CN104915671A - FGAK (Fast Global Alignment Kernels) based abnormal trajectory detection method - Google Patents

Abstract

The invention relates to an FGAK (Fast Global Alignment Kernels) based abnormal trajectory detection method. According to the method, a kernel matrix K is constructed by using an FGAK kernel function, trajectory point data in an original trajectory space is mapped to a high-dimensional trajectory feature space, and original nonlinear trajectory data is converted into linear feature data in the high-dimensional feature space; then KPCA (Kernel Principal Component Analysis) is adopted to carry out feature extraction on the kernel matrix K, classification is carried out on trajectories by using a one-class support vector machine, unsupervised learning is carried out on the extracted trajectory feature data through setting the width sigma and the extraction ratio P of the kernel function, and whether a certain trajectory is an abnormal trajectory or not is judged through a decision function. According to the method provided by the invention, a detection range for the abnormal trajectory is expanded on traditional longitudes and latitudes, abnormity detection can be carried out from other feature aspects of the trajectory points, such as the speed, the direction and the like, people need not to make any change on the method when additional detection factors are added, the FGAK based kernel function is adopted, and the method can be effectively applied to a trajectory data set with the trajectory length difference being great.

Description

Based on the abnormal track-detecting method of FGAK

Technical field

The present invention relates to a kind of method of abnormal track detection, particularly a kind ofly can detect abnormal track in multifactor and the abnormal track-detecting method based on FGAK that can be applied to that course length differs greatly.

Background technology

For track data, except the longitude and latitude on locus, other attributes such as speed, direction of tracing point are also the key factors that can not be ignored, particularly in abnormal track detection field.Existing abnormal track detection algorithm majority carries out abnormality detection based on the locus in initial trace space, but locus attribute only can represent mobile object once in this regional activity mistake.The characteristic attribute of track effectively can not be extracted in initial trace space, and existing algorithm can not be applied in the track data set that course length differs greatly well, need to carry out resampling to track data in advance, which results in track data feature and destroyed artificially.

In track data acquisition, some track is very similar in shape in locus, but their direction is but contrary, if only consider locus factor, these two tracks all can be judged as normal trace, if consider D-factor, the track that so that direction is contrary is exactly abnormal track, although it is normal on locus.

FGAK (Fast Global Alignment Kernels) proposed concurrent table name in 2011 by Marco Cuturi and is on the 28th international Conference on Machine Learning " Fast Global Alignment Kernels " paper.The deficiency that traditional DTW kernel function exists is detailed in literary composition, summary should be used as to GAK (Global Alignment Kernels) kernel function, the basis of GAK kernel function proposing FGAK kernel function for accelerating the calculating of GAK kernel function, demonstrating the orthotropicity of FGAK kernel function simultaneously.

KPCA (Kernel Principal Component Analysis) is a kind of conventional dimension reduction method, is proposed at first by people such as Smola A in 1997.Traditional PCA (Principal Component Analysis) dimension reduction method seems unable to do what one wishes when in the face of high dimensional data, so Smoba A etc. propose the solution of KPCA and give the derivation of KPCA.

Such as TRAOD algorithm is when carrying out track abnormality detection, only considers that the locus factor of track carries out staging treating to track, some is existed to the abnormal track detection poor effect of winding; TOD-KPCA algorithm is before carrying out abnormal track detection, and need to carry out over-sampling process to track data, so that all tracks have identical length, this obviously understands the raw data of failure confine.

Summary of the invention

The object of the invention is to provide a kind of abnormal track-detecting method based on FGAK, abnormal track can be detected in multifactor, and the abnormality detection of the track data collection that course length differs greatly can be applied to, solve existing abnormal track-detecting method main it is considered that the exception of locus, and little problem that other factors are considered, and need the defect of track data being carried out to resampling before detection.

