CN107423682A - A kind of analysis of complexity method of non-linear EEG signals - Google Patents
A kind of analysis of complexity method of non-linear EEG signals Download PDFInfo
- Publication number
- CN107423682A CN107423682A CN201710432360.2A CN201710432360A CN107423682A CN 107423682 A CN107423682 A CN 107423682A CN 201710432360 A CN201710432360 A CN 201710432360A CN 107423682 A CN107423682 A CN 107423682A
- Authority
- CN
- China
- Prior art keywords
- mrow
- msubsup
- mfrac
- sequence
- msub
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/08—Feature extraction
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
Abstract
The invention discloses a kind of analysis of complexity method of non-linear EEG signals.Arrangement entropy is largely used in non linear complexity analysis with Sample Entropy algorithm, but it has the shortcomings that certain.Although Sample Entropy has certain advantage with good robustness and in the degree of accuracy, its computational efficiency lacks not fully up to expectations；Although and arrange entropy and calculate not as Sample Entropy is accurate but it has the quick characteristic of calculating.For problem above, invent a kind of method that EEG signals are carried out with non linear complexity analysis, first EEG signals are filtered with processing, extract effective frequency range, it is ranked up afterwards and carries out etc. dividing symbolism assignment according to two rules, finally carries out m dimensions respectively and m+1 dimension phase space constructions carry out the calculating of entropy.The present invention improves the degree of accuracy to the arrangement entropy of nonlinear method before, and computational efficiency is improved to Sample Entropy method.
Description
Technical field
The present invention relates to Analysis of nonlinear signals field, more particularly to one-dimensional sequential EEG signals analysis of complexity skill
Art.
Background technology
EEG signals record and the electric wave change of description brain activity are brain nervous cell electrical activities in cerebral cortex
Or the overall reflection of scalp surface.Traditional brain electricity analytical method mainly extracts EEG signals time domain and the feature of frequency domain.It is near
Year research shows that brain is a Kind of Nonlinear Dynamical System, and corresponding brain electricity analytical also turns to non-from traditional Time-frequency method
Linear method, therefore relevant nonlinear kinetics is joined with complexity for such as correlation dimension, lyapunov index, Wavelet Entropy
Number is used for the research of EEG signals.Because brain electricity reflects the electrical brain activity with nonlinear system feature, therefore can
Produce chaotic characteristic.In most of physics and biosystem, the motion of most systems has chaotic characteristic, completely really
Fixed system there's almost no in nature, and compared with traditional linear system describes method, nonlinear system is more suitable for retouching
State the physics and Biology seed coating in nature.
In the nonlinear characteristic method of brain electricity, arrangement entropy is largely employed with Sample Entropy, but arranges entropy and sample
The shortcomings that certain be present in entropy.Although Sample Entropy has certain advantage with good robustness and in the degree of accuracy, its
Computational efficiency lacks not fully up to expectations, and the similar component number due to after phase space reconfiguration, reconstructing component is by by other institutes
It is important to be compared one by one with certain threshold value and drawn, therefore calculating time complexity will be very big, when data volume mistake
Showed when big particularly evident.And entropy is arranged because after phase space reconfiguration, permutation calculation has been carried out to reconstruct component,
Different value in component is classified as several specific pattern of rows and columns, although calculating not as accurate its of Sample Entropy has calculating fast
The characteristic of speed.
On the other hand, Sample Entropy reconstruct component with the tolerance limit of standard deviation Linear proportional using compared with taking threshold value r, r
Value is too small, and Sample Entropy is easily influenceed by exceptional value interference, and r values are too big, as a result can lose sensitiveness.
The content of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the invention provides a kind of complexity of non-linear EEG signals point
Analysis method.Symbolism is carried out to signal using arrangement entropy method before phase space reconfiguration, calculating reconstruct component uses sample when equal
The computational methods of this entropy, take into account the efficiency and accuracy of calculating.
This method need to meet following two conditions to determine the cut off value of symbolism, it is assumed that symbolism postorder is classified as S (j).
1) number occurred in the symbol sebolic addressing S (i) of distinct symbols s (j) after reconstitution is as equal as possible.2) former sequence
Identical symbol is necessarily corresponded in the symbol sebolic addressing of the data of medium value after reconstitution.
