CN106845541A - A kind of image-recognizing method based on biological vision and precision pulse driving neutral net - Google Patents

Abstract

The present invention proposes a kind of image-recognizing method based on biological vision and precision pulse driving neutral net.The present invention is inspired by biological vision hierarchical system, in the characteristic extraction part of image, using the cell operating mechanism of HMAX modeling receptive fields, first with the marginal information of Gabor filtering reinforcing images, max pooling treatment is carried out to the image by the filtered all directions of Gabor again, the purpose for extracting topmost feature and dimension-reduction treatment is reached.In character image data processing method, phase coding technology is selected, the Pixel Information of image has been converted into pulse phenomenon, so not only allowed for the spatial information of image, it is also contemplated that the temporal information of image.The present invention has certain biological basis, and with good feasibility and robustness, and it for the identification and classification of image, especially the accuracy in noise image is greatly improved.

Description

A kind of image-recognizing method based on biological vision and precision pulse driving neutral net

Technical field

The present invention relates to pattern-recognition and class brain calculating field, and in particular to one kind is driven based on biological vision with precision pulse The image-recognizing method of dynamic neutral net.

Background technology

Pattern-recognition is one of topic most hot at present of artificial intelligence field, and its target is entered by the image for gathering Certain treatment is gone to obtain the relevant information of target scene.But Chinese Academy of Sciences Tan car pusher academician is in 2016 Chinese artificial intelligence conferences Pointed out on (CCAI 2016)：General PRS is shouldered heavy responsibilities --- and its Main Bottleneck is robustness, adaptivity With can three aspects of generalization.These technical barriers cause that the development of pattern-recognition cannot adapt to the need of society and Vehicles Collected from Market Ask.

And class brain calculates the brain for not only simulating people, and Other subjects are combined, including signal transacting science, meter Calculation machine technology, statistics, physics, applied mathematics, cognitive science are refreshing and through physiology etc., cause national governments and research aircraft The extensive concern of structure, and have great breakthrough in terms of three big bottleneck problems of pattern-recognition.USA and EU is also thrown this Enter huge fund, be successively proposed respective human brain project：" human brain plan " (the Human Brain in the U.S. Project) it is devoted to exploring neuron, the relation between neural circuit and cerebral function, " the brain work of European Union from neuron aspect It is whole that cardon spectrum plan " (Brain Activity Map Project, or Brain Initiative) is then devoted to simulation Human brain.

Impulsive neural networks be class brain calculating field expert and scholar propose third generation neutral net, its with based on arteries and veins The traditional artificial neural network for rushing frequency coding information is compared, and possesses more powerful computing capability, can simulate various nerve letters Number and arbitrary continuous function, be especially suitable for realizing the process problem of cerebral nerve signal, be to carry out complicated space time information treatment Effective tool.Although currently the research of the PRS based on impulsive neural networks of correspondence technical barrier has just just risen Step, document both domestic and external is not a lot, but scholars have begun to propose the fruitful and full recommendation method of innovation.And And the research based on neural network filter theory is considered as always the most successful one side of Application of Neural Network, it Development be can be described as with neural network theory it is complementary, and in nearly all existing impulsive neural networks physical model All it is successfully applied in area of pattern recognition.Impulsive neural networks theory makes progress can be to the hair of pattern recognition theory Exhibition brings inspiration；Conversely, the progress of pattern recognition theory again can driving pulse neural network theory significantly long-run development.

The content of the invention

The main purpose of the present invention be for present mode identifying system robustness, adaptivity and can generalization three Big bottleneck, builds an image-recognizing method for driving neutral net with precision pulse based on biological vision.To different figures Picture is pre-processed, including image characteristics extraction, during Object representation, human vision hierarchical system is simulated, using HMAX Model realization is operated；The input of pulse is converted thereof into according to the view data that obtains afterwards, consequently facilitating follow-up based on class The treatment that brain is calculated；Categorised decision is carried out finally by impulsive neural networks learning algorithm.Its particular content is as follows：

The feature extraction of 1 biological vision system

In order to improve the practicality of object identification, a kind of vision layered system is employed, for the extraction of characteristics of image. HMAX models and traditional SR (Sparse Repesentaiton, rarefaction representation) are compared, and can preferably describe the entirety of data Structure, so as in the data problem of such as image characteristics extraction etc, there is obvious advantage.