The object of the present invention is achieved like this: a kind of abnormal track-detecting method based on FGAK, can detect abnormal rail, and can be applied to the abnormality detection of the track data collection that course length differs greatly in multifactor; In the method, FGAK kernel function is utilized to build nuclear matrix K, by the tracing point data-mapping in initial trace space in higher-dimension track characteristic space, the track data of primary nonlinear is converted to the characteristic of high-dimensional feature space neutral line, to extract track data feature better; After track data is mapped to high-dimensional feature space, KPCA is adopted to carry out feature extraction to track data core matrix K; After obtaining the characteristic of track, one-class support vector machine is utilized to classify to track, by setting kernel function width cs, three angular dimensions T and extraction ratio P, unsupervised learning is carried out to the track characteristic data after extracting, when unsupervised learning, judge whether certain track is abnormal track, and concrete steps are as follows by decision function:

Step 1) from track data set, read the tracing point data of every bar track;

Step 2) adopt the every bar track of Min-max methodological standardization;

Step 3) utilize kernel function FGAK to calculate track data to be mapped to the eigenmatrix after high-dimensional feature space, i.e. nuclear matrix K; Different nuclear matrix can be obtained by regulating the width cs of kernel function FGAK;

Step 4) centralization nuclear matrix K, obtain nuclear matrix KL;

Step 5) calculate the eigenwert e of nuclear matrix KL ₁..., e _nand characteristic of correspondence vector v ₁..., v _n;

Step 6) to eigenwert e ₁..., e _ncarry out descending sort, characteristic of correspondence vector also can auto-sequencing;

Step 7) orthogonalized eigenvectors, obtain the proper vector α after orthogonalization ₁..., α _n;

Step 8) the contribution rate p of cumulative each characteristic attribute ₁..., p _n, summation is carried out to p and obtains Pt (P _t=p ₁+ ...+p _t), according to given extraction ratio P, if P _t>=P, then t principal component α before extracting ₁..., α _t, t orthogonalized proper vector before being also;

Step 9) calculate projection Y=KL α on feature space, wherein, α=(α ₁..., α _t);

Step 10) obtain new track characteristic data set by step 9 wherein χ _irepresent the proper vector of a track, χ _i={ α ₁..., α _t, wherein α _trepresent track χ _it principal component;

Step 11) for data set χ _ievery bar track sample χ in ∈ χ _i, utilize decision function to judge χ _iwhether be abnormal track, if so, then by track χ _iexport as an abnormal track, and corresponding track label label is set _ifor-1.

Beneficial effect, owing to have employed such scheme, is not only confined on the attribute of locus the detection of the abnormal track of mobile object, but can considers other key characters such as direction, speed of tracing point.First need every bar track to carry out standardization when carrying out abnormal track detection, the property value of each tracing point is normalized between 0 and 1, remove the unit restriction of data, be converted to nondimensional pure values, the index being convenient to not commensurate or magnitude can compare.After standardization track data, by selected kernel function, track data is mapped in the feature space of High-dimensional Linear, the principal character component of track is extracted according to given extraction ratio, map finally by feature space and obtain new track data set, again unsupervised learning is carried out to each track, judge whether every bar track is abnormal track.

When carrying out spatial mappings, can by controlling the width cs of kernel function by initial trace data-mapping in different high-dimensional feature spaces.During principal character component extraction to track, the size of extraction ratio can be controlled to obtain different principal components for subsequent treatment.

Advantage: the method is expanded on traditional locus the sensing range of abnormal track, abnormality detection can be carried out from other characteristic aspects of tracing point, the speed, direction etc. of such as tracing point, do not need when adding additional detections factor to carry out any change to method, method adopts suitable kernel function, effectively can apply to the track data that course length differs greatly and concentrate.Final abnormal track detection also accurate and effective more.

Accompanying drawing explanation

Fig. 1 is algorithm flow chart of the present invention.

Fig. 2 is second embodiment of the invention algorithm flow chart.

Fig. 3 is TOD-KPCA algorithm Detection results figure.

Fig. 4 is algorithm Detection results figure of the present invention.

Embodiment

Embodiment 1: one can detect abnormal track in multifactor, and can be applied to the method for the abnormality detection of the track data collection that course length differs greatly; In the method, FGAK kernel function is utilized to build nuclear matrix K, by the tracing point data-mapping in initial trace space in higher-dimension track characteristic space, the track data of primary nonlinear is converted to the characteristic of high-dimensional feature space neutral line, to extract track data feature better; After track data is mapped to high-dimensional feature space, KPCA is adopted to carry out feature extraction to track data core matrix K; After obtaining the characteristic of track, one-class support vector machine is utilized to classify to track, by setting kernel function width cs, three angular dimensions T and extraction ratio P, unsupervised learning is carried out to the track characteristic data after extracting, when unsupervised learning, judge whether certain track is abnormal track, realizes with following steps by decision function:

(1) from track data set, read the tracing point data of every bar track;

