CN105931271A - Behavior locus identification method based on variation BP-HMM - Google Patents

Abstract

The invention discloses a behavior locus identification method based on a variation BP-HMM. The method comprises the following steps: extracting features of a behavior sample, and establishing a behavior locus and a data set; determining a model used for simulating the behavior locus, wherein the model employs the variation BP-HMM; initializing prior super parameters of a Beta process; obtaining a trained variation BP-HMM by training the model by use of the prior super parameters; and based on the trained variation BP-HMM, identifying the behavior locus of people by use of a maximum likelihood method. According to the invention, the variation BP-HMM which can be used for identifying the behavior locus of the people is created and used. The variation BP-HMM constructs a feature selection matrix and can automatically lean the feature selection matrix. The self-learning updating process of the variation BP-HMM is derived at the same time, a detailed derivation algorithm is given, and the identification method is given in an instructive manner.

Description

A kind of action trail recognition methods of people based on variation BP-HMM

Technical field

The present invention relates to field of computer technology, relate to the Activity recognition technology of people, particularly to a kind of based on variation BP-HMM The action trail recognition methods of people.

Background technology

The invention mainly relates to four bulk background technologies: beta process, HMM, the BP-HMM of sampling, variation Reasoning.

1) beta process (Beta Process)

Beta process is suggested in survival analysis for the first time.Beta process is applied to hidden factor model as without ginseng priori. This is a kind of important application of beta process.Beta process is also used for choosing the hidden state set of HMM as without ginseng priori. Beta process at the beginning is defined as at arithmetic number (R⁺), it was extended to space (e.g., R more widely later⁺)。

Beta process B～BP (α, B₀) it is a positive L é vy process.Wherein α is concentration parameter, and B₀It is that on Ω fixes Estimate.Make γ=B₀(Ω), then beta process can be written as follows form,

$B_K=\underset{k=1}{\overset{\mathrm{\∞}}{\Σ}}{\mathrm{\π}}_k{\mathrm{\δ}}_{{\mathrm{\ω}}_k},---\left(0.1\right)$

${\mathrm{\ω}}_{i_j}\stackrel{i.i.d.}{~}\frac{1}{\mathrm{\γ}}{B}_0.$

Here set { ω } is the atom collection in B.If B₀Be continuous print, then the L é vy process of BP can be represented as,

ν (d ω, d π)=α (ω) π^-1(1-π)^c(ω)-1dπB₀(dω). (0.2)

If B₀It is discrete, and hasSuch structure, then B and B₀In atom have identical subscript. It can represent by following form,

$B_K=\underset{k=1}{\overset{K}{\Σ}}{\mathrm{\π}}_k{\mathrm{\δ}}_{{\mathrm{\ω}}_k},$

${\mathrm{\π}}_k\stackrel{i.i.d.}{~}Beta(\frac{\mathrm{\α}\mathrm{\γ}}{K},\mathrm{\α}(1-\frac{\mathrm{\γ}}{K}\left)\right),$

${\mathrm{\ω}}_k\stackrel{i.i.d.}{~}\frac{1}{\mathrm{\γ}}{B}_0.$

As K → ∞, H_kDuring → ∞, B is a beta process.In order to preferably introduce beta process, the present invention is inevitable Bernoulli process be will now be described.Bernoulli process with beta process as parameter can be denoted as F～BeP (B).It can Using by as a L é vy process, the L é vy of this L é vy process estimates is

μ (d π, d ω)=δ₁(dπ)B(dω). (0.3)

If B is continuous print here, then F is the Poisson process with B as intensity.It can be by tableWherein N～Poisson (B).If B is discrete, andHere b_kBe one with π_kFor probability Independent Bernoulli Jacob's variable.If B is a beta process, then

B～BP (α, B₀), (0.4)

F～BeP (B),

This is referred to as beta-Bernoulli process (Beta-Bernoulli process).In Di, Cray process is a kind of important can joining as nothing The stochastic process of priori, it has two kinds of generating modes: (1) Chinese-style restaurant process；(2) folding rod process.With Cray process (Dirichlet in Di Process) similar, beta process also has two kinds of main modes of production, (1) Indian Restaurant process；(2) folding rod process.Wherein India's buffet process is that (the most hidden factor model can be understood as observation and is subject to without ginseng priori for a kind of hidden factor model important The model of a series of hidden features impact).If didactic consideration, India's cafeteria process is a kind of Gu as its name Visitor selects the process of service plate.Beta-the Bernoulli process generated by India's cafeteria process is then considered following one Individual process,

(1) first client comes into restaurant, have chosenPart plate；

(2) i-th client comes into restaurant, and this client hasProbability choose the plate being selected, (wherein m_kIt is Choose the number of kth plate).Simultaneously, i-th client also hasProbability choosing Take new plate.

Definetti mixed distribution can be counted as using India's cafeteria process as the beta-Bernoulli process of the process of generation.

Beta process B～BP (α, B₀) folding rod process formulation form be

$B=\underset{i=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{j=1}{\overset{C_i}{\Σ}}{V}_{i_j}^{\left(i\right)}\underset{l}{\overset{i-1}{\Π}}(1-V_{i_j}^{\left(l\right)}){\mathrm{\δ}}_{{\mathrm{\ω}}_{i_j}},$

$C_i\stackrel{i.i.d.}{~}Poisson\left(\mathrm{\γ}\right),$

$V_{i_j}^{\left(l\right)}\stackrel{i.i.d.}{~}Beta(1,\mathrm{\α}),$

${\mathrm{\ω}}_{i_j}\stackrel{i.i.d.}{~}\frac{1}{\mathrm{\γ}}{B}_0.---\left(0.5\right)$

From the equations above it is recognised that take turns (here takes turns an iteration indexed by i referred to), C each_iIndividual atom quilt Pick out (wherein C_iObey Poisson (γ)), their weight then obeys the folding rod process of i time, each folding rod The rod length being selected obeys Beta (1, α).

