CN106604229A - Indoor positioning method based on manifold learning and improved support vector machine - Google Patents
Indoor positioning method based on manifold learning and improved support vector machine Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/021—Services related to particular areas, e.g. point of interest [POI] services, venue services or geofences
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
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Abstract
The invention discloses an indoor positioning method based on manifold learning and an improved support vector machine. The method comprises a step of determining a positioning area, dividing the positioning area according to an indoor structural characteristic and a layout characteristic, and obtaining a classification result, a step of obtaining offline training data, and collecting hotspot RSS signal values which can be received by the reference points in different classification area as a training data set, a step of using an isometric mapping algorithm to carry out training data characteristic extraction, a step of using the training data to carry out support vector machine classified training, using a taboo search algorithm to carry out support vector machine classification hyper parameter searching, and establishing the support vector regression model of each category at the same time, a step of carrying out online positioning, collecting the RSS signal value of each hotspot of a target, using a support vector machine classification model to carry out classification, and obtaining the rough positioning area of the target, and a step of carrying out the accurate positioning of the target by using the support vector regression model according to the classification result. According to the method, the time-varying characteristic of the wireless signal intensity is effectively suppressed, and the precision is obviously improved.
Description
Technical field
Indoor positioning field of the present invention, more particularly to it is a kind of based on manifold learning with improve support vector machine indoor positioning
Method.
Background technology
It is accurately positioned in problem indoors, Chinese scholars have carried out correlational study, is constantly proposed numerous effective and feasible
Location algorithm.Wherein as WLAN (WLAN) can accomplish all standing, low cost and other advantages, the scene based on WLAN point
Analysis indoor positioning algorithms become the main direction of studying of domestic and international colleges and universities and research institution.This algorithm is referred to as fingerprint location,
Its essence is to set up the mapping relations one by one of RSS (signal intensity) and particular location, so as to be positioned.The difficult point of this method
It is the foundation of mapping relations data base (fingerprint database).And the RSS values of each signal access point (AP) have time-varying characteristics,
Cause positioning precision to reduce, therefore noise reduction and feature extraction are carried out to RSS signal demands, so as to reduce the introducing of signal time-varying characteristics
Error.Meanwhile, the rise with machine Learning Theory with develop rapidly, researchers are by neutral net, support vector machine etc.
Machine learning algorithm is fused in wireless indoor fingerprinting localization algorithm, improves the precision of wireless indoor positioning.Numerous studies are tied
Fruit shows that support vector machine (SVM) are strong with generalization ability, compared to neural network algorithm, can effectively overcome Expired Drugs.
Thus SVM has the advantages that other machines learning algorithm is incomparable in terms of positioning indoors.During SVM sets up, which surpasses
The selection of parameter directly affects result of calculation, and traditional grid-search algorithms precision is low, and search time is long, affects indoor positioning
Real-time, thus it is also particularly important to the choosing method of SVM hyper parameters.
The content of the invention
Goal of the invention：The invention aims to improve indoor position accuracy, it is proposed that it is a kind of based on manifold learning with
Improve the algorithm of support vector machine.Invention carries out being accurately positioned for indoor objects using the algorithm, using the method for manifold learning
Data Dimensionality Reduction is carried out except making an uproar, indoor wireless positioning precision is improved.
Technical scheme：It is a kind of based on manifold learning and the indoor orientation method for improving support vector machine, it is including following
Step：
Step 1：Determine positioning region, root doors structure feature is classified to positioning region, obtains specification area；
Step 2：Offline training data is obtained, each focus that the reference point in different classifications region can be received is gathered
RSS signal values are used as training dataset；
Step 3：Offline training data feature extraction is carried out using Isometric Maps algorithm to the training dataset in step 2,
Carry out dimensionality reduction and denoising；
Step 4：Vector machine classification based training is supported using the Offline training data in step 2, is calculated using TABU search
Method is supported the search of vector machine hyper parameter, obtains the support vector cassification model for training, while setting up of all categories propping up
Hold vector regression model；
Step 5：Tuning on-line is carried out, the RSS signal values of each focus at target are gathered, using propping up for training in step 4
Hold vector machine disaggregated model to be classified, obtain target positioning region substantially；Wherein, carry out when gathering echo signal value multi-party
To collection；
Step 6：According to classification results, the accurately fixed of target is carried out using the support vector regression model set up in step 4
Position.
