CN105528072A - Brain-computer interface speller by utilization of dynamic stop strategy - Google Patents

Abstract

The present invention discloses a brain-computer interface speller by utilization of a dynamic stop strategy. The brain-computer interface speller comprises a P300 visual stimulation device, an EEG acquisition system and a computer. The P300 visual stimulation device is used for generating flicker stimulation on target characters, which a user wants to spell, in a flicker stimulation mode. The EEG acquisition system is used for detecting EEG signals and performing amplification and filtering processing. The computer is used for receiving the processed EEG signals transmitted by the EEG acquisition system, extracting visual evoked P300 potential characteristic signals from the processed EEG signals, and determining whether to output the target characters according to the visual evoked P300 potential characteristic signals and threshold values of the dynamic stop strategy on the basis of the Bayes rule. The defect of low information transmission rate of a traditional static flicker stimulation mode is overcome, the brain-computer interface speller is more practical, key technology guarantee is expected to provide for a novel BCI-Speller, and foundation is laid for rapid wide-range application of the brain-computer interface.

Description

Brain-computer interface spelling system under a kind of dynamic stopping strategy

Technical field

The present invention relates to field of brain-computer interfaces, particularly relate to the brain-computer interface spelling system under a kind of dynamic stopping strategy.

Background technology

The definition of the BCI that first time brain-computer interface (Brain-ComputerInterface, BCI) international conference provides is: " BCI is a kind of communication control system not relying on brain nervus peripheralis and the normal output channel of muscle." in current achievement in research; it is mainly by gathering and analyze the EEG signals of different conditions servant; then use certain engineering means directly to exchange and control channel with setting up between computing machine or other electronic equipment at human brain; thus realize a kind of brand-new message exchange and control technology; and namely can not need language or limb action, directly express wish by brain electric control or handle external device.For this reason, BCI technology also more and more comes into one's own.

In the research of brain-computer interface, brain-computer interface based on P300 signal is generally considered the brain control spell mode of most stability and high efficiency, belong to brain-computer interface spelling system (BCI-Speller), it tests simple and convenient easy without the need to training tested.The electrode that signals collecting needs is less, and six to ten electrodes just can collect enough information, have very strong operability.In addition, scalp just can be recorded to stronger P300 signal, have very high signal to noise ratio (S/N ratio) and stable lock time property.Based on above-mentioned advantage, the further investigation of P300 signal and a kind of practical portable brain control spelling system of exploitation are contributed to clearly understanding human brain, realizes real man-machine interaction, there is very strong theory and using value.

Along with feature extraction, algorithm for pattern recognition increasingly mature, to the research refinement more of BCI-Speller, the rate of information throughput is one of important indicator evaluating BCI-Speller system performance, but the achievement in research of current BCI-Speller is unsatisfactory, the application that real life exchanges still can not be met.Mainly be in system, for the BCI-Speller of instruction output mode after fixed instruction collection and fixed number of times visual stimulus, system speed and accuracy can restrict mutually, thus the rate of information throughput of influential system.So what export decision mode to character instruction is designed to one of focus in order to study, the performance of vision BCI-Speller effectively can be improved by the mode changing discrimination instruction output policy.

Therefore, consider the equilibrium problem between system speed, accuracy, provide the strategy that a kind of novel dynamic stopping discrimination instruction exporting, the practical research for BCI-Speller system is significant.

Summary of the invention

The invention provides the brain-computer interface spelling system under a kind of dynamic stopping identification tactic, the present invention is at the parameter strategy utilizing adjustment based on stopping criterion dynamic under bayesian criterion, dynamically, BCI-Speller visual stimulus and instruction output is realized online, closer to actual interactive application, be expected to for novel B CI-Speller provides gordian technique guarantee, described below:

A brain-computer interface spelling system under dynamic stopping strategy, described brain-computer interface spelling system comprises: P300 visual stimulus device, eeg collection system and computing machine,

Described P300 visual stimulus device, for stimulation normal form of glimmering, wanting the target character spelt that flicker occurs to user stimulates;

Described eeg collection system, for detecting EEG signals, and carry out amplifying, filtering process;

Described computing machine, receive described eeg collection system transmission process after EEG signals, vision induced P300 current potential characteristic signal is extracted EEG signals after process, according to described vision induced P300 current potential characteristic signal and based on the threshold value dynamically stopping strategy under bayesian criterion, differentiate that whether target character exports.