Present invention employs following technical scheme and realize step：
Time series is carried out first etc. dividing symbolism to handle, then carry out the reconstruct of phase space and carry out the meter of entropy
Calculate, calculated from traditional Sample Entropy unlike, phase space vector similar Rule of judgment is changed to be replaced with the equal of symbolic vector
Generation.
1) brain electricity time series X={ x (i) }, i=1,2,3 ..., n are set.N takes positive integer by sequence x (1), x (2) ...,
X (N) is arranged from small to large ord：
x(k1)≤x(k2)≤x(k3)≤…≤x(kn)
Wherein x (k1) it is minimum value, x (kn) it is maximum, k1, k1, for the sequence number 2 after sequence) sequence number after sequence is entered
Row L deciles, use n1, n2, n3... represent cut-point pair
The sequence number answered.
That is n1=0, nL=n
Then njTo meet the cut-point of condition 1, sequence may be unsatisfactory for second condition after segmentation, i.e., near division points
There is identical value, might not be equal after symbolism, following processing need to be done.If the data equal with x (k) have, m is individual, i.e., identical
First time series sequence number corresponding with last of data is respectively j1And jm。
Cut-point sequence number carries out symbolism processing after all determining：
S(ki)=s (j) j=1,2 ..., L；I=1,2 ..., n；nj-1+1≤i≤nj
Symbolism sequence is obtained, as m ≠ 1 and j1≠ j or j1During ≠ j symbol may might not strict decile, in n ＞
During ＞ L, it can accomplish that the number that kinds of characters occurs in the symbol sebolic addressing of reconstruct is equal or of substantially equal.
3) symbol sebolic addressing S={ s (i) }, i=1,2,3 ..., n after converting.By sequence s (1), s (2) ..., s (N) is pressed
Order composition m n dimensional vector ns, i.e.,
Sm(i)=[s (i), s (i+1) ... s (i+m-1)],
1≤i≤N-m+1
For each 1≤i≤N-m, count and Sm(i) equal numberAnd with vector sum N-m-1 ratio,
It is denoted as
In formula：1≤j≤N-m, i ≠ j.Seek its average value all to i
4) for m+1 point vectors, equally have
In formula：1≤j≤N-m, i ≠ j.Seek its average value all to i
5) entropy of this sequence is
But N can not possibly be ∞ in actually calculating, and when N takes finite value, be approximately equal to
SampEn (m, r, N)=- ln [Am(r)/Bm(r)]
Compared with prior art, the beneficial effects of the invention are as follows：
1：Computational efficiency is improved compared to Sample Entropy, accuracy rate is improved compared to arrangement entropy.
2：Result is not influenceed by non-stationary signal mutation disturbance, thus handle asking for extreme exceptional value well
Topic.
3：A kind of change resolution of codomain is realized, i.e., less symbol is used in sparse region to reduce redundancy,
Improve the utilization rate of information.More symbols are used to improve information resolution in the less region of codomain scope,
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 be Logistic mapping coefficients from 3.5 with step-length 0.001 to 4.0 when, the total sequence of systematic steady state；
Fig. 3 is Liapunov exponent correspondence system result；
Fig. 4 is that Sample Entropy algorithm maps the sequential value required by each coefficient in Logistic；
Fig. 5 is that arrangement plan method maps the sequential value required by each coefficient in Logistic；
When Fig. 6 is different partitioning parameters, Logistic mapping coefficients are the entropy curve of 3.6,3.8,4.0 three signals.
Embodiment
This experiment maps simulated timing diagrams signal, Logistic i.e. using matlab2016 as emulation tool, with Logistic
Mapping is to study dynamical system, chaos, a classical model of the complication system behavior such as point shape, is the dynamic of time discrete
Force system, i.e., iterated according to equation below：
X (t+1)=μ x (t) (1-x (t))
Wherein, t walks for iteration time, and for arbitrary t, x (t) ∈ [0,1], μ are an adjustable parameter, in order to ensure to reflect
The x (t) for penetrating to obtain is always positioned in [0,1], μ ∈ [0,4].When different parameter μs are changed, the equation can be shown
Different kinetic limitations behaviors.When 0<μ<When 3, final x (t) is point of safes, as 3≤μ<When 3.58, x (t) is eventually 2
Jumped between individual or multiple numerical value, this stage is the phase of the cycles, as 3.5≤μ<When 4, the track of iteration operation will be in week
Toggled between phase type and chaos type.Until μ=4, system is in the state of Complete Chaos.The sequence length is taken to be
2000, μ from 3.5 to 4 by 0.001 step-length respectively obtain 501 x (t) it is final in the form of it is as shown in Figure 1：
With sample rate 1000Hz, the signal of 7000 signaling points is simulated, 5000 are used as stabilization signal after taking.First to upper
The every time series signal stated carries out etc. dividing symbolism to handle, and then carries out the reconstruct of phase space and carries out the calculating of entropy,
Unlike being calculated from traditional Sample Entropy, phase space vector similar Rule of judgment is changed to be substituted with the equal of symbolic vector.