Further, carry out to positioning region in the step 1 classification is whether to carry out mutation to carry out according to signal
Classification.
Further, the step 2 is specially：According to the size cases of each specification area, arrange with reference to points, every
Multi-direction gathered data in individual reference point, it is ensured that the data multidirectional of reference point；Signal strength threshold is set simultaneously, works as signal
When intensity is less than threshold value, the focus is 0 for the positioning point of reference of the reference point, and its RSS value is set to 0, obtains training number
According to collection.
Further, data are trained using Isometric Maps algorithm to the training dataset in step 2 in the step 3
Feature extraction, carries out dimensionality reduction and denoising；Specially：
To the RSS signal data collection X for givingi, i=1,2 ..., k, k are sample total number：
4) the field figure of each point in data sample X is set up by K nearest neighbor algorithms,
5) geodesic curve distance is calculated, sets up X*X distance relation matrixes；If sample point and each other neighborhood sample point, the two
Between geodesic curve distance be Euclidean distance, otherwise, using heap optimization dijkstra's algorithm calculate shortest path, use shortest path
To represent geodesic distance；
6) Nonlinear Dimension Reduction is carried out by multidimensional scaling algorithm, obtains the low-dimensional character representation of high dimensional data；Adjust the distance square
Battle array centralization simultaneously carries out singular value decomposition, calculates d eigenvalue of maximum (λ of distance matrix1,...,λd) and corresponding feature
Vectorial U, constructs diagonal matrix Λ=diag (λ1,...,λd), obtain the low-dimensional character representation of sample data X.
Further, the step 4 is specially：
In the case of linear separability, an optimum Optimal Separating Hyperplane is found, be spaced geometry and reach maximum, hyperplane
For：
ωTX+b=0 formulas (1)
Wherein, w represents weight vector, and x is input vector, and b represents bias vector；
If set of data samples and its being expressed as (xi,yi), i=1 ..., k, x ∈ Rd, y ∈ { -1 ,+1 }, wherein
Inputs of the x for data, y are exported for result；In order to find this hyperplane, the quadratic programming problem of following formula is solved：
s.t.,yi(ωTxi+ b) >=1, i=1 ..., n
Above-mentioned quadratic programming problem is solved by Lagrange duality method, abbreviation obtains following formula：
Wherein α is Lagrange multiplier, and the α in formula (3) is fixed, partial derivative is sought to w and b respectively, their local derviation is made
Number is zero, and result is rewinded formula (3), and abbreviation is obtained：
s.t.,αi>=0, i=1 ..., n formulas (5)
α is obtained according to formula (5)iValue, just can rewind the value that formula (4) obtains w, the value of b is solved by supporting vector, and
Suzanne Lenglen day multiplier αiThe corresponding sample that is not zero is supporting vector；
Under nonlinear situation, a mapping phi () is introduced, nonlinear data is mapped to into a higher dimensional space so as to
Become linear separability, the Nonlinear Classification of indoor positioning is solved the problems, such as by introducing gaussian kernel function, introduce slack variable and come
This problem is solved, the abbreviation form of non-linear Lagrange function is obtained：
s.t.,0≤αi≤ C, i=1 ..., n formulas (6)
In formula：C be introduce slack variable after parameter, referred to as penalty factor, and support vector machine need optimization amount,
Gaussian kernel functionNonlinear Classification function is accordingly：
Wherein, it is as follows come the Nonlinear Classification flow process for solving the problems, such as indoor positioning by introducing gaussian kernel function：
(5) Tabu search algorithm initialization；According to parameter searching step sizes, the initialization of taboo list length is carried out, generated super
The search grid of parameter (C, σ), designs the producing method and maximum iteration time of neighborhood；Neighborhood generating mode is：According to number
Radius, the square neighborhood centered on current solution are set according to size；
(6) fitness is calculated, checks estimated performance；According to each solution design support vector machine, tested using k- folding intersections
The fitness of card method inspection solution, k value determine according to training data size, limit minimum and must not be less than 4, if k- folding cross validations
Prediction probability inverse as fitness value；
(7) update the taboo element of taboo list and record current optimal value, it is first as taboo using changing value is solved
Element；
(8) cyclic search, checks whether and reaches termination condition or reach maximum iteration time, reach, stop search,
Output optimal solution.