In described EEG signals, the concrete extracting method of vision induced P300 current potential characteristic signal is:

$\hat{s}\left(k\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{x}_i\left(k\right)=s\left(k\right)+\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{n}_i\left(k\right)$

In formula, for the superposed average to repetitive measurement EEG signals; x _ik () represents the EEG signals be recorded to for i-th time; The vision induced P300 current potential characteristic signal of s (k) for extracting in EEG signals; n _ik () represents the noise signal be recorded to for i-th time; Variable k represents a kth sampled value in record.

Described according to described vision induced P300 current potential characteristic signal and based on the threshold value dynamically stopping strategy under bayesian criterion, differentiate that whether target character exports and be specially:

Carry out Classification and Identification by linear discriminant analysis to the vision induced P300 current potential characteristic signal extracted, identifying current stimulation is target or non-targeted character;

When character probabilities is greater than setting threshold value, then export current character instruction, enter the spelling of character late, namely achieve the dynamic stopping that character instruction exports.

Described character probabilities is specially:

$p\left(C\right|x_i,S_i,X)=\frac{p\left(C\right|X)p\left(x_i\right|C,S_i)}{\underset{i}{\Σ}p\left(C\right|X)p\left(x_i\right|C,S_i)}$

In formula, p (C|X) is that to export according to existing sorter the current character obtained be the probability estimate of target character; P (x _i| C, S _i) be that sorter exports as x _ipossibility, represent character whether in flicker S set _iin; Denominator represents the current all character probabilities sums under i-th flicker set, i.e. total probability.

The beneficial effect of technical scheme provided by the invention is: the embodiment of the present invention achieves the dynamic stopping that the instruction of visual stimulus BCI-Speller system characters exports, the parameter strategy of dynamic stopping criterion under utilizing adjustment bayesian criterion, brain control spelling process can be realized dynamically, online, overcome traditional static flicker and stimulate the defect that the rate of information throughput of normal form existence is low, closer to practical application, be expected to for novel B CI-Speller provides gordian technique guarantee, also lay the foundation for brain-computer interface steps into the widespread adoption stage as early as possible.

Accompanying drawing explanation

Fig. 1 (a) is the structured flowchart of the brain-computer interface spelling system under a kind of dynamic stopping strategy;

Fig. 1 (b) to lead distribution plan for brain wave acquisition;

Fig. 2 is that P300 flickering vision stimulates normal form;

Fig. 3 is for stimulating normal form time diagram;

Fig. 4 is based on the dynamic stopping application of policies process flow diagram under bayesian criterion;

Fig. 5 is five tested DSC strategies and transfer rate contrast effect figure under SSC strategy.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly, below embodiment of the present invention is described further in detail.

Normal person when be subject to small probability (10%-30%) target event stimulate after can produce a kind of AD HOC signal be present in brain electricity, i.e. P300 signal, because of its in EEG signals, be positioned at stimulation point after about 300ms a forward spike potential and gain the name.Tradition becomes based on dynamically stopping method of discrimination decision instruction output mode based on instruction output mode after the BCI-Speller fixed number of times visual stimulus of P300 signal by native system design, thus improves system real time and the rate of information throughput thereof.

Its techniqueflow is: online design is tested, put up the eeg signal acquisition device needed for experiment, then under experimental system instructs, acquisition operations person's EEG signals data, certain pre-service, feature extraction, Classification and Identification is carried out again after being stored, and then the dynamic stopping method of discrimination decision instruction under use bayesian criterion exports, the real-time of ultimate analysis system and the rate of information throughput.

Embodiment 1

Brain-computer interface spelling system under a kind of dynamic stopping strategy, see Fig. 1 (a), Fig. 1 (b) and Fig. 2, this brain-computer interface spelling system comprises: P300 visual stimulus device 1, eeg collection system 2 (comprising electrode for encephalograms and eeg amplifier etc.) and computing machine 3.