(2) the every bar track of Min-max methodological standardization is adopted;

(3) eigenmatrix after utilizing kernel function FGAK calculating track data to be mapped to high-dimensional feature space, i.e. nuclear matrix K; Different nuclear matrix can be obtained by regulating the width cs of kernel function FGAK;

(4) centralization nuclear matrix K, obtains nuclear matrix KL;

(5) the eigenwert e of nuclear matrix KL is calculated ₁..., e _nand characteristic of correspondence vector v ₁..., v _n;

(6) to eigenwert e ₁..., e _ncarry out descending sort;

(7) orthogonalized eigenvectors, obtains the proper vector V after orthogonalization ₁..., V _n;

(8) the contribution rate p of cumulative each characteristic attribute ₁..., p _n, according to given extraction ratio P, if P _t>=P (P _t=p ₁+ ...+p _t), then t principal component α before extracting ₁..., α _t;

(9) the projection Y=KL α on feature space is calculated, wherein, α=(α ₁..., α _t)

(10) new track data collection is obtained by (9) wherein χ _irepresent the proper vector of a track, χ _i={ α ₁..., α _t, wherein α _trepresent track χ _it principal component;

(11) for data set χ _ievery bar track sample χ in ∈ χ _i, utilize decision function to judge χ _iwhether be abnormal track, if so, then by track χ _iexport as an abnormal track, and corresponding track label label is set _ifor-1.

Concrete grammar is as follows:

Based on the abnormal track-detecting method of FGAK, first should adopt the every bar track of Min-max methodological standardization.Described tracing point data comprise longitude x, the latitude y of tracing point, speed v and direction d; Min-max method is exactly by tracing point set in value be mapped between 0 and 1, specific formula for calculation is $x_t^{\′}=\frac{x_t-\min \left(\right\{x_t\left\}\right)}{max\left(\right\{x_t\left\}\right)-\min \left(\right\{x_t\left\}\right)},$ $y_t^{\′}=\frac{y_t-\min \left(\left\{y_t\right\}\right)}{\max \left(\left\{y_t\right\}\right)-\min \left(\left\{y_t\right\}\right)},v_t^{\′}=\frac{v_t-\min \left(\left\{v_t\right\}\right)}{\max \left(\left\{v_t\right\}\right)-\min \left(\left\{v_t\right\}\right)},d_t^{\′}=\frac{d_t-\min \left(\left\{d_t\right\}\right)}{\max \left(\left\{d_t\right\}\right)-\min \left(\left\{d_t\right\}\right)}.$

Then FGAK kernel function is utilized to carry out space transforming, by initial trace data-mapping to high-dimensional feature space to the track data after standardization.Nuclear matrix K is the eigenmatrix after track data is mapped to high-dimensional feature space.Kernel function FGAK is a positive definite kernel function, and effectively can process elongated track set.FGAK kernel function is: wherein $f_{\mathrm{\σ}}\left(i,j\right)=\frac{1}{2{\mathrm{\σ}}^2}{||i-j||}^2+log(2-e^{-\frac{{||i-j||}^2}{2{\mathrm{\σ}}^2}}),$ In formula, σ is the width of kernel function, and i, j represent the sequence number of track in track set, and the method is the createMatrix method building nuclear matrix K.

Then carry out to nuclear matrix K the nuclear matrix KL that centralization obtains centralization.Calculate the eigenwert e of nuclear matrix KL again ₁..., e _nand characteristic of correspondence vector v ₁..., v _n; Descending sort is carried out to eigenwert, then orthogonalized eigenvectors obtains the proper vector V after orthogonalization ₁..., V _n.

After processing nuclear matrix KL, need the contribution rate p of cumulative each characteristic attribute ₁..., p _n, according to given extraction ratio P, if P _t>=P (P _t=p ₁+ ...+p _t), then t principal component α before extracting ₁..., α _t.

After extracting principal component, the projection Y=KL α on feature space can be asked for, wherein, α=(α ₁..., α _t).So just can obtain new track data set wherein χ _irepresent the proper vector of a track, χ _i={ α ₁..., α _t, wherein α _trepresent track χ _it principal component.

Finally, track set is traveled through for bar track sample χ every in data set χ _i, utilize decision function to judge χ _iwhether be abnormal track, if so, then by track χ _iexport as an abnormal track, and corresponding track label label is set _ifor-1.