2) HMM

HMM is a state-space model.It can carry out modelling sequence number with the Markov Chain of discrete variable Can be using a state as condition according to, the most each observation, and each state can a corresponding discrete hidden variable.The brightest Aobvious this is one and is adapted to modelling seasonal effect in time series probabilistic model, and particularly the association of itself is not between those sequence datas It is but that the most obvious each data can be relevant to a phrase or special state, also deposits between these special states simultaneously At transformational relation, and this conversion and time correlation.HMM is proved to the Activity recognition people, indoor positioning and voice In some row real world applications such as identification the most effective.

Assume that observation sequence is X={x₁,…,x_NIt is N × d matrix and Z={z₁,…,z_NBe a N-dimensional hidden variable to Amount, and the value space Ω that these hidden variables have a size to be K₁.The Joint Distribution of X and Z can be expressed as following form,

$p(X,Z|\mathrm{\θ})=p\left(z_1\right|\mathrm{\π})\left\{\underset{n=2}{\overset{N}{\Π}}p\left(z_n\right|z_{n-1},A)\right\}\underset{m=1}{\overset{N}{\Π}}p\left(x_m\right|z_m,\mathrm{\φ}),---\left(0.6\right)$

Wherein θ={ π, A, φ }, and A is a K × K matrix.Element inside AWherein T={1 ..., N-1}, i, j ∈ Ω₁Simultaneouslyπ is the vector of K dimension, π_k=p (z₁=k), k ∈ Ω₁Simultaneously ∑_kπ_k=1.Further, matrix A is expressed as A=Dir (π), wherein π={ π with Cray distribution in Di_i,i∈Ω_1}。 The probability graph model present invention of HMM is given in figure one.

If x_i, i={1 ..., N} is discrete, and to have size be that D value collects Ω₂.φ is the matrix of a K × D, in φ The element in face isi∈Ω₁,j∈Ω₂.A and φ is known respectively as transfer matrix and emission matrix.As Really x_i, i ∈ 1 ..., N} is continuous print, then emission matrix should replace with a transmitting distribution.φ can also replace with distribution, Such as Gauss distribution p (x_t|z_t=k)～N (x_t|μ_k,Σ_k),k∈Ω₁.Generally, μ_k,Σ_kTable can be carried out with stochastic variable Showing, these stochastic variables can obey Normal Inverse Wishart distribution or the Gauss distribution of band Gamma distribution.

Likelihood is used to evaluate the most important standard of the degree of a HMM matching current data.Two of HMM most important Learning algorithm be (1) Viterbi algorithm, (2) Baum-Welch algorithm.In given transfer matrix and the situation of emission matrix Under, in the present invention, use Viterbi algorithm can extrapolate, by maximizing likelihood, the hidden shape that current time sequence pair is answered State sequence.Baum-Welch algorithm can be understood as the HMM version of EM in fact, and he is by forward backward algorithm and EM In conjunction with being derived by transfer and emission matrix.

HMM can identify that the time series of that length also can divide that short time series.For short time series, classification Can consider into is hidden state, then obtains classification results by Viterbi algorithm.For long time series, can pass through Maximum likelihood obtains classification results.Such as, for the set λ, λ of HMM_i, i={1 ..., M} is used for training time sequence X_i, wherein θ_iIt is λ_iParameter.For a new time series to be test for, its classification can obtain in the following way,

K=argmax_ip(Xⁱ|θ_i), (0.7)

Class=y_k,

Wherein, y={y₁,y₂,…,y_i,…,y_k,…,y_N-1,y_N, y_iIt is i-th seasonal effect in time series classification, p (Xⁱ|θ_i) can with to Front backward algorithm is calculated.

In Baum-Welch algorithm, derivation needs to the suitable initial value of the parameter of HMM, because this is an office The algorithm that portion is optimum, the quality of result can be had by initial value the most directly to be affected.It is true that shift-matrix A and initial vector π are As long as reasonable through being proved to specified value, the change of value is the most little on the impact of result.It is crucial that the initial value of emission matrix.Nothing Opinion is that the experiment in the achievement of substantial amounts of forefathers or the present invention all shows, for Baum-Welch algorithm, launches The variable of the initial value of matrix, can have a great impact result.

3) BP-HMM sampled

In order to simultaneously to multiple behavior modelings, and it can be found that can be present in the behavior that needs distinguish in the Activity recognition of people The total quantity of action, and find the public action between different behavior, BP-HMM is proposed out.

First, present invention assumes that X={X₁,X₂,…,X_i,…X_N, N ∈ N⁺, wherein X_iIt it is i-th track.Each track Carrying out modelling with a HMM, these HMM share a infinitely-great overall situation hidden state set Ω.Hidden condition selecting matrix F is The matrix of one N × ∞, the element inside itRepresent equal to 1 and there is the hidden state of kth in i-th track. The transfer matrix of i-th HMM is

$Z_1^{\left(i\right)}~{\mathrm{\π}}_{\left(0\right)}^{\left(i\right)},Z_{t+1}^{\left(i\right)}|Z_t^{\left(i\right)}~{\mathrm{\π}}_{\left(z_t\right)}^{\left(i\right)},t=1...T^{\left(i\right)},---\left(0.8\right)$

Its initial vector is

The emission matrix of i-th HMM is

(A_k,Σ_k)～NIW (u₀,λ₀,Φ₀,υ₀).

Inside BP-HMM, present invention F represents the hidden state set that the inside sequence has.Here, F is constructed by BP-BeP.