Brain electricity digital acquisition system (i.e. the described eeg collection system 2 of Fig. 1 (a)) that the embodiment of the present invention uses Neuroscan company to produce gathers brain electricity, gather the eeg data of six passages (Fz, Cz, Pz, Oz, P7, P8, see Fig. 1 (b)).

See Fig. 2, user is undisturbedly seated at and is about on the arm-chair of 1m apart from screen, watches the flicker (i.e. Fig. 1 (a) described P300 visual stimulus device 1) of the stimulation normal form on computer screen attentively.Respective user wants the target character spelt that flicker occurs in the process stimulates, its brain electricity also can produce corresponding change: EEG signals produces at cerebral cortex, through eeg amplifier amplification, filtering after inputs Fig. 1 (a) described computing machine 3 after being detected by electrode for encephalograms.The eeg data collected extracts corresponding vision induced P300 current potential characteristic signal through the data processing that this computing machine 3 is follow-up again, these vision induced P300 current potential characteristic signals are applied to the pattern-recognition of experimental duties, and then whether application exports based on dynamically stopping the threshold value discrimination instruction of strategy under bayesian criterion.

In sum, brain-computer interface spelling system under a kind of dynamic stopping strategy that the embodiment of the present invention provides, the dynamic stopping of visual stimulus BCI-Speller system characters instruction output is achieved by above-mentioned P300 visual stimulus device 1, eeg collection system 2 and computing machine 3, the parameter strategy of dynamic stopping criterion under utilizing adjustment bayesian criterion, can realize brain control spelling process dynamically, online.

Embodiment 2

Below in conjunction with concrete mathematical formulae, Fig. 3, Fig. 4, example, the scheme in embodiment 1 is described in detail, refers to hereafter:

1, the design of stimulating module

The P300 of the brain-computer interface spelling system of embodiment of the present invention design brings out normal form and has write on Matlab platform, stimulates normal form as shown in Figure 2.First be off-line model training process, first screen points out user to need the target character watched attentively, then 6 row 6 arrange the random flicker without repeating, travel through one time and be called the flicker taking turns (round), 1 takes turns flicker is called 1 experiment examination time (trail), namely 10 trail complete the scitillation process of a character, are called an experimental group (session).

Each duration of a scintillation is 75ms, and blinking intervals is 100ms, stimulates normal form sequential as shown in Figure 3.The on-line testing stage is entered after off-line modeling completes, sequential and flicker stimulation present consistent with off-line procedure, but flicker stimulation wheel number is unfixed, by determining the rear output character spelling result of how many wheel flickers with dynamically stopping identification tactic real-time online, namely reach the effect of real-time characters spells.

During specific implementation, the concrete value of the embodiment of the present invention to above-mentioned parameter does not limit, and sets according to the needs in practical application.

2, the extraction of vision induced P300 current potential characteristic signal and classification

1) vision induced P300 current potential characteristic signal is extracted by coherence average algorithm;

Coherent averaging technique is utilized to extract vision induced P300 current potential characteristic signal, if the EEG signals be recorded to is expressed as:

x _i(k)＝s(k)+n _i(k)(1)

In formula, x _ik () represents the EEG signals be recorded to for i-th time; The EEG signals that s (k) is objective reality, the vision induced P300 current potential characteristic signal that namely will extract; n _ik () represents the noise signal i=1 be recorded to for i-th time, 2 ..., N; Variable k represents a kth sampled value k=1 in record, 2 ... M.

$\hat{s}\left(k\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{x}_i\left(k\right)=s\left(k\right)+\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{n}_i\left(k\right)---\left(2\right)$

In formula, obtain according to initial hypothesis $\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{n}_i\left(k\right)=0,$ Namely $\hat{s}\left(k\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{x}_i\left(k\right)=s\left(k\right).$ So the signal after superposed average be in final EEG signals vision induced P300 current potential characteristic signal s (k) that will extract.

2) by LDA algorithm, Classification and Identification is carried out to the vision induced P300 current potential characteristic signal extracted.