Beneficial effect：The characteristics of present invention is using according to building structure and indoor arrangement carries out region division, does not rely on
Hotspot's distribution situation, strong adaptability.The dimensionality reduction of data is carried out except making an uproar using the method for manifold learning, RSS signals time-varying is reduced special
Property the impact that brings, improve indoor position accuracy.Combined with returning using support vector cassification, entered using tabu search algorithm
Row hyper parameter is searched for, and improves positioning precision.The present invention effectively inhibits the time-varying characteristics of wireless signal strength, in off-line training number
In the case of less, compared to traditional location algorithm, precision is significantly improved.
Description of the drawings
Fig. 1 is the inventive method schematic flow sheet；
Fig. 2 is equidistant mapping algorithm flow chart in the present invention；
Fig. 3 is the residual variance schematic diagram in the present invention；
Fig. 4 is the simulated environment schematic diagram of the present invention；
Fig. 5 is the simulation result comparison diagram of the present invention.
Specific embodiment
The present invention is described in further detail with implementation example below in conjunction with the accompanying drawings：
As shown in figure 1, the present invention be it is a kind of based on manifold learning with improve support vector machine indoor orientation method, including
Following step：
Step 1：Determine positioning region, positioning region is classified.Any one piece of region in building has oneself
Construction characteristic, any one room have its spatial layout feature, these features be all to maintain in most of time it is constant, or even
It is changeless.And the RSS signals of focus (AP) also can be distributed according to such structure, RSS signal intensitys are general not
Can be mutated, but if running into obstacle or certain reason can cause mutation, so whether we be able to can enter according to signal
Being classified, the signal intensity feature of such classification can be especially apparent for row mutation, to classification based training with predict it is also further accurate.
And judge that the mutation of signal is determined according to the construction featuress and layout of building oneself itself here.For example we can will be every
Individual room is used as a region class, or is have a bookshelf in room, or it is other decorate to being separated by, such room
Between can be divided into two classes according to separator.This is a kind of sorting technique for not relying on AP distributions, compared to according to AP distributions
To be classified, the suitability is higher.
Step 2：Offline training data is obtained, each focus that the reference point in different classifications region can be received is gathered
(AP) RSS signal values are used as training dataset.According to the size cases of each specification area, appropriate reference points are set,
In time allowed band, reference point is as more as possible.The multi-direction gathered data in each reference point, it is ensured that the data of reference point are more
Directivity.Signal strength threshold is set simultaneously, when signal intensity is less than threshold value, it is believed that the AP is determined for the reference point
Position point of reference is 0, and its RSS value is set to 0, simplifies and calculates.
Step 3：Data characteristicses extraction is trained using Isometric Maps algorithm, dimensionality reduction and denoising effect is reached.It is initial to instruct
Practice data and be usually associated with numerous noises, and RSS signals also have the change such as time-varying characteristics, temperature, humidity affect RSS letters
Number.Therefore, in order to adapt to this change, need to find the dependency between signal.These changes overall can change RSS signals,
But the dependency between each reference point still can be remained.Meanwhile, present wireless network application is ripe, and one piece of region has
More than ten or even tens AP access points, this can cause the training data of higher-dimension, cause the difficult of calculating.And manifold learning
This two point are solved the problems, such as simultaneously can.