B～BP (α, B₀), (0.11)

f_i| B～BeP (B).

Because India's cafeteria process is the most easily sampled, so BP herein uses India's buffet procedure construction.From above Formula can be seen that, wants so that hidden condition selecting matrix F is more sparse, and it is bigger that concentration parameter α will be arranged.And want Want that it is bigger that γ will be set so that more hidden state is chosen.

In many is tested, the hidden number of states of each track can be obtained, moreover, between different tracks by study automatically Public hidden state also can be found.Different tracks direct public hidden state is all clearly presented in laboratory report Out.This makes the track collection for there is public hidden state set between those tracks, and BP HMM is combining the multiple tracks of modeling Time ratio HMM more flexibly and performance is more preferable.

4) variation reasoning

The present invention usesN₁∈N⁺Carry out all of hidden variable in labelling Bayesian model of the present invention, useN₂∈N⁺The all of observational variable of labelling, finally usesN₃∈N⁺。 The log edge likelihood of probabilistic model of the present invention can be decomposed in the following form,

Wherein,

$KL\left(q\right|\left|p\right)=-\∫q\left(Z\right)ln\left\{\frac{p\left(Z\right|X,\mathrm{\θ})}{q\left(Z\right)}\right\}dZ.---\left(0.13\right)$

KL (q | | p) is the Kullback-Leibler divergence between q (Z) and Posterior distrbutionp p (Z | X, θ) and KL (q | | p) >=0, and and if only if The when of q (Z)=p (Z | X, θ), equal sign is set up.ThereforeIt it is the lower bound of lnp (X | θ).Inside variation reasoning,Claimed For variation lower bound.So q (Z) can approximate obtain p (Z | X, θ) by maximizing the variation next time.

The element of Z is divided into the set Z of not UNICOM by the present invention_i, i={1 here ..., M}, M ∈ N⁺.Then present invention assumes that Variation distribution q (Z) can be according to these set-partitions, i.e.

$q\left(Z\right)=\underset{i}{\overset{M}{\Π}}{q}_i\left(Z_i\right)\·---\left(0.14\right)$

One solves q_i(Z_i) the general formulae of optimal solution as follows,

This variation reasoning algorithm that q (Z) factorization approximates Posterior distrbutionp is referred to as variation mean field.

Having some needs to be noted, variation reasoning when, the priori of all of parameter is all assigned.Although in theory On, the present invention is not to independent factor q_i(Z_i) functional form do any appointment, but in actual application, the present invention can thing First one posterior form of relatively simple variation of appointment.Therefore, to factor set q_i(Z_i) make and suitably initializing after, The present invention just can update variation distribution according to (0.15).

Summary of the invention

The present invention proposes the action trail recognition methods of a kind of people based on variation BP-HMM, comprises the steps:

Step one: extract the feature of behavior sample, set up action trail and data set thereof；

Step 2: determine the model for simulating action trail, described model uses variation BP-HMM model；

Step 3: initialize the priori hyper parameter of beta process；

Step 4: utilize described priori hyper parameter to train described model, the variation BP-HMM model after being trained；

Step 5: based on the variation BP-HMM model after described training, utilize the action trail of method of maximum likelihood identification people.

In the described action trail recognition methods that the present invention proposes, described variation BP-HMM model represents with equation below:

$B=\underset{k=1}{\overset{\mathrm{\∞}}{\Σ}}{V}_k{e}^{-T_k}{\mathrm{\δ}}_{{\mathrm{\ω}}_k},$

$V_k\stackrel{i.i.d.}{~}Beta\left(1,\mathrm{\α}\right),$

T_k～Gamma (d_k-1,α),

${\mathrm{\ω}}_k\stackrel{i.i.d.}{~}\frac{B_0}{\mathrm{\γ}}.$

f_i| B～BeP (B),

$Z_1^{\left(i\right)}~{\mathrm{\π}}_{\left(0\right)}^{\left(i\right)},Z_{t+1}^{\left(i\right)}|Z_t^{\left(i\right)}~{\mathrm{\π}}_{\left(z_t\right)}^{\left(i\right)},t=1...T^{\left(i\right)},$

(A_k,Σ_k)～NIW (u₀,λ₀,Φ₀,υ₀).

Wherein, B is beta process, and the atom of B is ω_k, atom weight isV is the vector of a 1* ∞, Its each element and one are with beta distribution independent same distribution that (1, α) is parameter；And T_kExpression formula beT_kObedience parameter is d_kThe Gamma distribution of-1 and α；d_kIt is that an indicator is for marking Note kth atom occurs in d_kIn wheel；Here, α can be constant can also be variable, it is beta process Concentration parameter；B₀It is that on the space Ω of beta process B place is fixing to estimate；And γ=B₀(Ω)；Represent Time series is at the hidden state value of the HMM corresponding to t；F_iIt is feature selection vector, which determines i-th track All of hidden state；It is the vector of a two-value simultaneously, and it obeys the Bernoulli process with B as parameter；π⁽ⁱ⁾It is The transfer matrix of HMM, its first row is the priori vector of hidden state；π⁽ⁱ⁾Obey with [r, r ..., r+ κ, r ...] and f_iOne Cray in Di that vector is parameter obtained that is multiplied of one is distributed；AndObey with [r, r ..., r, r ...] and f_iOne to one Be multiplied Cray distribution in Di that vector is parameter obtained；Here X is observation track data,Obey one withVector be average andMatrix is the Multi-dimensional Gaussian distribution of covariance；And (A_k,Σ_k) combine obedience one with u₀,λ₀,Φ₀,υ₀Normal Inverse Wishart for parameter is distributed, u₀It is vector, λ₀And v₀It is scalar, Φ₀It is Matrix.