Linear discriminant analysis (Lineardiscriminantanalysis, LDA) is through being usually used in the Classification and Identification of EEG signals.The general type of LDA algorithm basic function is:

g(x)＝ω ₁x ₁+ω ₂x ₂+...+ω _nx _n+ω ₀(3)

g(x)＝W ₀ ^TX+ω ₀(4)

In formula, n dimensional feature vector X=[x ₁, x ₂..., x _n] ^t, wherein x _iit is the i-th dimensional feature; ω ₀for constant, be called threshold weights; W ₀=[ω ₁, ω ₂..., ω _n] ^tfor weight vector or parametric variable, wherein ω _ibe weight coefficient corresponding to weight coefficient that the i-th dimensional feature is corresponding or the i-th class, have a weight coefficient corresponding with it for every one-dimensional characteristic.For linear two classification problems, the discriminant function of sorter is shown below:

g(x)＝g ₁(x)-g ₂(x)(5)

In formula, g ₁x () is the value of first kind discriminant function; g ₂x () is the value of Equations of The Second Kind discriminant function; G (x) is the decision value of two discriminant classification functions.Decision rule is g (x) > 0, then x ∈ ω ₁, first kind weight coefficient is dominant, and is divided into the first kind; G (x) < 0, then x ∈ ω ₂, Equations of The Second Kind weight coefficient is dominant, and is divided into Equations of The Second Kind; G (x)=0, then x ∈ ω ₁or x ∈ ω ₂, two class weights are identical.

Therefore, the core concept of LDA is exactly seek the optimum discriminant function composition and classification device corresponding to weight coefficient, reaches two classification spacing and maximizes.EEG signals in the embodiment of the present invention is divided into two classes: after goal stimulus, EEG signals (vision induced P300 current potential characteristic signal s (k)) and non-targeted stimulate rear EEG signals, according to LDA categorised decision rule, going out current stimulation by above-mentioned sorter identifiable design is target or non-targeted, and then orients the target character that user wants spelling.

3, the dynamic stopping strategy under bayesian criterion

The core of the embodiment of the present invention is exactly propose a kind of dynamic stopping strategy based on bayesian criterion, realizes the self-adaptation of BCI-Speller visual stimulus instruction, and the result can carrying out BCI online exports.Fig. 4 is dynamic stopping criterion (DynamicStoppingCriterion, the DSC) algorithm flow chart that the embodiment of the present invention adopts.Under being illustrated as BCI-Speller system background, and be described expression based on LDA classification results.

In off-line process, as a line process description above in Fig. 4, sorter can return in experiment the Output rusults often organizing target (Target) and non-targeted (Non-target) character, Kernel density Estimation algorithm (a kind of method of estimation to Gaussian distributed data analysis) is called by these result application one, can to the probability density function (probabilitydensityfunction of sorter Output rusults possibility, pdf) estimate, so just have the probability density that two important, i.e. target character probability density p (x _i| H ₁) and non-targeted character probabilities density p (x _i| H ₀), wherein x _ipresentation class device for the output of once glimmering, i.e. the decision value of LDA bis-discriminant classification function, H ₁(H ₀) whether what represent appearance is target character.

The parameter that off-line obtains is used in the real-time control of online data process, and algorithm flow is as shown in a line below Fig. 4.Here crucial is exactly show whether blinking character is for target character and the need of the decision proceeding to stimulate, what this decision was paid close attention to is the posterior probability (posteriorprobability) obtained by the consequent parameter of off line data analysis and online data sorter Output rusults, and here is principle explanation.

Character is the probability updating of target character is provide based on bayesian criterion (Bayesrule) below:

$p\left(C\right|X)=\frac{p\left(X\right|C)p\left(C\right)}{p\left(X\right)}---\left(6\right)$

In formula, p (C|X) is that after the result of current all sorters exports, character becomes the probabilistic estimated value of target character, and X is the same; P (C) is the prior probability of character; P (X|C) is the possibility (namely off line data analysis Kernel estimates the result that obtains above) that sorter exports; P (X) is the probability that sorter exports.According to total probability formula, conversion denominator p (X) obtains formula below:

$p\left(C\right|X)=\frac{p\left(X\right|C)p\left(C\right)}{\underset{C}{\&Sigma;}p\left(X\right|C)p\left(C\right)}---\left(7\right)$