Its specific algorithm is as follows:
1) for time series X={ x (i) }, i=1,2,3 ..., n.By sequence x (1), x (2) ..., x (N) are pressed from small
Arranged to big order：
x(k1)≤x(k2)≤x(k3)≤…≤x(kn)
Wherein x (k1) it is minimum value, x (kn) it is maximum, k1, k1, for the sequence number after sequence.Sequence number after sequence is entered
Row L deciles, use n1, n2, n3... represent sequence number corresponding to cut-point.
That is n1=0, nL=n
Then njTo meet the cut-point of condition 1, sequence may be unsatisfactory for above-mentioned second condition, i.e. division points after segmentation
Nearby there is identical value, might not be equal after symbolism, following processing need to be done.If the data equal with x (k) have m, i.e.,
First time series sequence number corresponding with last of identical data is respectively j1And jm。
Cut-point sequence number carries out symbolism processing after all determining：
S(ki)=s (j) j=1,2 ..., L；I=1,2 ..., n；nj-1+1≤i≤nj
2) symbol sebolic addressing S={ s (i) }, i=1,2,3 ..., n after converting.By sequence s (1), s (2) ..., s (N) is pressed
Order composition m n dimensional vector ns, i.e.,
Sm(i)=[s (i), s (i+1) ... s (i+m-1)],
1≤i≤N-m+1
For each 1≤i≤N-m, count and Sm(i) equal numberAnd with vector sum N-m-1 ratio,
It is denoted as
In formula：1≤j≤N-m, i ≠ j.Seek its average value all to i
For m+1 point vectors, equally have
In formula：1≤j≤N-m, i ≠ j.Seek its average value all to i
3) entropy of this sequence is
But N can not possibly be ∞ in actually calculating, and when N takes finite value, be approximately equal to
SampEn (m, r, N)=- ln [Am(r)/Bm(r)]
In order to the reliability for dividing symbolism entropy algorithm such as study, using Liapunov exponent as reference.Li Yapunuo
Husband's index is the index of a very effective measurement system discrete type.If the index of a system is greater than zero, then
Whole system is exactly what index dissipated, is the system of a chaos, if less than zero, then system does not possess the feature of chaos.For
Reference is done, while adds Sample Entropy, arranges entropy, 3 algorithms is obtained and maps different μ corresponding result sequences for Logistic
Row, such as Fig. 2, shown in 3,4,5,6：
It may be seen that the Liapunov exponent general trend of Logistic mappings is increased as the change of μ values is big
Add, also verify the increase with μ, the final state of system is to enter chaos type by period type.Decile symbol entropy algorithm simultaneously
The feature of Logistic mappings can be captured, tendency is close with Liapunov exponent.In order to quantify to judge effect, use
Pearson correlation coefficients are as index.Pearson correlation coefficients are a kind of linearly dependent coefficients, for reacting two variables
The statistic of degree of correlation, it can be used for calculating two vectorial similarities in other words.Sample Entropy is obtained respectively, arranges entropy, etc.
Divide symbolism Entropy sequence and the coefficient correlation of Liapunov exponent sequence as shown in table 1：
1 three algorithms of table and Liapunov exponent coefficient correlation
The coefficient correlation for arranging entropy is minimum, also illustrate that the arrangement entropy mentioned before is defeated by the degree of accuracy of algorithm
Sample Entropy, based on the coefficient correlation highest of decile symbolism entropy, closest to the tendency of Liapunov exponent.Reach
0.932。
Divide symbolism entropy parameter L influence to eliminate etc. simultaneously, L is taken 3,5 ..., 20, Logistic mapping coefficients
3.6,3.8,4.0 are taken to calculate its entropy respectively, as shown in Figure 6
It can be seen that first increase the trend that tends towards stability afterwards in the entropy with L increase, three sequences, it is special when μ is 4.0
It is unobvious, this show with L increase make that the complexity of each subsignal shows in entropy more and more substantially, i.e., with
The expressive force of L increase entropy is strengthening.Their maximum difference of the two sequences of μ=4.0 and μ=3.8 is 0.45, minimum
Difference is 0.28.μ=3.8 are 0.19 with their maximum difference of μ=3.6, minimal difference 0.102.