In the described action trail recognition methods that the present invention proposes, the priori hyper parameter initializing beta process comprises the steps:

Step a1: determine behavior kind to be identified in the data set of described action trail；

Step a2: determine the average length of all action trail；

Step a3: determine the dimension of described action trail；

Step a4: determine the hyper parameter of beta process in BP-HMM according to form；

Step a5: all action trail are concentrically formed the action trail after set；

Step a6: utilize K-means algorithm that the action trail after described set is carried out clustering processing, obtains cluster knot Really；

Step a7: utilize described cluster result statistics to obtain the hyper parameter of HMM in BP-HMM model.

In the described action trail recognition methods that the present invention proposes, described model is trained to comprise the steps:

Step b1: set maximum number of run and variation lower bound change threshold；

Step b2: when variation lower bound changing value is less than or equal to variation lower bound change threshold, or number of run is less than or equal to During big number of run；

Step b21: keep current variation lower bound；

Step b22: for each action trail；

I) transfer and emission matrix are calculated according to the HMM parameter of current track；

Ii) result of current track forward backward algorithm part is calculated；

Iii) parameter of the transfer matrix of HMM is calculated according to result the most backward；

Step b23: update the parameter representing behavior atom；

Step b24: update the parameter of beta process；

Step b25: recalculate variation lower bound and preserve；

Step b26: cumulative number of run, returns step b2.

In the described action trail recognition methods that the present invention proposes, before updating the parameter of beta process, parameter is updated.

In the described action trail recognition methods that the present invention proposes, the parameter updating beta process comprises the steps:

Step b241: use gradient ascent algorithm optimization variation lower bound, solve and renewal combines beta process and HMM In conjunction with the parameter of selection matrix；

Step b242: use gradient ascent algorithm to solve optimized variation lower bound to solve undated parameter V；

Step b243: use gradient ascent algorithm to solve optimized variation lower bound to solve undated parameter T；

Step b244: utilize factorization variation reasoning to solve parameter alpha；

Step b245: utilize factorization variation reasoning to solve parameter γ.

In the described action trail recognition methods that the present invention proposes, utilize method of maximum likelihood identification based on described variation BP-HMM model The action trail of people comprises the steps:

Step c1: input the parameter of the variation BP-HMM model after described training；

Step c2: extract the feature of behavior to be tested, obtains action trail to be measured and data set thereof；

Step c3: for described action trail and data set thereof, successively by the variation BP-HMM model after described training Parameter as likelihood condition, be calculated likelihood value；

Step c4: choose the behavior of the likelihood value of maximum, identify the action trail of behavior to be measured.

The beneficial effects of the present invention is: the learning algorithm of variation BP-HMM is derived by the present invention.The present invention is directed to study The behavior that the method identification of the variation BP-HMM maximum likelihood arrived is new.

Accompanying drawing explanation

Fig. 1 is the flow chart of the action trail recognition methods of people based on variation BP-HMM.

Fig. 2 is the probability graph model of variation BP-HMM model.

Detailed description of the invention

In conjunction with implementing in detail below and accompanying drawing, the present invention is described in further detail.Implement the process of the present invention, condition, Experimental techniques etc., outside the lower content mentioned specially, are universal knowledege and the common knowledge of this area, and the present invention does not has Limit content especially.

As it is shown in figure 1, the action trail recognition methods of present invention people based on variation BP-HMM, comprise the steps:

Step one: extract the feature of behavior sample, set up action trail and data set thereof；

Step 2: determine the model for simulating action trail, described model uses variation BP-HMM model；

Step 3: initialize the priori hyper parameter of beta process；

Step 4: utilize described priori hyper parameter to train described model, the variation BP-HMM model after being trained；

Step 5: based on the variation BP-HMM model after described training, utilize the action trail of method of maximum likelihood identification people.

Need the hidden state set specifying each HMM in advance different from conventional HMM, the variation BP-HMM model Beta of the present invention The procedure construction selection matrix of one hidden state, selectes the hidden state set of each HMM by each vector of matrix, and hidden Condition selecting matrix is then to obtain during the model learning of variation reasoning.In variation BP-HMM, all of HMM shares one Individual big hidden state set, then selects the hidden state set of oneself by hidden condition selecting matrix.This is that variation BP-HMM is with existing The difference that HMM model is maximum.Because constructed the Feature Choice Matrix of HMM by Beta process, so being total between different tracks Enjoying action can be learnt out, this contributes to distinguishing different tracks, and this is that HMM cannot accomplish.Secondly, the BP-HMM of variation Oneself can learn to obtain this point of hidden state set and also more conform to current demand.Because in not all reality, The hidden state set that track is corresponding can be determined in advance, and if it will be apparent that the setting of hidden state set correctly will be to HMM's Identification ability causes weakening greatly.So variation BP-HMM is more flexible than HMM.

The following is the specific algorithm of model learning.

In fig. 2, first will initialize the hyper parameter of all of BP-HMM, the variation then updating the HMM in Fig. 2 is joined Number, then update the parameter of beta process.