1.1 S1 layers of Gabor filtering process

S1 layers representative be in visual cortex receptive field (Receptive Field) simple cell treatment picture signal Mode.When the V1 areas simple cell of receptive field carries out the matching of unit, feature is extracted using the higher order filter of sparse coding.Perhaps Many researchers establish the computation model of sparse coding using two-dimensional Gabor filter function.The general type of sparse coding It is：

SC=AH

Wherein sc_i, a_i, h_jIt is sparse piece of element of SC of unit, A is the basic function of sparse coding, and H is sparse.A's The most frequently used expression-form is：

||·||_fIt is Frobenius normal forms, μ is normal number.Gabor respond G (x, y) can be approximate be converted into it is sparse The form of coding：

G (x, y)=S (x, y) K (x, y),

Wherein S (x, y) represents complicated sine functions, and its span is [- 1,1], therefore meets above-mentioned basic function A Form.K (x, y) is the envelope function of two-dimensional discrete Gauss equation, and λ represents wavelength, and its value is no more than image length and width 1/5。It is phase offset, at [- 180 °, 180 °], γ represents length-width ratio to value, determines that image is filtered by Gabor Shape.σ depends on bandwidth b：

For simplicity the real part part filtered using Gabor is learnt to characteristics of image：

X'=x cos θ+y sin θs, y'=-x sin θ+y cos θ

In the present invention, offset phase is set respectivelyWavelength X and bandwidth b are 0 °, 10 and 1, therefore σ=0.56 λ.

In S1 layers, the Gabor filtering of (0 °, 45 °, 90 °, 135 °) four direction is chosen, and its result is normalized to [-1,1]。

1.2 C1 layers of maximum pond treatment

Image enhances its marginal information after S1 layers, carries out extraction and the dimensionality reduction of feature using maximum pond at C1 layers, It embodies as follows：

Wherein m is the size of the sliding window in maximum pond.

2 pulse codes

In the present invention, selected phase encryption algorithm (a kind of time encoding scheme) produces pulse train.Coding unit Structure be made up of three parts：Positive neuron (POS), negative neurons (NEG), output neuron (EOUT).Entirely compiling During code, each incoming spiking represents a neuron activity, is connected to a receptive field region, i.e., one volume Code unit is connected to a pixel.Subthreshold membrane potential oscillation (SMOS) is also related to action potential, and each pixel is strong in RF Angle value is converted into a rectilinear oscillation for the time action potential for processing meticulously, and this is described as cosine function：

WhereinIt is i-th concussion function of encoding nerve unit, in periodically；A is amplitude, and ω represents angular speed, φ₀ It is initial phase, i-th offset phase φ of encoding nerve unit_iComputing formula be：

φ_i=φ₀+(i-1)·Δφ

Wherein Δ φ is minimum offset identity, and its value is 2 π/n, and n is the number of neuron.Concussion cycle t is set_maxFor 200ms.Each pixel of image is represented with for example following formula of the relation of time：

Wherein x_iThe pixel value of representative image ith pixel.When the incoming coding layer of pixel, will cause upwardly or downwardly Film vibration, if film potential exceed threshold value, stimulate produce.The product of pulse train can be controlled by adjusting amplitude and threshold value It is raw.

3 impulsive neural networks learn

Impulsive neural networks mainly learn to the pulse train that image is produced, and pulse train is represented by：

Wherein, t^fF-th pulse Time Of Release is represented, δ (x) represents Dirac delta functions, at that time x=0, δ (x)= 1, otherwise δ (x)=0.The present invention uses the supervised learning algorithm of impulsive neural networks, the purpose is to：It is multiple defeated for what is given Enter pulse train S_i(t) and multiple target pulse sequence S_dT (), finds the suitable synaptic weight matrix w of impulsive neural networks, make The output pulse sequence S of neuron_o(t) and corresponding target pulse sequence S_dT () is as close possible to i.e. both error assessment Functional value is minimum.

