefficient, lambda is greater than or equal to 0 and sufficiently small.
Further, when the residual sum of squares function G is minimized, there is the equation:
(DTD+λI)W＝DTYobs
where I is an identity matrix, λ is adjusted to make W unique, and (D)TD + λ I) is reversible, the equation becomes:
W＝(DTD+λI)-1DTYobs
Yest＝DW＝D(DTD+λI)-1DTYobs。
further, introducing non-linear operators
Figure BDA0002751611270000033
Then
Figure BDA0002751611270000034
Further, λ is a regular term coefficient, λ is 0 when the cognitive matrix is non-singular, λ is a random number of [0, 0.01] when the cognitive matrix is odd, and iteration is performed with 0.01 as a step length, and whether the cognitive matrix is reversible or not is judged once each iteration until the cognitive matrix is reversible.
The present invention also provides a computer readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the NSET-based improved assessment method as defined in any of the above.
The invention also provides the use of an improved NSET-based assessment method as defined in any one of the preceding claims for the assessment of breast cancer data.
Further, all input estimation vectors are obtained through calculation, the Euclidean distance between each estimation vector and the corresponding input vector is calculated, and the state of the input vector is evaluated according to the Euclidean distance.
According to the NSET-based improved evaluation method, the form of a final cognitive matrix is changed by introducing a Tikhonov-Phillips regular term when a residual minimum value is calculated, so that a regular term coefficient is attached to the cognitive matrix, and the cognitive matrix is reversible by adjusting the regular term coefficient near a small number, so that the final form of an NSET model is directly changed, the form of the cognitive matrix is changed, the cognitive matrix is added with a product term of one regular term coefficient and an identity matrix, the problem that the cognitive matrix is not reversible can be solved, the cognitive matrix is directly solidified in a code, the problem that the cognitive matrix is not reversible is automatically solved, and the NSET-based improved evaluation method can be widely applied to evaluation of a nonlinear state evaluation method.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 discloses breast cancer data for UCI provided by examples;
fig. 2 is a schematic diagram of the euclidean distance between each estimated vector and the corresponding input vector in fig. 1 calculated by the method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides an improved evaluation method based on NSET, which comprises the following steps: inputting historical observation vectors in the NSET model to form a memory matrix D, and generating a cognitive matrix according to the memory matrix D
Figure BDA0002751611270000051
And introduces a weight vector W to generate an estimate vector Yest(ii) a Inputting an observation vector Y to be estimatedobs(ii) a According to the calculation of the observation vector Y to be estimatedobsAnd an estimated vector YestThe minimum value of the residual errors between the two groups of the data points obtains a W value; when the minimum value of the residual error is calculated, a Tikhonov-Phillips regular term is added into a residual error square sum function to constrain the weight W so as to make the value of W unique; substituting the W value into step S1, and finally outputting the estimated vector Yest(ii) a Judging the input observation vector YobsAnd an estimated vector Y of the outputestAnd used to assess sample abnormalities.
According to the NSET-based improved evaluation method, the form of a final cognitive matrix is changed by introducing a Tikhonov-Phillips regular term when a residual minimum value is calculated, so that a regular term coefficient is attached to the cognitive matrix, and the cognitive matrix is reversible by adjusting the regular term coefficient near a small number, so that the final form of an NSET model is directly changed, the form of the cognitive matrix is changed, the cognitive matrix is added with a product term of one regular term coefficient and an identity matrix, the problem that the cognitive matrix is not reversible can be solved, the cognitive matrix is directly solidified in a code, the problem that the cognitive matrix is not reversible is automatically solved, and the NSET-based improved evaluation method can be widely applied to evaluation of a nonlinear state evaluation method.
Further, the historical observation vector has n variables, and the historical observation vector is:
X＝[x1，x2，…，xn]T。
further, the memory matrix D is used to store historical observation vectors, and there are m historical observation vectors, the memory matrix D is n × m, and the memory matrix D is:
Figure BDA0002751611270000052
further, the weight vector W is:
W＝[w1，w2，…，wm]T
the estimation vector YestExpressed as:
Yest＝DW＝w1X(1)+w2X(2)+…+wmX(m)
namely, it is
Figure BDA0002751611270000061
Further, the residual between the observation vector and the estimation vector is:
Figure BDA0002751611270000062
further, adding a Tikhonov-Phillips regularization term to a residual sum-of-squares function G to constrain the weight W, where the residual sum-of-squares function G is:
Figure BDA0002751611270000063
wherein lambda is a regular term coefficient, lambda is greater than or equal to 0 and sufficiently small.
Further, when the residual sum of squares function G is minimized, only a Tikhonov-Phillips regular term needs to be added to the residual sum of squares function to constrain the weight W:
Figure BDA0002751611270000064
wherein lambda is a regular term coefficient, lambda is not less than 0 and sufficiently small, and the derivation can be obtained as follows:
Figure BDA0002751611270000071
the method is simplified and can be obtained:
Figure BDA0002751611270000072
the linear equation set can be ensured to be a non-pathological equation set by adjusting the regular term coefficient, the weight W is ensured to have a unique solution, and the form of writing into a matrix is as follows:
(DTD+λI)W＝DTYobs
where I is an identity matrix, λ is adjusted to make W unique, and (D)TD + λ I) is reversible, the equation becomes:
W＝(DTD+λI)-1DTYobs
Yest＝DW＝D(DTD+λI)-1DTYobs。
further, a nonlinear operation box is introduced
Figure BDA0002751611270000073
Figure BDA0002751611270000074
Further, λ is a regular term coefficient, λ is 0 when the cognitive matrix is non-singular, λ is a random number of [0, 0.01] when the cognitive matrix is odd, and iteration is performed with 0.01 as a step length, and whether the cognitive matrix is reversible or not is judged once each iteration until the cognitive matrix is reversible.
The present invention also provides a computer readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the NSET-based improved assessment method as defined in any of the above.
The invention also provides the use of an improved NSET-based assessment method as defined in any one of the preceding claims for the assessment of breast cancer data. Taking fig. 1 as an example, the data shown in fig. 1 is breast cancer data disclosed by UCI, wherein diagnosese is listed as M malignant and B benign. In fig. 1, there are 357 benign records in total, 300 of which are used as memory matrices D, the remaining 57 are used as input observation vectors, 57 of which are also used as observation vectors in malignancy, and the benign input vector and the malignant input vector are combined together and the benign one is placed in front. All input estimation vectors are obtained by using NSET calculation of the invention, then the Euclidean distance between each estimation vector and the corresponding input vector is calculated (other similarity measurement methods can be used), and the state of the input vector is evaluated according to the Euclidean distance. As shown in fig. 2, the euclidean distance is plotted as follows: the first 57 are benign, so the euclidean distance values are overall small; the latter 57 are malignant, so the euclidean distance values are overall large. In practical applications, a suitable threshold is selected, which is probably between 400 and 500 (depending on specific indexes), and the common method is to maximize f1-score so that the accuracy and the recall rate can be well balanced.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (12)