Specific algorithm is as follows:

1, first according to input data initialization all of BP hyper parameter；

2, initialize all of HMM hyper parameter with K-means；

3, set maximum number of run, and variation lower bound change threshold；

4, While (variation lower bound changing value≤variation lower bound change threshold | | number of run≤maximum number of run)

B21: keep current variation lower bound；

The each track of b22:Foreach；

I. transfer and emission matrix are calculated according to the HMM parameter of current track；

Ii. the result of current track forward backward algorithm part is calculated；

Iii. the parameter of the transfer matrix of HMM is calculated according to result the most backward；

B23: update the parameter representing behavior atom；

B24: update the parameter of beta process；

B25: recalculate variation lower bound and preserve；

B26: number of run ++；

By the learning process of above variation BP-HMM it is recognised that the model learning of variation BP-HMM is an iteration Process, the end condition of iteration is exactly that number of run exceeds standard or variation lower bound is the most constant.Model is during study First having to update the parameter of HMM, the parameter being the most so because HMM updates the most relevant with track data, by Parameter in each HMM is different, so to update the parameter of all HMM one by one respectively, the most right The parameter of Beta process updates.During updating, Beta process can update slower about V, the parameter of T, F.Why So being because renewal process and employ gradient decline, but solution should increase overall iterations reduce V, T, F Parameter update required precision.The reason selecting such solution is at V, and when T, F update, other parameters are not correct Value, even if it is the best result that study does not the most represent to the highest precision.Variation BP-HMM is at the such track of 50*100 Substantially the effect of 50 iteration convergences can be reached in data.Pace of learning is far faster than sampling BP-HM, in precision because structure side Formula is different with sampling BP-HMM so precision has also promoted than sampling BP-HMM.So variation BP-HMM is a kind of The comparatively faster model of pace of learning, is a kind of reasonably track identification model.

Update in order to the parameter of the beta process in model of the present invention is done, the present invention coupleIt is made in 1 The Taylor expansion at place.Δ the most of the present invention_kM () carrys out the item in labelling Taylor expansion,

${\mathrm{\Δ}}_k\left(m\right)=\frac{1}{m}\frac{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}\right)}{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+m\right)}\frac{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}+m\right)}{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}\right)}{\left(\frac{v_{k^{\′}}}{v_{k^{\′}}+m}\right)}^{u_{k^{\′}}},$

Due to character Γ (x+1)=x Γ (x) of Gamma function, the present invention can obtain

$\frac{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}\right)}{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+m\right)}\frac{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}+m\right)}{\mathrm{\Γ}\left({\mathrm{\τ}}_{k_1}\right)}=\underset{i=1}{\overset{m}{\Π}}\frac{{\mathrm{\τ}}_{k_1}+i-1}{{\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+i-1}.$

Variation reasoning algorithm in the present invention can use Δ when updating the parameter of beta distribution_k(m) aboutu′_kWith u '_k, this A little local derviations will make introductions all round.In order to that states becomes apparent from, the present invention defines With

RightRenewal:

Because π_jWithIn Di, Cray distribution can not be associated link address can resolve directly, so present invention gradient ascent algorithm updates I ∈ 1 ..., C}.Here C is the classification number of track.AboutLocal derviation be

To q (d_k) renewal:

This joint listsAt given r=1 ..., the more new formula of R.If r=1, then

It is when r=1 when, T_kDo not exist.If r ＞ 2, then

Here ρ (r)=(r-1) (Ψ (k₁)-lnk₂)-lnΓ(r-1)+(r-2)(Ψ(u'_k)-lnv'_k), andThe present invention from formula it can be seen thatNot only it is subject to and kth hidden state phase The parameter closed affects also by d_k', the impact of k ' ≠ k.α and γ is the biggest,Decline the fastest.

To q (V_k) renewal:

By the present invention in that and carry out associated update with gradient ascent algorithmHere gradient be variation lower bound about Gradient.In order to allow more new formula seem more clear, the present invention has done some and has set, and allows

WithTwo local derviations are respectively

Because Ψ (x) can be represented asAnd its derivative isSo

$\begin{array}{c}\frac{\∂{\mathrm{\Δ}}_k(\·)}{\∂{\mathrm{\τ}}_{k_1}}=\underset{m=1}{\overset{M}{\Σ}}\{\frac{1}{m}{\left(\frac{v_{k^{\′}}}{v_{k^{\′}}+m}\right)}^{u_{k^{\′}}}\underset{i=1}{\overset{m}{\Π}}\frac{{\mathrm{\τ}}_{k_1}+i-1}{{\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+i-1}\×\\ \{\mathrm{\Ψ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+m\right)+\mathrm{\Ψ}\left({\mathrm{\τ}}_{k_1}\right)-\mathrm{\Ψ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}\right)-\mathrm{\Ψ}\left({\mathrm{\τ}}_{k_1}+m\right)\}\},\end{array}$

With

$\begin{array}{c}\frac{\∂{\mathrm{\Δ}}_k(\·)}{\∂{\mathrm{\τ}}_{k_2}}=\underset{m=1}{\overset{M}{\Σ}}\{\frac{1}{m}{\left(\frac{v_{k^{\′}}}{v_{k^{\′}}+m}\right)}^{u_{k^{\′}}}\underset{i=1}{\overset{m}{\Π}}\frac{{\mathrm{\τ}}_{k_1}+i-1}{{\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+i-1}\\ \×\left(\mathrm{\ψ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+m\right)-\mathrm{\Ψ}\left({\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}\right)\right)\}.\end{array}$

To q (T_k) renewal:

By the present invention in that and carry out associated update (u ' with gradient ascent algorithm_k, v '_k), gradient here is that variation lower bound is about (u '_k, v '_k) Gradient.The two local derviation is respectively

Here,

$\frac{\∂{\mathrm{\Δ}}_k(\·)}{\∂v_{k^{\′}}}=\underset{m=1}{\overset{M}{\Σ}}\{\frac{1}{m}\underset{i=1}{\overset{m}{\Π}}\frac{{\mathrm{\τ}}_{k_1}+i-1}{{\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+i-1}{\left(\frac{v_{k^{\′}}}{v_{k^{\′}}+m}\right)}^{u_{k^{\′}}}\left(\ln \left(v_{k^{\′}}\right)-\ln \left(v_{k^{\′}}+m\right)\right),$

$\frac{\∂{\mathrm{\Δ}}_k(\·)}{\∂v_{k^{\′}}}=\underset{m=1}{\overset{M}{\Σ}}\{\frac{1}{m}\underset{i=1}{\overset{m}{\Π}}\frac{{\mathrm{\τ}}_{k_1}+i-1}{{\mathrm{\τ}}_{k_1}+{\mathrm{\τ}}_{k_2}+i-1}{u}_{k^{\′}}{\left(\frac{v_{k^{\′}}}{v_{k^{\′}}+m}\right)}^{u_{k^{\′}}-1}\frac{m}{{\left({v_{k^{\′}}}^2+m\right)}^2}.$

Renewal to q (α):

(k₁, k₂) more new formula be

Can be seen that from formulaRenewal to α is useless.