Precise-spike-driven synaptic plasticity (PSD) utilize precise time pulse coded information Pulse train to image learns, and its basis is leaky integrate-and-fire models.When using this study During rule adjustment weight, postsynaptic potential (PSP) is the summation of the weight of the afferent nerve of all input pulses：

Wherein ω_iAnd t_iIt is respectively synapse weight and the duration of ignition of i ＆ lt input, V_restIt is reset voltage.K is double fingers The kernel function of number form formula：

Wherein t^fIt is i-th f-th pulse of neuron generation；V₀It is normalized parameter, it makes the value of K be not more than 1； τ_sExpression slow-decay constant, and τ_fRefer to rapid decay constant, make τ_s/τ_f=4.Postsynaptic currents be PSD rule in one it is important Parameter, it meets following formula：

WhereinIt is the synaptic currents of i ＆ lt input；H (x) is Heaviside functions, works as x<Its value is 0 when 0, works as x= Its value is 0.5 when 0, works as x>Its value is 1 when 0.Widrow-Hoff rule synapse weight Changing Pattern be：

And weight change can be typically expressed as：

PSD rules change the inspiration that synapse weight receives Widrow-Hoff rules, and its form is：

In the study stage, the step-length of impulsive neural networks is set to 100 times.

4 discriminant classifications

Image sequence by after PSD rule learnings, set of pulses output sequence can be produced, using van Rossum Metric carries out discriminant classification to result.This method depends on the distance between output sequence and target sequence：

Wherein τ is a constant, takes τ=10, and f (t) and g (t) are respectively two filter functions of pulse train.Selection is most Classification corresponding to small Dis is used as the last result classified.

Compared with prior art, the present invention has the following advantages：

The present invention is inspired by biological vision hierarchical system, in the characteristic extraction part of image, is processed using human eye and connect The form of image is received, using the cell operating mechanism of HMAX modeling receptive fields, first with the side of Gabor filtering reinforcing images Edge information, then maximum pond treatment is carried out to the image by the filtered all directions of Gabor, reach the topmost feature of extraction And the purpose of dimension-reduction treatment.This causes that the present invention has certain biological basis.In character image data processing method, select Phase coding technology, by the Pixel Information of image is converted to pulse phenomenon, so not only allows for the spatial information of image, also Consider the temporal information of image.In learning algorithm, impulsive neural networks (SNN) are selected, this is third generation neutral net, The biological nerve information transmission means of vivider simulation, has been greatly reduced the power consumption of experiment.

The present invention proposes a kind of image-recognizing method based on biological vision and precision pulse driving neutral net.Experiment Prove, the present invention have certain biological basis, with good feasibility and robustness, and its for image identification with Classification, especially the accuracy in noise image is greatly improved.

Brief description of the drawings

Fig. 1 is the system of the image-recognizing method that neutral net is driven based on biological vision and precision pulse of the present invention Structure chart；

Fig. 2 is the graph of a relation that the cell in receptive field interacts；

Fig. 3 is the schematic diagram how PSD rules change synapse weight by output pulse sequence and target pulse sequence；

Fig. 4 is that, using different learning rules, the noise image to having 10% is classified with regard to comparative result figure.

Specific embodiment

The present invention is further described below in conjunction with the accompanying drawings.

In Fig. 1, the system knot based on biological vision with the image-recognizing method of precision pulse driving neutral net is described Composition, detailed description is given with reference to Fig. 1.