1. An improved NSET-based assessment method, comprising:
s1: inputting historical observation vectors in the NSET model to form a memory matrix D, and generating a cognitive matrix according to the memory matrix D
Figure FDA0002751611260000012
And introduces a weight vector W to generate an estimate vector Yest；
S2: inputting an observation vector Y to be estimatedobs；
S3: according to the calculation of the observation vector Y to be estimatedobsAnd an estimated vector YestThe minimum value of the residual errors between the two groups of the data points obtains a W value; when the minimum value of the residual error is calculated, a Tikhonov-Phillips regular term is added into a residual error square sum function to constrain the weight W so that the value W is unique；
S4: substituting the W value into step S1, and finally outputting the estimated vector Yest；
S5: judging the input observation vector YobsAnd an estimated vector Y of the outputestAnd used to assess sample abnormalities.
2. The NSET-based improvement assessment method of claim 1, wherein: the historical observation vector has n variables, and is:
X＝[x1，x2，…，xn]T。
3. the NSET-based improvement assessment method of claim 2, wherein: the memory matrix D is used for storing historical observation vectors, m historical observation vectors exist, the memory matrix D is n × m, and the memory matrix D is:
Figure FDA0002751611260000011
4. the NSET-based improvement assessment method of claim 3, wherein: the weight vector W is:
W＝[w1，w2，…，wm]T
the estimation vector YestExpressed as:
Yest＝DW＝w1X(1)+w2X(2)+…+wmX(m)
namely, it is
Figure FDA0002751611260000021
5. The NSET-based improvement assessment method of claim 4, wherein: the residual between the observation vector and the estimation vector is:
Figure FDA0002751611260000022
6. the NSET-based improvement assessment method of claim 5, wherein: adding a Tikhonov-Phillips regular term into a residual sum-of-squares function G to constrain the weight W, wherein the residual sum-of-squares function G is as follows:
Figure FDA0002751611260000023
wherein lambda is a regular term coefficient, lambda is greater than or equal to 0 and sufficiently small.
7. The NSET-based improvement assessment method of claim 6, wherein: when minimizing the residual sum of squares function G, there is the equation:
(DTD+λI)W＝DTYobs
where I is an identity matrix, λ is adjusted to make W unique, and (D)TD + λ I) is reversible, the equation becomes:
W＝(DTD+λI)-1DTYobs
Yest＝DW＝D(DTD+λI)-1DTYobs。
8. the NSET-based improvement assessment method of claim 7, wherein: introducing non-linear operators
Figure FDA0002751611260000031
Then
Figure FDA0002751611260000032
9. The NSET-based improvement assessment method of claim 8, wherein: and when the cognitive matrix is not singular, the lambda is 0, when the cognitive matrix is odd, the lambda is a random number of [0, 0.01], iteration is performed by taking 0.01 as a step length, and whether the cognitive matrix is reversible or not is judged once each iteration until the cognitive matrix is reversible.
10. A computer-readable storage medium characterized by: the computer readable storage medium stores computer instructions which, when executed by a processor, implement the NSET-based improved assessment method of any of claims 1-9.
11. Use of an NSET-based improved assessment method according to any of claims 1-9 for the assessment of breast cancer data.
12. Use of an NSET-based improved assessment method according to claim 11 for the assessment of breast cancer data, wherein: and calculating to obtain all input estimation vectors, calculating the Euclidean distance between each estimation vector and the corresponding input vector, and evaluating the state of the input vector according to the Euclidean distance.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080010045A1 (en) * 1999-04-30 2008-01-10 Smartsignal Corporation Method and System for Non-Linear State Estimation
CN108595381A (en) * 2018-04-27 2018-09-28 厦门尚为科技股份有限公司 Health status evaluation method, device and readable storage medium storing program for executing
CN110162743A (en) * 2019-05-08 2019-08-23 孙力勇 A kind of data administering method based on k neighborhood nonlinear state Eq algorithm

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080010045A1 (en) * 1999-04-30 2008-01-10 Smartsignal Corporation Method and System for Non-Linear State Estimation
CN108595381A (en) * 2018-04-27 2018-09-28 厦门尚为科技股份有限公司 Health status evaluation method, device and readable storage medium storing program for executing
CN110162743A (en) * 2019-05-08 2019-08-23 孙力勇 A kind of data administering method based on k neighborhood nonlinear state Eq algorithm

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