Renewal to q (γ):

AboutMore new formula be

τ₁=K+b₁,

From formula, the present invention can be seen that τ₁Will not change during iteration updates, but τ₂Can the most more Newly, and update depend on

To q (A_k,∑_k) renewal:

To q (A_k,Σ_k) the renewal of variational parameter be analysable and more new formula is

$u_k=\frac{1}{{\mathrm{\λ}}_0+\underset{n}{\overset{N}{\Σ}}\underset{t}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right)}\left(\underset{n}{\overset{N}{\Σ}}\underset{t}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right)X_t^{\left(n\right)}+{\mathrm{\λ}}_0{u}_0\right),$

${\mathrm{\λ}}_k={\mathrm{\λ}}_0+\underset{n}{\overset{N}{\Σ}}\underset{n}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right),$

${\mathrm{\υ}}_k={\mathrm{\υ}}_0+\underset{n}{\overset{N}{\Σ}}\underset{t}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right),$

$\begin{array}{c}{\mathrm{\Φ}}_k={\mathrm{\λ}}_0{u}_0^{,}{u}_0+\underset{n=1}{\overset{N}{\Σ}}\underset{t=1}{\overset{N^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right)\×X_t^{{\left(n\right)}^{,}}{X}_t^{\left(n\right)}+{\mathrm{\Φ}}_0-\frac{1}{{\mathrm{\λ}}_0+\underset{n}{\overset{N}{\Σ}}\underset{n}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right)}\\ \×{\left(\underset{n}{\overset{N}{\Σ}}\underset{t}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right)X_t^{\left(n\right)}+{\mathrm{\λ}}_0{u}_0\right)}^{,}\left(\underset{n}{\overset{N}{\Σ}}\underset{t}{\overset{T^{\left(n\right)}}{\Σ}}q\left(Z_t^{\left(n\right)}=k\right)X_t^{\left(n\right)}+{\mathrm{\λ}}_0{u}_0\right).\end{array}$

To q (π_j) renewal:

In order to update the π of the track of classification in i-th_j, wherein the difference for j value is divided into two kinds.Both of which is Analysable.For j ＞ 0, π_jLog series model can be updated by equation below,

Wherein,

$p\left(Z_{t+1}^{\left(i\right)}\right|\mathrm{\π},Z_t^{\left(i\right)}=j)={\Π}_{t=1}^{T-1}{\Π}_{j2=1}^K{\mathrm{\π}}_{j_{j_2}}^{\mathrm{\δ}\left(Z_t^{\left(i\right)}=j,Z_{t+1}^{\left(i\right)}=j_2\right)}$

And

$p\left({\mathrm{\π}}_j\right|f_n,r,k)=\frac{1}{B}{\Π}_{k\≠j}^K{\mathrm{\π}}_{jk}^{\left(r\right)f_{n_k}-1}{\mathrm{\π}}_{jj}^{(r+k)f_{n_j}-1}$

Here Cray distribution q (π in B is Di_j) norming constant.The present invention can obtain

$\begin{array}{c}\ln q\left({\mathrm{\π}}_j\right)=\underset{h=1}{\overset{K}{\Σ}}\left(\underset{\left(i\right),y^{\left(i\right)}=n}{\overset{N}{\Σ}}\underset{t=0}{\overset{T-1}{\Σ}}q\left(Z_t^{\left(i\right)}=j,Z_{t+1}^{\left(i\right)}=h\right)+\left(r\right){\mathrm{\υ}}_{n_h}-1\right)\ln \left({\mathrm{\π}}_{j_h}\right)\\ +\left(\left(r+k\right){\mathrm{\υ}}_{n_j}-1+\underset{\left(i\right)y^{\left(i\right)}=n}{\overset{N}{\Σ}}\underset{t}{\overset{T-1}{\Σ}}q\left(Z_t^{\left(i\right)}=j,Z_{t+1}^{\left(i\right)}=j\right)\right)\ln \left({\mathrm{\π}}_{j_j}\right).\end{array}$

So Cray distribution q (π in Di_j) parameter r_j, can be updated according to below equation,

$r_{j_h}=\underset{\left(i\right),r^{\left(i\right)}=n}{\overset{N}{\Σ}}\underset{t=1}{\overset{T-1}{\Σ}}q\left(Z_t^{\left(i\right)}=j,Z_{t+1}^{\left(i\right)}=h\right)+\left(r\right){\mathrm{\υ}}_{n_h},j\≠h,$

$r_{j_j}=\underset{\left(i\right),y^{\left(i\right)}=n}{\overset{N}{\Σ}}\underset{t=1}{\overset{T-1}{\Σ}}q\left(Z_t^{\left(i\right)}=j,Z_{t+1}^{\left(i\right)}=j\right)+\left(r+\mathrm{\κ}\right){\mathrm{\υ}}_{n_j},j=h.$

As j=0, π_jIt it is the probability of hidden state.The present invention can obtain

$r_{0_h}=\underset{i,y^{\left(i\right)}=n}{\Σ}q\left(Z_1^{\left(i\right)}=h\right)+\left(r\right){\mathrm{\υ}}_{n_h}.$

R is the balance factor of the impact effect determining the impact effect of Baum-Welch arithmetic result and υ, and r is the biggest,Shadow Ring effect the biggest.