Isomap (Isometric Maps algorithm) is that Josh Tenenbaum exist《Science》On the manifold learning delivered it is initiative
Algorithm, it has started the new battlefield of a data processing, and its advantage is to maintain the geometry feature between all data points pair,
Noise resisting ability is strong, and learning performance is stable, it is ensured that the robustness and Global Optimality of result, has to processing RSS signal noises
Good rejection ability.The theoretical frame of Isomap is MDS (Multidimensional Scaling), but is placed on manifold
In theoretical frame.MDS is a kind of Method of Data with Adding Windows, and its principle is just so that distance keeps not the point after dimensionality reduction between any two
Become.But MDS is designed just for theorem in Euclid space, for the calculating of distance is also what is completed using Euclidean distance.And Isomap
Euclidean distance has simply been changed into algorithm geodesic curve (geodesic) distance in manifold.In Isomap, geodesic curve distance is just
It is that beeline algorithm can use the classic algorithm in computer graph theory, such as come approximate with the beeline on figure between 2 points
Dijkstra's algorithm etc..If to the RSS signal data collection X, i=1,2 ... that give, k, k are sample total number, then the algorithm stream
Journey is as shown in Figure 2：
1) field of each point in data sample X is set up by KNN (kNN, k-NearestNeighbor) nearest neighbor algorithm
Figure, the value of Neighbourhood parameter k is too small here, and precision can be caused to reduce, while influence of noise is larger, k value is excessive, can bring not phase into
The point of pass, reduces efficiency of algorithm, and the principle that we choose k value here is
2) geodesic curve distance is calculated, sets up X*X distance relation matrixes.If sample point and each other neighborhood sample point, they it
Between geodesic curve distance be the Euclidean distance between them, otherwise, using heap optimization dijkstra's algorithm calculate shortest path,
Geodesic distance is represented with shortest path.
3) Nonlinear Dimension Reduction is carried out by MDS (multidimensional scaling algorithm), obtains the low-dimensional character representation of high dimensional data.To away from
From matrix centralization and singular value decomposition is carried out, calculate d eigenvalue of maximum (λ of distance matrix1,...,λd) and it is corresponding
Characteristic vector U, constructs diagonal matrix Λ=diag (λ1,...,λd), so just can calculate the low-dimensional feature of sample data X
Represent.
By the algorithm, we can obtain the dimensionality reduction result of any low-dimensional, and Fig. 3 is the data redundancy after 1 to 5 dimension is reduced to
Variogram.
Step 4：Vector machine (SVM) classification based training is supported using training data, SVM is carried out using tabu search algorithm
Hyper parameter is searched for, and gives up traditional grid search, improves search speed.Set up support vector regression model of all categories simultaneously.
Support vector machine (Support Vector Machine, SVM) are a kind of engineerings based on Statistical Learning Theory
Learning method, improves the generalization ability of learning machine by seeking structuring least risk, realizes empiric risk and fiducial range
Minimize, so as to reach in the case where statistical sample amount is less, can also obtain the purpose of good statistical law.The essence of SVM
It is two graders, in the case of linear separability, SVM attempts to look for an optimum Optimal Separating Hyperplane, is spaced geometry
Maximum is reached, hyperplane is as shown in Equation 1：
ωTX+b=0 (1)
Wherein, w represents weight vector, and b represents bias vector.