In formula, provide a kind of after off-line data collecting completes calculating character be the method for the posterior probability of target character, owing to being two classification problems herein, denominator summation scope C=H ₁or H ₀.But for on-line Algorithm, posterior probability needs once to upgrade afterwards often glimmering.If consider that sorter exports as X=[x ₁, x ₂..., x _n..., x _n], and suppose that sorter is separate between exporting, the character probabilities under this condition has at n output time:

p(C|x ₁,...,x _n)∝p(x ₁,...,x _n|C)p(C)

＝p(x _n|C)p(x ₁,...,x _n-1|C)p(C)(8)

＝p(x _n|C)p(C|x ₁,...,x _n-1)

In formula, p (C|x ₁..., x _n) for n flicker stimulate after the posterior probability of character; P (x ₁..., x _n| C) for n flicker stimulate before the prior probability of character; P (x _n| C) be that n-th flicker stimulates the sorter of current character to export possibility, obtained by above-mentioned probability density curve; P (x ₁..., x _n-1| C) for n-1 flicker stimulate before the prior probability of character; P (C|x ₁..., x _n-1) for n-1 flicker stimulate after the posterior probability of character; ∝ is for being proportional to symbol.

Therefore, in the moment after n-th flicker stimulates, current character is the posterior probability of target character, and the ratio that can be the posterior probability of target character by the output possibility in sorter n moment and the character in n-1 moment obtains.If flicker is stimulated and (is set to S by the process of aggregation of some _i), then character probabilities just can be drawn by formula below:

$p\left(C\right|x_i,S_i,X)=\frac{p\left(C\right|X)p\left(x_i\right|C,S_i)}{\underset{i}{\&Sigma;}p\left(C\right|X)p\left(x_i\right|C,S_i)}---\left(9\right)$

In formula, p (C|X) is that to export according to existing sorter the current character obtained be the probability estimate of target character; P (x _i| C, S _i) be that sorter exports as x _ipossibility, represent character whether in flicker S set _iin; Denominator represents the current all character probabilities sums under i-th flicker set, i.e. total probability, and summation here will stimulate two classifications and each flicker all sues for peace.Visible, export possibility p (x for the sorter upgrading character probabilities _i| C, S _i) depend on this character and whether glimmered, whether target character glimmers on the impact of character probabilities in table 1.

$p\left(x_i\right|C,S_i)=\left\{\begin{array}{cc}p\left(x_i\right|H_1)& C\&Element;S_i\\ p\left(x_i\right|H_0)& C\&NotElement;S_i\end{array}\right.---\left(10\right)$

In formula, give flicker S set _iin whether comprise two kinds of situations of target character.If S _iin comprise target character, sorter ideal export be large value.A large sorter decision value exports and will cause p (x _i| H ₁) high possibility and p (x _i| H ₀) low possibility.In the process then upgraded, p (x _i| H ₁) take large values and cause target character probability to increase progressively, and p (x _i| H ₀) get the small value and cause non-targeted character probabilities to successively decrease, target character probability exceed setting threshold value time and exportable.

The impact whether table 1 target character glimmers

After certain flicker stimulates set to complete, character probabilities all can decide current character instruction and whether can be used as target character and export compared with setting threshold value, and wherein whether threshold value represents correct characters selected confidence level out.

The selection of general threshold value compares according to many experiments the ratio preferably empirical value drawn, the size of threshold value directly have influence on accuracy and operation time this conflict.Then export current character instruction when character probabilities is greater than setting threshold value, enter the spelling of character late, namely achieve the dynamic stopping that character instruction exports.

From eeg signal acquisition, extract, Classification and Identification, dynamically stop application of policies until the whole data handling procedure of instruction output is as shown in Fig. 1 (a) Computer 3 content.

In sum, brain-computer interface spelling system under a kind of dynamic stopping strategy that the embodiment of the present invention provides, the dynamic stopping of visual stimulus BCI-Speller system characters instruction output is achieved by above-mentioned P300 visual stimulus device 1, eeg collection system 2 and computing machine 3, the parameter strategy of dynamic stopping criterion under utilizing adjustment bayesian criterion, can realize brain control spelling process dynamically, online.