Renewal to q (Z):

For every kind of track,

Wherein p is observational variable X_tDimension.

From above formula it can be seen that the present invention needs q (Z_t=j) and q (Z_t=j₁,Z_t+1=j₂).The two item detailed Next calculating process will be given, and they are to be calculated by forward backward algorithm.Forward algorithm is

${\mathrm{\ι}}_i^t=P(X_1=x_1,X_2=x_2,\mathrm{...},X_t=x_t,Z_t=i|W),$

${\mathrm{\ι}}_i^1=a_{0j}^{*}{b}_{ti}^{*},$

${\mathrm{\ι}}_j^{t+1}=b_{t+1j}^{*}\underset{i=1}{\overset{K}{\Σ}}{\mathrm{\ι}}_i^t{a}_{ij}^{*}.$

Back pass is

β_i(t)=P (X_t+1=x_t+2,X_t+2=x_t+2,…,X_T=x_T|Z_t=i, W),

β_i(T)=1,

${\mathrm{\β}}_i\left(T\right)=\underset{j=1}{\overset{K}{\Σ}}{\mathrm{\β}}_j(t+1)a_{ij}^{*}{b}_{t+1j}^{*}.$

Like this, Posterior distrbutionp just can be expressed as

$q\left(Z_t=j\right)=\frac{{\mathrm{\ι}}_i\left(t\right){\mathrm{\β}}_i\left(t\right)}{\underset{j=1}{\overset{K}{\Σ}}{\mathrm{\ι}}_j\left(t\right){\mathrm{\β}}_j\left(t\right)},$

$q\left(Z_t=j_1,Z_{t+1}=j_2\right)=\frac{{\mathrm{\ι}}_i\left(t\right)a_{ij}^{*}{\mathrm{\β}}_i\left(t\right)b_{t+1j}^{*}}{\underset{k=1}{\overset{K}{\Σ}}{\mathrm{\ι}}_k\left(t\right){\mathrm{\β}}_k\left(t\right)}.$

According to the above formula, the variational parameter iteration in BP-HMM just can be have updated by the present invention.The present invention is under change In the case of boundary stops change or is basically unchanged, stop iteration renewal process.Concrete update algorithm is given in algorithm one. Concrete recognition function:

$class=y_{{\mathrm{argmax}}_{i}p\left(X^i|{\left\{a^{*}\right\}}^i,u,\mathrm{\λ},\mathrm{\υ},\mathrm{\Φ}\right)}$

Wherein y is classification.

Variation BP-HMM model in the present invention can not only be used in the Activity recognition of people being applied to many The field of track identification, the process identifying behavior of variation BP-HMM needs first to use variation BP-HMM to track Data modeling, and with a HMM, the track of one kind is modeled.In the transfer matrix arrived to study and transmitting The parameter { { a of matrix^*}ⁱ, u, λ, υ, Φ } after, one needs to be test for track and can be identified by the way of following,

$class=y_{{\mathrm{argmax}}_{i}p\left(X^i|{\left\{a^{*}\right\}}^i,u,\mathrm{\λ},\mathrm{\υ},\mathrm{\Φ}\right)}---\left(0.16\right)$

Wherein { a^*}ⁱIt is referred to as the transfer matrix of i-th track.Learning after all parameters of model, in (0.18) Likelihood p (Xⁱ|{a^*}ⁱ, u, λ, υ, Φ) can be calculated by the forward backward algorithm of HMM.

This classification mechanism is more more reasonable than sample, and transfer matrix here learns to obtain from model, and not It is as existing sampling BP-HMM, track one HMM model of study, then owning a classification Transfer matrix takes average, obtains the transfer matrix of this classification.

Comprising the following steps that of sorting algorithm,

(1) for data to be identified, extract characteristic processing and become rational track.

(2) assume that maximum likelihood value is 0.

(3) HMM model that all study of Foreach is arrived

I () calculates likelihood p (Xⁱ|{a^*}ⁱ, u, λ, υ, Φ),

(ii) size is compared with maximum likelihood value.If bigger than maximum likelihood, updating maximum likelihood is current likelihood value, And record current HMM for optimum HMM.

(4) the most current track classification testing data of current optimum track classification corresponding for HMM.

This categorizing process is the process that maximum likelihood selects in fact, and likelihood is the standard of a kind of energy good descriptive model matching quality, The current HMM matching track of the biggest expression of likelihood is the best, and that just represents track classification that this HMM represents and more conforms to Current track.

The present embodiment experimental data is the parking data collected from video.Wherein there are six kinds of behaviors, the behavior class of training set Distinguishing label is obtained by artificial labelling.Six kinds are respectively: 1, receive (PTSS) through south；2, through east street Road (PTES)；3, return (GA)；4, it is horizontally through parking lot (CPH)；5, before being parked in building (WFB), 6, (WTS) is walked in uppermost street.

The predicted classification of table 1 and classification accuracy thereof

Table 1 above is the confusion matrix of the classification accuracy of this data set.The accuracy of identification of model of the present invention has reached 95%. Exceed well over the 91% of sampling model.

The protection content of the present invention is not limited to above example.Under the spirit and scope without departing substantially from inventive concept, this area skill Art personnel it is conceivable that change and advantage be all included in the present invention, and with appending claims as protection domain.