Step S1, feature extraction

1.1 Gabor filtering process

When the V1 areas simple cell of receptive field carries out the matching of unit, extract special using the higher order filter of sparse coding Levy, and the computation model of sparse coding is established using two-dimensional Gabor filter function.The general type of sparse coding is：

SC=AH

Wherein sc_i, a_i, h_jIt is sparse piece of element of SC of unit, A is the basic function of sparse coding, and H is sparse.A's The most frequently used expression-form is：

||·||_fIt is Frobenius normal forms, μ is normal number.But sparse coding typically uses Independent Component Analysis Image is processed, this causes that it is to need very big memory headroom to calculate view data, is unfavorable for practical operation.And Gabor Memory headroom needed for filtering is small, and Gabor responds the form for being converted into sparse coding that G (x, y) can be approximate：

G (x, y)=S (x, y) K (x, y),

Wherein S (x, y) represents complicated sine functions, and its span is [- 1,1], therefore she meets above-mentioned base letter The form of number A.K (x, y) is the envelope function of two-dimensional discrete Gauss equation, and λ represents wavelength, and its value is no more than image length and width 1/5.It is phase offset, at [- 180 °, 180 °], γ represents length-width ratio to value, it determines that image is filtered by Gabor Shape afterwards.σ depends on bandwidth b：

For simplicity the real part part filtered using Gabor is learnt to characteristics of image：

X'=x cos θ+y sin θs, y'=-x sin θ+y cos θ

Offset phase is set respectivelyWavelength X and bandwidth b are 0 °, 10 and 1, therefore σ=0.56 λ.

In Gabor filtering, the Gabor filtering of (0 °, 45 °, 90 °, 135 °) four direction is chosen, and by its result normalizing Change to [- 1,1].

1.2 maximum pond treatment

Image enhances its marginal information after being filtered through Gabor, and extraction and the dimensionality reduction of feature are carried out using maximum pond, its Embody as follows：

Wherein m is the size of the sliding window of maximum pond operation.In former HMAX models, maximum pond operation is to warp Filtered 4 directions of Gabor take overall maximum, and consider that human eye is different to the susceptibility of all directions in the present invention And its pertinent literature, 4 pictures in direction have all been carried out with maximum pond operation.

Step S2, phase code

Selected phase encryption algorithm (a kind of time encoding scheme) produces pulse train.The intensity of each pixel in RF Value is converted into a rectilinear oscillation for the time action potential for processing meticulously, and this is described as cosine function：

WhereinIt is i-th concussion function of encoding nerve unit, in periodically；A is amplitude, and ω represents angular speed, φ₀ It is initial phase, i-th offset phase φ of encoding nerve unit_iComputing formula be：

φ_i=φ₀+(i-1)·Δφ

Wherein Δ φ is minimum offset identity, and its value is 2 π/n, and n is the number of neuron.Concussion cycle t is set_maxFor 200ms.Each pixel of image is represented with for example following formula of the relation of time：

Wherein x_iThe pixel value of representative image ith pixel.When the incoming coding layer of pixel, will cause upwardly or downwardly Film vibration, if film potential exceed threshold value, stimulate produce.The product of pulse train can be controlled by adjusting amplitude and threshold value It is raw.

Step S3, pulse study

Impulsive neural networks mainly learn to the pulse train that image is produced, and pulse train is represented by：

Wherein, t^fF-th pulse Time Of Release is represented, δ (x) represents Dirac delta functions, at that time x=0, δ (x)= 1, otherwise δ (x)=0.

PSD rules are learnt using precise time pulse coded information to the pulse train of image, and its basis is leaky Integrate-and-fire models.When weight is adjusted using this learning rules, postsynaptic potential (PSP) is all inputs The summation of the weight of the afferent nerve of pulse：

Wherein ω_iAnd t_iIt is respectively synapse weight and the duration of ignition of i ＆ lt input, V_restIt is reset voltage.K is double fingers The kernel function of number form formula：

Wherein t^fIt is i-th f-th pulse of neuron generation；V₀It is normalized parameter, it makes the value of K be not more than 1； τ_sExpression slow-decay constant, and τ_fRefer to rapid decay constant, make τ_s/τ_f=4.Postsynaptic currents be PSD rule in one it is important Parameter, it meets following formula：

WhereinIt is the synaptic currents of i ＆ lt input；H (x) is Heaviside functions, works as x<Its value is 0 when 0, works as x= Its value is 0.5 when 0, works as x>Its value is 1 when 0.Widrow-Hoff rule synapse weight Changing Pattern be：

And weight change can be typically expressed as：

PSD rules change the inspiration that synapse weight receives Widrow-Hoff rules, and its form is：

In the study stage, the step-length of impulsive neural networks is set to 100 times.