Embodiment 3

Below in conjunction with Fig. 5, feasibility checking is carried out to the scheme in embodiment 1 and 2, described below:

For the feasibility dynamically stopping strategy introducing in the brain-computer interface spelling system under a kind of dynamic stopping strategy that the checking embodiment of the present invention provides, carry out control experiment test: experimental group is 5 tested rate of information transmission introducing spelling 20 characters under the BCI-Speller condition dynamically stopping strategy, control group is identical tested at traditional static standard (StandardStateCriterion, the rate of information transmission of spelling 20 characters under the BCI-Speller condition of SSC) strategy (i.e. flicker stimulate number of times fix), result as shown in Figure 5.

Can obviously find out, the DSC strategy that the embodiment of the present invention proposes in BCI-Speller system is compared with SSC strategy, the former is significantly improved by rate of information transmission, demonstrates further based on dynamically stopping strategy introducing the validity improved BCI-Speller system performance under bayesian criterion.

In sum, the embodiment of the present invention devises a kind of BCI-Speller system based on dynamically stopping identification tactic under bayesian criterion.This system may be used for the fields such as disabled person is auxiliary, electronic entertainment, Industry Control, aerospace engineering, studies the brain-computer interface system that can improve further, is expected to obtain considerable Social benefit and economic benefit.

The embodiment of the present invention is to the model of each device except doing specified otherwise, and the model of other devices does not limit, as long as can complete the device of above-mentioned functions.

It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number, just to describing, does not represent the quality of embodiment.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (4)

1. dynamically stop the brain-computer interface spelling system under strategy, described brain-computer interface spelling system comprises: P300 visual stimulus device, eeg collection system and computing machine, is characterized in that,

Described P300 visual stimulus device, for stimulation normal form of glimmering, wanting the target character spelt that flicker occurs to user stimulates;

Described eeg collection system, for detecting EEG signals, and carry out amplifying, filtering process;

Described computing machine, receive described eeg collection system transmission process after EEG signals, vision induced P300 current potential characteristic signal is extracted EEG signals after process, according to described vision induced P300 current potential characteristic signal and based on the threshold value dynamically stopping strategy under bayesian criterion, differentiate that whether target character exports.

2. the brain-computer interface spelling system under a kind of dynamic stopping strategy according to claim 1, it is characterized in that, in described EEG signals, the extracting method of vision induced P300 current potential characteristic signal is specially:

$\hat{s}\left(k\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\&Sigma;}}{x}_i\left(k\right)=s\left(k\right)+\frac{1}{N}\underset{i=1}{\overset{N}{\&Sigma;}}{n}_i\left(k\right)$

In formula, for the superposed average to repetitive measurement EEG signals; x _ik () represents the EEG signals be recorded to for i-th time; The vision induced P300 current potential characteristic signal of s (k) for extracting in EEG signals; n _ik () represents the noise signal be recorded to for i-th time; Variable k represents a kth sampled value in record.

3. the brain-computer interface spelling system under a kind of dynamic stopping strategy according to claim 1, it is characterized in that, described according to described vision induced P300 current potential characteristic signal and based on the threshold value dynamically stopping strategy under bayesian criterion, differentiate that whether target character exports and be specially:

Carry out Classification and Identification by linear discriminant analysis to the vision induced P300 current potential characteristic signal extracted, identifying current stimulation is target or non-targeted character;

When character probabilities is greater than setting threshold value, then export current character instruction, enter the spelling of character late, namely achieve the dynamic stopping that character instruction exports.

4. the brain-computer interface spelling system under a kind of dynamic stopping strategy according to claim 3, it is characterized in that, described character probabilities is specially:

$p\left(C\right|x_i,S_i,X)=\frac{p\left(C\right|X)p\left(x_i\right|C,S_i)}{\underset{i}{\&Sigma;}p\left(C\right|X)p\left(x_i\right|C,S_i)}$

In formula, p (C|X) is that to export according to existing sorter the current character obtained be the probability estimate of target character; P (x _i| C, S _i) be that sorter exports as x _ipossibility, represent character whether in flicker S set _iin; Denominator represents the current all character probabilities sums under i-th flicker set, i.e. total probability.