Claims (7)

1. the action trail recognition methods of a people based on variation BP-HMM, it is characterised in that comprise the steps:

Step one: extract the feature of behavior sample, set up action trail and data set thereof；

Step 2: determine the model for simulating action trail, described model uses variation BP-HMM model；

Step 3: initialize the priori hyper parameter of beta process；

Step 4: utilize described priori hyper parameter to train described model, the variation BP-HMM model after being trained；

Step 5: based on the variation BP-HMM model after described training, utilize the action trail of method of maximum likelihood identification people.

2. action trail recognition methods as claimed in claim 1, it is characterised in that described variation BP-HMM model is with following public Formula represents:

$B=\underset{k=1}{\overset{\mathrm{\∞}}{\Σ}}{V}_k{e}^{-T_k}{\mathrm{\δ}}_{{\mathrm{\ω}}_k},$

$V_k\stackrel{i.i.d.}{~}Beta(1,\mathrm{\α}),$

T_k～Gamma (d_k-1,α),

${\mathrm{\ω}}_k\stackrel{i.i.d.}{~}\frac{B_0}{\mathrm{\γ}}.$

f_i| B～BeP (B),

$Z_1^{\left(i\right)}~{\mathrm{\π}}_{\left(0\right)}^{\left(i\right)},Z_{t+1}^{\left(i\right)}|Z_t^{\left(i\right)}~{\mathrm{\π}}_{\left(z_t\right)}^{\left(i\right)},t=1...T^{\left(i\right)},$

(A_k,Σ_k)～NIW (u₀,λ₀,Φ₀,υ₀).

Wherein, B is beta process, ω_kIt is the atom of B,Being atom weight, V is the vector of a 1* ∞, it Each element and one are with beta distribution independent same distribution that (1, α) is parameter；T_kExpression formula be T_kObedience parameter is d_kThe Gamma distribution of-1 and α；d_kIt is that an indicator occurs in d for labelling kth atom_kIn wheel； α is constant or variable, for representing the concentration parameter of beta process；B₀It is that on the space Ω of beta process B place is fixing to survey Degree；γ=B₀(Ω)；The time series represented is at the hidden state value of the HMM corresponding to t；F_iIt is feature selection vector, For determining all of hidden state of i-th track, also it is the vector of a two-value simultaneously, obeys the Bai Nu with B as parameter Profit process；π⁽ⁱ⁾Being the transfer matrix of HMM, its first row is the priori vector of hidden state, π⁽ⁱ⁾Obey with [r, r ..., r+ κ, r ...] With f_iCray distribution in man-to-man Di that vector is parameter obtained that is multiplied；Obey with [r, r ..., r, r ...] and f_iPhase one to one Multiplied to Di that vector is parameter in Cray distribution；X is observation track data,Obey one withVector is equal Value andMatrix is the Multi-dimensional Gaussian distribution of covariance；(A_k,Σ_k) combine obedience one with u₀,λ₀,Φ₀,υ₀Normal for parameter Inverse Wishart is distributed, u₀It is vector, λ₀And v₀It is scalar, Φ₀It it is matrix.

3. action trail recognition methods as claimed in claim 1, it is characterised in that initialize the priori hyper parameter of beta process Comprise the steps:

Step a1: determine behavior kind to be identified in the data set of described action trail；

Step a2: determine the average length of all action trail；

Step a3: determine the dimension of described action trail；

Step a4: determine the hyper parameter of beta process in BP-HMM according to form；

Step a5: all action trail are concentrically formed the action trail after set；

Step a6: utilize K-means algorithm that the action trail after described set is carried out clustering processing, obtain cluster result；

Step a7: utilize described cluster result statistics to obtain the hyper parameter of HMM in BP-HMM model.

4. action trail recognition methods as claimed in claim 1, it is characterised in that train described model to comprise the steps:

Step b1: set maximum number of run and variation lower bound change threshold；

Step b2: when variation lower bound changing value is less than or equal to variation lower bound change threshold, or number of run runs less than or equal to maximum During number of times；

Step b21: keep current variation lower bound；

Step b22: for each action trail；

I) transfer and emission matrix are calculated according to the HMM parameter of current track；

Ii) result of current track forward backward algorithm part is calculated；

Iii) parameter of the transfer matrix of HMM is calculated according to result the most backward；

Step b23: update the parameter representing behavior atom；

Step b24: update the parameter of beta process；

Step b25: recalculate variation lower bound and preserve；

Step b26: cumulative number of run, returns step b2.

5. action trail recognition methods as claimed in claim 3, it is characterised in that before updating the parameter of beta process, parameter is carried out Update.

6. action trail recognition methods as claimed in claim 3, it is characterised in that the parameter updating beta process includes walking as follows Rapid:

Step b241: use gradient ascent algorithm optimization variation lower bound, solves and updates and combine what beta process and HMM combined The parameter of selection matrix；

Step b242: use gradient ascent algorithm to solve optimized variation lower bound to solve undated parameter V；

Step b243: use gradient ascent algorithm to solve optimized variation lower bound to solve undated parameter T；

Step b244: utilize factorization variation reasoning to solve parameter alpha；

Step b245: utilize factorization variation reasoning to solve parameter γ.

7. action trail recognition methods as claimed in claim 3, it is characterised in that utilize based on described variation BP-HMM model The action trail of maximum-likelihood method identification people comprises the steps:

Step c1: input the parameter of the variation BP-HMM model after described training；

Step c2: extract the feature of behavior to be tested, obtains action trail to be measured and data set thereof；

Step c3: for described action trail and data set thereof, successively by the parameter of the variation BP-HMM model after described training As likelihood condition, it is calculated likelihood value；

Step c4: choose the behavior of the likelihood value of maximum, identify the action trail of behavior to be measured.