Step S4, discriminant classification

Image sequence by after PSD rule learnings, set of pulses output sequence can be produced, using van Rossum Metric carries out discriminant classification to result.This method depends on the distance between output sequence and target sequence：

Wherein τ is a constant, takes τ=10, and f (t) and g (t) are respectively two filter functions of pulse train.Selection is most Classification corresponding to small Dis is used as the last result classified.

The structure of biological vision hierarchical system is as shown in Fig. 2 the cell in receptive field can be divided into two kinds：Simple cell (simple cell) and complex cell (complex cell).Simple cell carries out sparse coding operation, and complex cell is carried out most Great Chi is operated.HMAX is an object identification model for really being able to imitative visual structure work, and it is based on being confirmed on biology Gabor wavelet base and multilayer feature combination, and using the filter response on adjacent space and yardstick take maximum and extract, make Obtain image table and reveal the features such as yardstick and translation invariant, and a vector will be converted to per pictures.

Describe how PSD rules change synapse weight by output pulse sequence and target pulse sequence in figure 3. For the multiple input pulse sequence S for giving_i(t) and multiple target pulse sequence S_dT (), finds impulsive neural networks suitable Synaptic weight matrix w, makes the output pulse sequence S of neuron_o(t) and corresponding target pulse sequence S_d(t) as close possible to, I.e. both error assessment functional values are minimum.

Fig. 4 is the displaying of experimental result, the image recognition of vision layered system combination PSD rule proposed by the present invention and point Class algorithm, with good robustness.Its concrete operations is as follows：

For a big small picture for n × n, it is expressed as：

Input direction [0 °, 45 °, 90 °, 135 °] will be distinguished after its binaryzation, window size is m_G×m_GGabor filtering In, obtain the filtering image that four width sizes are n × n：

It is m that this four width image is distinguished into incoming window size_p×m_pMaximum pond in, and the image that will be obtained once splices, Then new images are converted into a vector：

This vector is input in phase code and obtains pulse trainIt is entered into PSD algorithms, utilizes The rule of supervised learning, obtains synapse weight matrix：

Wherein c is the classification sum of classification.

When classifying to test set image, by input pulse sequenceIn coming into PSD neutral nets, with cynapse Weight matrix carries out being calculated a group output pulse sequence accordinglyRespectively by itself and expectation pulse train S_d T () calculates Dis, according to classifying rules to final result.As can be drawn from Figure 4, the present invention better than general image recognition and Sorting algorithm, there is good robustness and accuracy of identification.

Claims (1)

1. a kind of image-recognizing method for driving neutral net based on biological vision and precision pulse, it is characterised in that the method bag Include following steps：

The feature extraction of step 1. biological vision system

Step 1.1.S1 layers of Gabor filtering process

S1 layers of representative is mode that simple cell in visual cortex receptive field processes picture signal；The V1 areas of receptive field are simple When cell carries out the matching of unit, feature is extracted using the higher order filter of sparse coding；The form of sparse coding is：

${\mathrm{sc}}_i=\underset{i,j}{\&Sigma;}{a}_i{h}_j,$

SC=AH

Wherein sc_i, a_i, h_jIt is sparse piece of element of SC of unit, A is the basic function of sparse coding, and H is sparse；The expression of A Form is：

$min\left|\right|SC-AH|{|}_f^2+\mathrm{\&mu;}\underset{j=1}{\overset{k}{\&Sigma;}}|\left|s_j\right|{|}_1,$

$s.t.\left|\right|a_i|{|}^2\&le;1,\&ForAll;i=1,...,m$

||·||_fIt is Frobenius normal forms, μ is normal number；What Gabor responded that G (x, y) can be approximate is converted into sparse coding Form：