If set of data samples and its being expressed as (xi,yi), i=1 ..., k, x ∈ Rd, y ∈ { -1 ,+1 }, wherein
Inputs of the x for data, y are exported for result.In order to find this hyperplane, can pass through to solve the quadratic programming problem of following formula：
s.t.,yi(ωTxi+ b) >=1, i=1 ..., n
Above-mentioned quadratic programming problem can be solved by Lagrange duality method, abbreviation obtains following formula：
Wherein α is Lagrange multiplier, and the α in (3) formula is fixed, partial derivative is sought to w and b respectively, their local derviation is made
Number is zero, and result is rewinded (3) formula, and abbreviation is obtained：
s.t.,αi>=0, i=1 ..., n (5)
By (4), (5) are as can be seen that no w, two variables of b, it is only necessary to according to (5) in Lagrangian formula
Obtain αiValue, just can rewind the value that (4) obtain w, the value of b can be solved by supporting vector, and Suzanne Lenglen day multiplier αiNo
Be sample corresponding to zero be exactly supporting vector required for us.
Under nonlinear situation, it would be desirable to introduce a mapping phi (), nonlinear data is mapped to into a higher-dimension
Space so as to become linear separability, but the nonlinear mapping for introducing can cause the dimension disaster for calculating, and kernel function exactly may be used
To avoid this problem.Therefore, herein by introducing gaussian kernel function solving the problems, such as the Nonlinear Classification of indoor positioning.Due to
There is noise jamming in RSS signals, indivedual supporting vectors can be caused to deviate just datas, it is therefore desirable to by introduce slack variable come
Solve this problem.(6) abbreviation form of the formula for non-linear Lagrange function.
s.t.,0≤αi≤ C, i=1 ..., n (6)
In formula：C be introduce slack variable after parameter, referred to as penalty factor, and support vector machine need optimization amount,
Gaussian kernel functionNonlinear Classification function is accordingly：
The quality of the prediction effect of SVM has vital effect to positioning precision, finds in research, different types of
Kernel function is less to SVM performance impacts, and the parameter of kernel function and penalty factor be affect SVM prediction effects key because
Element.TABU search (TS) algorithm is a kind of heuristic global Stepwise optimization algorithm, is one kind simulation to human mind's process.Prohibit
Avoid fully demonstrate in searching algorithm collection neutralization diffusion two it is tactful, embody a concentrated reflection of in the local search ability of TS, can from one
Row solution is set out, and seeks preferably solution, terminated with reaching local optimum in the neighborhood of this feasible solution.Meanwhile, in order to jump out
Locally optimal solution, algorithm devise Diffusion Strategy.Function of the Diffusion Strategy by taboo list, in taboo list, record has arrived at
Some information, algorithm is by the taboo to these table midpoints, and reaches some points do not searched for, so as to realize bigger region
Search.
Gaussian kernel function is selected herein, and hyper parameter (C, σ) is the parameter that we need to optimize.Algorithm flow is as follows：
1) Tabu search algorithm initialization.According to parameter searching step sizes, the initialization of taboo list length is carried out, generate super ginseng
The search grid of number (C, σ), designs the producing method and maximum iteration time of neighborhood.The neighborhood generating mode for adopting herein
For：Radius, the square neighborhood centered on current solution are set according to size of data.
2) fitness is calculated, checks estimated performance.According to each solution design SVM, using k- folding cross validation method inspections
The fitness of solution is looked into, k value is determined according to training data size, but in order to ensure precision, limit minimum and must not be less than 4.This literary grace
The Prediction sum squares of cross validation are rolled over as fitness value with k-.
3) update the taboo element of taboo list and record current optimal value, adopt herein and changing value is solved as taboo
Element.
4) cyclic search, checks whether and reaches termination condition or reach maximum iteration time, reach, stop search, defeated
Go out optimal solution.
Step 5：Tuning on-line is carried out, the RSS signal values of each AP at target is gathered, using the svm classifier model for training
Classified, obtained target positioning region substantially.Equally, need to carry out multi-direction collection when gathering echo signal value.
Step 6：According to classification results, being accurately positioned for target is carried out using support vector regression model.