Embodiment 2:

Utilize FGAK kernel function that the track data after standardization is mapped to high-dimensional feature space, build nuclear matrix K;

Projection is carried out to the track characteristic data in high-dimensional feature space and obtains track characteristic matrix, specifically with following steps

Realize:

1) track data (N bar track, m eigenwert) after standardization is write as the matrix T of a N × m.

2) value of each element in nuclear matrix K is calculated.By matrix T vector set represent, wherein v _nrepresent the row vector of the track data after n-th standardization.Use FGAK kernel function to carry out spatial mappings, can obtain: K [m] [n]=k (v _m, v _n).

3) define the matrix of a N × N, wherein the value of each element is 1/N, carries out centralization obtain KL, KL=K-1 to nuclear matrix K _nk-K1 _n+ 1 _nk1 _n.

4) eigenspace projection Y=KL α is carried out to the nuclear matrix KL of centralization, α=(α ₁..., α _t) obtain the characteristic set χ of track.

5) track characteristic data acquisition χ is returned.

Method createMatrix is for building high-dimensional feature space nuclear matrix K, and K [m] [n] represents the correlativity between m article of track and n-th article of track.Need when changing from luv space to high-dimensional feature space to use nonlinear transformation Φ (v _i) inner product operation, but nonlinear transformation Φ (v _i) be difficult to determine and calculate, suitable kernel function can be used to replace for its inner product operation, i.e. k (v, v')=Φ (v) ^tΦ (v'), the element so in nuclear matrix can calculate, K [m] [n]=k (v _m, v _n).After calculating nuclear matrix K, also need centralization nuclear matrix K, KL=K-1 _nk-K1 _n+ 1 _nk1 _n, 1 _nrepresent the matrix of N × N, and each element value in matrix is 1/N.Finally on the nuclear matrix KL calculated, carry out eigenspace projection, i.e. Y=KL α, projection Y is final track characteristic set of extracting.

Embodiment 3: the present invention compares with TOD-KPCA method

In order to verify validity of the present invention, the data of Atlantic hurricane data 1990-2006 are adopted to verify.Fine rule in Fig. 3 and Fig. 4 represents normal trace, and thick line represents abnormal track.As can be seen from Figure 3, the abnormal track that TOD-KPCA algorithm detects concentrates on edge zone mostly, and bad for the track detection effect that direction reverse is larger.The present invention does not carry out resampling to initial trace data, maintains the characteristic of initial trace, and adds speed and two, direction factor when carrying out abnormality detection, and Detection results is more rationally also more effective compared to TOD-KPCA, as shown in Figure 4.

Embodiment 4: the application of algorithm of the present invention in stock market

This algorithm can help stock invester in stock market, find the stock of tendency novelty.Often can prop up time of a stock and corresponding share price point as this shares changing tendency figure, these points be coupled together the trajectory path just having become this stock.The process finding novel stock is exactly detect the process of abnormal stock track.By the abnormality detection to a large amount of stock trajectory path, those dystropic stock can be found, by can stock invester be instructed better to choose stock to the research of these dystropic stocks.

Specifically realize with following steps:

(1) image data, gathers the point of share price corresponding to the time point and this time point that often prop up stock as stock track, forms the set of stock track after gathering.

(2) set of above-mentioned stock track is input in this algorithm as input data, and corresponding algorithm parameter is set.

(3) dystropic stock track can be obtained after algorithm calculates, the stock that this stock belongs to novel in stock set is described, further can study these dystropic stock, thus find the stock having more value.

Claims (5)

1. based on an abnormal track-detecting method of FGAK, it is characterized in that: abnormal track can be detected in multifactor, and the abnormality detection of the track data collection that course length differs greatly can be applied to; In the method, FGAK kernel function is utilized to build nuclear matrix K, by the tracing point data-mapping in initial trace space in higher-dimension track characteristic space, the track data of primary nonlinear is converted to the characteristic of high-dimensional feature space neutral line, to extract track data feature better; After track data is mapped to high-dimensional feature space, KPCA is adopted to carry out feature extraction to track data core matrix K; After obtaining the characteristic of track, one-class support vector machine is utilized to classify to track, by setting kernel function width cs, three angular dimensions T and extraction ratio P, unsupervised learning is carried out to the track characteristic data after extracting, when unsupervised learning, judge whether certain track is abnormal track, and concrete steps are as follows by decision function:

Step 1) from track data set, read the tracing point data of every bar track;

Step 2) adopt the every bar track of Min-max methodological standardization;

Step 3) utilize kernel function FGAK to calculate track data to be mapped to the eigenmatrix after high-dimensional feature space, i.e. nuclear matrix K; Different nuclear matrix is obtained by regulating the width cs of kernel function FGAK;

Step 4) centralization nuclear matrix K, obtain nuclear matrix KL;

Step 5) calculate the eigenwert e of nuclear matrix KL ₁..., e _nand characteristic of correspondence vector v ₁..., v _n;

Step 6) to eigenwert e ₁..., e _ncarry out descending sort, characteristic of correspondence vector also can auto-sequencing;

Step 7) orthogonalized eigenvectors, obtain the proper vector α after orthogonalization ₁..., α _n;

Step 8) the contribution rate p of cumulative each characteristic attribute ₁..., p _n, summation is carried out to p and obtains Pt (P _t=p ₁+ ...+p _t), according to given extraction ratio P, if P _t>=P, then t principal component α before extracting ₁..., α _t, t orthogonalized proper vector before being also;

Step 9) calculate projection Y=KL α on feature space, wherein, α=(α ₁..., α _t);

Step 10) obtain new track characteristic data set by step 9 wherein χ _irepresent the proper vector of a track, χ _i={ α ₁..., α _t, wherein α _trepresent track χ _it principal component;

Step 11) for data set χ _ievery bar track sample χ in ∈ χ _i, utilize decision function to judge χ _iwhether be abnormal track, if so, then by track χ _iexport as an abnormal track, and corresponding track label label is set _ifor-1.

2. a kind of abnormal track-detecting method based on FGAK according to claim 1, is characterized in that: described tracing point data comprise longitude x, the latitude y of tracing point, speed v and direction d.

3. a kind of abnormal track-detecting method based on FGAK according to claim 2, is characterized in that: the every bar track of described Min-max methodological standardization is exactly for tracing point set in value be mapped between 0 and 1, specific formula for calculation is $x_t^{\′}=\frac{x_t-\min \left(\right\{x_t\left\}\right)}{\max \left(\right\{x_t\left\}\right)-\min \left(\right\{x_t\left\}\right)},y_t^{\′}=\frac{y_t-\min \left(\right\{y_t\left\}\right)}{\max \left(\right\{y_t\left\}\right)-\min \left(\right\{y_t\left\}\right)},$ $v_t^{\′}=\frac{v_t-\min \left(\right\{v_t\left\}\right)}{\max \left(\right\{v_t\left\}\right)-\min \left(\right\{v_t\left\}\right)},d_t^{\′}=\frac{d_t-\min \left(\right\{d_t\left\}\right)}{\max \left(\right\{d_t\left\}\right)-\min \left(\right\{d_t\left\}\right)}.$

4. a kind of abnormal track-detecting method based on FGAK according to claim 1, is characterized in that: described kernel function FGAK is a positive definite kernel function, and effectively can process elongated track set, and FGAK kernel function is: $k(i,j)=e^{-f_{\mathrm{\σ}}(i,j)},$ Wherein $f_{\mathrm{\σ}}(i,j)=\frac{1}{2{\mathrm{\σ}}^2}{||i-j||}^2+log(2-e^{\frac{{||i-j||}^2}{2{\mathrm{\σ}}^2}}),$ In formula, σ is the width of kernel function, and i, j represent the sequence number of track in track set, and the method is the createMatrix method building nuclear matrix K.

5. a kind of abnormal track-detecting method based on FGAK according to claim 1, is characterized in that: utilize FGAK kernel function the track data after standardization to be mapped to high-dimensional feature space and build nuclear matrix K, and the concrete steps of centralization nuclear matrix are:

Step 1) by the track data after standardization, N bar track, m eigenwert, is write as the matrix T of a N × m;

Step 2) calculate the value of each element in nuclear matrix K, by matrix T vector set represent, wherein v _nrepresent the row vector of the track data after n-th standardization, use FGAK kernel function to carry out spatial mappings, can obtain: K [m] [n]=k (v _m, v _n);

Step 3) definition a N × N matrix, wherein the value of each element is 1/N, carries out centralization obtain KL, KL=K-1 to nuclear matrix K _nk-K1 _n+ 1 _nk1 _n.