G (x, y)=S (x, y) K (x, y),

$K(x,y)=\exp (-\frac{x^2+{\mathrm{\&gamma;}}^2{y}^2}{2{\mathrm{\&sigma;}}^2})$

Wherein S (x, y) represents complicated sine functions, and its span is [- 1,1], therefore meets the shape of above-mentioned basic function A Formula；K (x, y) is the envelope function of two-dimensional discrete Gauss equation, and λ represents wavelength, 1/5 of its value no more than image length and width； It is phase offset, at [- 180 °, 180 °], γ represents length-width ratio to value, and it determines image by the filtered shapes of Gabor； σ depends on bandwidth b：

$b={\log }_2\frac{\frac{\mathrm{\&sigma;}}{\mathrm{\&lambda;}}+\sqrt{\frac{ln2}{2}}}{\frac{\mathrm{\&sigma;}}{\mathrm{\&lambda;}}-\sqrt{\frac{ln2}{2}}},\frac{\mathrm{\&sigma;}}{\mathrm{\&lambda;}}=\frac{1}{\mathrm{\&pi;}}\sqrt{\frac{ln2}{2}}\&CenterDot;\frac{2^b+1}{2^b-1}$

The real part part filtered using Gabor is learnt to characteristics of image：

X'=x cos θ+y sin θs, y'=-x sin θ+y cos θ

And offset phase is set respectivelyWavelength X and bandwidth b are 0 °, 10 and 1, therefore σ=0.56 λ；

In S1 layers, small greatly to one is the picture of n × n, 0 ° of selection, 45 °, 90 °, 135 ° of four directions, and window size is m_G× m_GGabor filtering, obtain the filtering image that four width sizes are n × n：

The max pooling treatment of C1 layers of step 1.2.

Image enhances its marginal information after S1 layers, carries out extraction and the dimensionality reduction of feature using max pooling at C1 layers, It embodies as follows：

Wherein m is the size of the sliding window of max pooling；The image that will be obtained once splices, and then changes new images It is a vector：

$I_{1\&times;\&lsqb;{\left(\frac{n}{m_p}\right)}^2\&times;4\&rsqb;}^{\&prime;}={\left[\begin{array}{ccc}{x}_{11}^{\&prime;}& \mathrm{...}& x_{\&lsqb;{\left(\frac{n}{m_p}\right)}^2\&times;4\&rsqb;}^{\&prime;}\end{array}\right]}_{1\&times;\&lsqb;{\left(\frac{n}{m_p}\right)}^2\&times;4\&rsqb;}$

Step 2. pulse code

Selected phase encodes to produce pulse train；The structure of coding unit is made up of three parts：Positive neuron, negative neuronal Unit, output neuron；In whole cataloged procedure, each incoming spiking represents a neuron activity, is connected to One receptive field region, i.e., one coding unit is connected to a pixel；Subthreshold membrane potential oscillation is also related to action potential, The intensity level of each pixel is converted into a rectilinear oscillation for the time action potential for processing meticulously in RF, is described as cosine letter Number：

$P_{OSC}^i=Acos({\mathrm{\&omega;t}}_i+{\mathrm{\&phi;}}_i)$

WhereinIt is i-th concussion function of encoding nerve unit, in periodically；A is amplitude, and ω represents angular speed, φ₀It is just Beginning phase, i-th offset phase φ of encoding nerve unit_iComputing formula be：

φ_i=φ₀+(i-1)·Δφ

Wherein Δ φ is minimum offset identity, and its value is 2 π/n, and n is the number of neuron；Concussion cycle t is set_maxFor 200ms；Each pixel of image is represented with for example following formula of the relation of time：

$t_i=\left\{\begin{array}{ccc}(i-1)\&CenterDot;\frac{t_{\max }}{n},& if& x=1\\ (i-1)\&CenterDot;\frac{t_{\max }}{n}+\frac{t_{\max }}{2},& if& x=0,andi\&le;\frac{n}{2}\\ (i-1)\&CenterDot;\frac{t_{\max }}{n}-\frac{t_{\max }}{2},& if& x=0,andi>\frac{n}{2}\end{array}\right.$