A kind of manifold learning and improvement support vector machine method of being based on proposed by the present invention is by MATLAB simulation softwares
Carry out emulation experiment, it is contemplated that many problems of indoor AP receiving points, we propose 10, and simulated environment is as shown in Figure 4.Simulation hardware
Environment is Intel (R) Core (TM) i5-2410M CPU 2.30GHz, 10 operating system of 4G RAM, Windows.Such as Fig. 5
It is shown, it is IMTS-SVM algorithms and traditional SVM algorithm and neural network algorithm accuracy comparison figure, it can be seen that neural
Network algorithm due to less in data volume, positioning it is interval it is big in the case of, study generalization ability is poor, and positioning precision is relatively low, is determining
Precision in the range of error 2m of position only has 48.4%., because of the good advantage of its generalization, positioning precision is higher than ANN for SVM algorithm, fixed
Precision in the range of error 2m of position is 53.2%, and the precision within 4m can reach 78.0%.But also due to positioning
Interval larger, the impact of RSS signals easily fluctuation, positioning precision are extremely difficult to satisfied degree.And set forth herein IMTS-SVM
Precision of the algorithm in the range of position error 2m reaches 63.6%, and the precision in the range of 4m has been up to 90.8%, compared to
In traditional SVM algorithm 2m, precision improves 10.4%, and the precision in 4m improves 12.8%, and positioning precision obtains higher lifting.
The present invention effectively inhibits the time-varying characteristics of wireless signal strength (RSS), in the less situation of Offline training data
Under, compared to traditional location algorithm, precision is significantly improved.This method is mainly comprised the following steps：Step one：It is determined that positioning
Region, by positioning region according to doors structure feature, spatial layout feature is divided, and obtains the stronger classification results of dependency；Step
Rapid two：Offline training data is obtained, each focus (AP) the RSS signals that the reference point in different classifications region can be received are gathered
Value is used as training dataset；Step 3：Data characteristicses extraction is trained using Isometric Maps algorithm, dimensionality reduction is reached and denoising is made
With；Step 4：Vector machine (SVM) classification based training is supported using training data, the super ginsengs of SVM is carried out using tabu search algorithm
Number search, gives up traditional grid search, improves positioning precision.Set up support vector regression model of all categories simultaneously；Step
Five：Tuning on-line is carried out, the RSS signal values of each AP at target is gathered, is classified using svm classifier model, obtain target big
The positioning region of cause；Step 6：According to classification results, being accurately positioned for target is carried out using support vector regression model.
Claims (5)
1. it is a kind of based on manifold learning with improve support vector machine indoor orientation method, it is characterised in that including following
Step：
Step 1：Determine positioning region, root doors structure feature is classified to positioning region, obtains specification area；
Step 2：Offline training data is obtained, each focus RSS letters that the reference point in different classifications region can be received are gathered
Number value as training dataset；
Step 3：Offline training data feature extraction is carried out using Isometric Maps algorithm to the training dataset in step 2, is carried out
Dimensionality reduction and denoising；
Step 4：Vector machine classification based training is supported using the Offline training data in step 2, is entered using tabu search algorithm
Row support vector machine hyper parameter search for, obtain the support vector cassification model for training, at the same set up support of all categories to
Amount regression model；
Step 5：Carry out tuning on-line, gather the RSS signal values of each focus at target, using the support trained in step 4 to
Amount machine disaggregated model is classified, and obtains target positioning region substantially；Wherein, multi-direction adopting is carried out when gathering echo signal value
Collection；
Step 6：According to classification results, being accurately positioned for target is carried out using the support vector regression model set up in step 4.
2. according to claim 1 based on manifold learning and the indoor orientation method for improving support vector machine, its feature exists
In carrying out classifying according to whether signal can be mutated to classify to positioning region in the step 1.
3. according to claim 1 based on manifold learning and the indoor orientation method for improving support vector machine, its feature exists
In the step 2 is specially：According to the size cases of each specification area, arrange with reference to points, it is multi-party in each reference point
To gathered data, it is ensured that the data multidirectional of reference point；Signal strength threshold is set simultaneously, when signal intensity is less than threshold value
When, the focus is 0 for the positioning point of reference of the reference point, and its RSS value is set to 0, training dataset is obtained.