Wherein x_iThe pixel value of representative image ith pixel；When the incoming coding layer of pixel, film upwardly or downwardly will be caused Vibration, if film potential exceedes threshold value, stimulates and produces；The generation of pulse train can be controlled by adjusting amplitude and threshold value；

Step 3. impulsive neural networks learn

Impulsive neural networks mainly learn to the pulse train that image is produced, and pulse train is expressed as：

$S\left(t\right)=\underset{f=1}{\overset{F}{\&Sigma;}}\mathrm{\&delta;}(t-t^f)$

Wherein, t^fF-th pulse Time Of Release is represented, δ (x) represents Dirac delta functions, at that time x=0, δ (x)=1, otherwise δ (x)=0；

PSD rules are learnt using precise time pulse coded information to the pulse train of image, and its basis is leaky Integrate-and-fire models；When weight is adjusted using this learning rules, postsynaptic potential is all input pulses Afferent nerve weight summation：

$V\left(t\right)=\underset{i}{\&Sigma;}{w}_i\underset{t_i}{\&Sigma;}K(t-t_i)+V_{rest}$

Wherein ω_iAnd t_iIt is respectively synapse weight and the duration of ignition of i ＆ lt input, V_restIt is reset voltage；K is double index shapes The kernel function of formula：

$K(t-t^f)=V_0\&CenterDot;\left(\exp \right(\frac{-(t-t^f)}{{\mathrm{\&tau;}}_s})-\exp (\frac{-(t-t^f)}{{\mathrm{\&tau;}}_f}\left)\right)$

Wherein t^fIt is i-th f-th pulse of neuron generation；V₀It is normalized parameter, it makes the value of K be not more than 1；τ_sTable Show slow-decay constant, and τ_fRefer to rapid decay constant, make τ_s/τ_f=4；Postsynaptic currents are an important ginsengs in PSD rules Number, it meets following formula：

$I_{PSC}^i=\underset{f=1}{\overset{F}{\&Sigma;}}(t-t_i^f)H(t-t_i^f)$

WhereinIt is the synaptic currents of i ＆ lt input；H (x) is Heaviside functions, works as x<Its value is 0 when 0, as x=0 Its value is 0.5, works as x>Its value is 1 when 0；Widrow-Hoff rule synapse weight Changing Pattern be：

${\mathrm{\&Delta;w}}_i=\mathrm{\&eta;}\&lsqb;S_d\left(t\right)-S_o\left(t\right)\&rsqb;I_{PSC}^i\left(t\right)$

And weight change is represented by：

${\mathrm{\&Delta;w}}_i=\frac{{\mathrm{dw}}_i\left(t\right)}{dt}$

PSD rules change the inspiration that synapse weight receives Widrow-Hoff rules, and its form is：

${\mathrm{\&Delta;w}}_i=\mathrm{\&eta;}\&lsqb;\underset{g=1}{\overset{G}{\&Sigma;}}\underset{f=1}{\overset{F}{\&Sigma;}}K(t_d^g-t_i^f)H(t_d^g-t_i^f)-\underset{h=1}{\overset{G}{\&Sigma;}}\underset{f=1}{\overset{F}{\&Sigma;}}K(t_o^h-t_i^f)H(t_o^h-t_i^f)\&rsqb;$

In the study stage, the step-length of impulsive neural networks is set to 100 times；The above-mentioned pulse train that obtains is input to PSD rules In, using the rule of supervised learning, obtain synapse weight matrix：

Wherein c is the classification sum of classification；

Step 4. discriminant classification

Image sequence by after PSD rule learnings, set of pulses output sequence can be produced, using van Rossum metric couple Result carries out discriminant classification；It depends on the distance between output sequence and target sequence：

$Dis=\frac{1}{\mathrm{\&tau;}}{\&Integral;}_0^{\mathrm{\&infin;}}{\&lsqb;f\left(t\right)-g\left(t\right)\&rsqb;}^{2}dt$

Wherein τ is a constant, and f (t) and g (t) are respectively two filter functions of pulse train；Select minimum Dis institutes right The classification answered is used as the last result classified.