4. according to claim 1 based on manifold learning and the indoor orientation method for improving support vector machine, its feature exists
In, in the step 3 to the training dataset in step 2 using Isometric Maps algorithm be trained data characteristicses extraction, carry out
Dimensionality reduction and denoising；Specially：
To the RSS signal data collection X for givingi, i=1,2 ..., k, k are sample total number：
1) the field figure of each point in data sample X is set up by K nearest neighbor algorithms,
2) geodesic curve distance is calculated, sets up X*X distance relation matrixes；If sample point and each other neighborhood sample point, therebetween
Geodesic curve distance be Euclidean distance, otherwise, using heap optimization dijkstra's algorithm calculate shortest path, with shortest path come table
Show geodesic distance；
3) Nonlinear Dimension Reduction is carried out by multidimensional scaling algorithm, obtains the low-dimensional character representation of high dimensional data；Adjust the distance in matrix
The heart simultaneously carries out singular value decomposition, calculates d eigenvalue of maximum (λ of distance matrix1,...,λd) and corresponding characteristic vector
U, constructs diagonal matrix Λ=diag (λ1,...,λd), obtain the low-dimensional character representation of sample data X.
5. according to claim 1 based on manifold learning and the indoor orientation method for improving support vector machine, its feature exists
In the step 4 is specially：
In the case of linear separability, an optimum Optimal Separating Hyperplane is found, be spaced geometry and reach maximum, hyperplane is：
ωTX+b=0 formulas (1)
Wherein, w represents weight vector, and x is input vector, and b represents bias vector；
If set of data samples and its being expressed as (xi,yi), i=1 ..., k, x ∈ Rd, y ∈ { -1 ,+1 }, wherein x is
The input of data, y are exported for result；In order to find this hyperplane, the quadratic programming problem of following formula is solved：
Above-mentioned quadratic programming problem is solved by Lagrange duality method, abbreviation obtains following formula：
Wherein α is Lagrange multiplier, and the α in formula (3) is fixed, partial derivative is sought to w and b respectively, and the partial derivative for making them is
Zero, result is rewinded into formula (3), abbreviation is obtained：
α is obtained according to formula (5)iValue, just can rewind the value that formula (4) obtains w, the value of b is solved by supporting vector, and bright lattice
Bright day multiplier αiThe corresponding sample that is not zero is supporting vector；
Under nonlinear situation, a mapping phi () is introduced, nonlinear data a higher dimensional space is mapped to into so as to become
Linear separability, solves the problems, such as the Nonlinear Classification of indoor positioning by introducing gaussian kernel function, introduces slack variable to solve
This problem, obtains the abbreviation form of non-linear Lagrange function：
In formula：C be introduce slack variable after parameter, referred to as penalty factor, and support vector machine need optimization amount, Gauss
Kernel functionNonlinear Classification function is accordingly：
Wherein, it is as follows come the Nonlinear Classification flow process for solving the problems, such as indoor positioning by introducing gaussian kernel function：
(1) Tabu search algorithm initialization；According to parameter searching step sizes, the initialization of taboo list length is carried out, generate hyper parameter
The search grid of (C, σ), designs the producing method and maximum iteration time of neighborhood；Neighborhood generating mode is：It is big according to data
Little setting radius, the square neighborhood centered on current solution；
(2) fitness is calculated, checks estimated performance；According to each solution design support vector machine, cross validation side is rolled over using k-
The fitness of method inspection solution, k value determine according to training data size, limit minimum and must not be less than 4, if k- folding cross validations is pre-
The inverse of probability is surveyed as fitness value；
(3) update the taboo element of taboo list and record current optimal value, adopt and changing value is solved as taboo element；
(4) cyclic search, checks whether and reaches termination condition or reach maximum iteration time, reach, stop search, output
Optimal solution.
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