Such result and three sequence chaos degree are consistent, and this shows L in any value between 3 to 21,
The difference that Logistic maps the complexity of this 3 signals can correctly be characterized.
One of decile symbolism entropy algorithm starting point is to reduce the computation complexity of Sample Entropy, above-mentioned 501 of statistics
Sequence
It is as shown in the table for overall time and average time used in the calculating of row
2 three Algorithms T-cbmplexities of table
As seen from the above table, Sample Entropy computational efficiency is minimum, is because algorithm will be used when phase space counts similar vectors
Circulating twice, arrangement entropy and the low Sample Entropy one-level of decile symbolism entropy time complexity, arrangement entropic efficiency improve 8 times, etc.
Point symbolism entropy algorithm average time puts down substantially in arrangement entropy, the problem of having reached optimization sample entropic efficiency.
It can be obtained by above-mentioned Logistic mapping simulations, decile symbolism entropy solves arrangement entropy accuracy in computation
It is low, the shortcomings that Sample Entropy computational efficiency is not high.The complexity of signal can stably be characterized by also demonstrating the method simultaneously, be had
Effective information of the effect difference containing different chaos degree, also illustrate that the reasonability that emotion EEG signals are analyzed with it.
Claims (2)
1. a kind of analysis of complexity method of non-linear EEG signals, this method need to meet following two conditions to determine symbolism
Cut off value, it is assumed that symbolism postorder is classified as S (j)；
1) number occurred in the symbol sebolic addressing S (i) of distinct symbols s (j) after reconstitution is as equal as possible；
2) identical symbol is necessarily corresponded in the symbol sebolic addressing of the data of former sequence medium value after reconstitution；
It is characterized in that：This method realizes that step is as follows,
Time series is carried out first etc. dividing symbolism to handle, then carry out the reconstruct of phase space and carry out the calculating of entropy, with
Unlike traditional Sample Entropy calculates, the similar Rule of judgment of phase space vector is changed to be substituted with the equal of symbolic vector；
1) brain electricity time series X={ x (i) }, i=1,2,3 ..., n are set；N takes positive integer by sequence x (1), x (2) ..., x (N)
Arranged from small to large ord：
x(k1)≤x(k2)≤x(k3)≤…≤x(kn)
Wherein x (k1) it is minimum value, x (kn) it is maximum, k1, k1, for the sequence number 2 after sequence) and L etc. is carried out to the sequence number after sequence
Point, use n1, n2, n3... represent sequence number corresponding to cut-point；
That is n1=0, nL=n
Then njTo meet the cut-point of condition 1, sequence may be unsatisfactory for second condition after segmentation, i.e. division points nearby have identical
Value, might not be equal after symbolism, following processing need to be done；If the data equal with x (k) have a m, i.e. the of identical data
One time series sequence number corresponding with last is respectively j1And jm；
<mrow>
<msub>
<mi>n</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>n</mi>
<msub>
<mi>j</mi>
<mn>1</mn>
</msub>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>j</mi>
<mo>&le;</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>n</mi>
<msub>
<mi>j</mi>
<mn>2</mn>
</msub>
</msub>
</mtd>
<mtd>
<mrow>
<mi>j</mi>
<mo>></mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Cut-point sequence number carries out symbolism processing after all determining：
S(ki)=s (j) j=1,2 ..., L；I=1,2 ..., n；nj-1+1≤i≤nj
Symbolism sequence is obtained, as m ≠ 1 and j1≠ j or j1During ≠ j symbol may might not strict decile, in n ＞ ＞ L
When, it can accomplish that the number that kinds of characters occurs in the symbol sebolic addressing of reconstruct is equal or of substantially equal；
3) symbol sebolic addressing S={ s (i) }, i=1,2,3 ..., n after converting；By sequence s (1), s (2) ..., s (N) group in order
Into m n dimensional vector ns, i.e.,
Sm(i)=[s (i), s (i+1) ... s (i+m-1)],
1≤i≤N-m+1
For each 1≤i≤N-m, count and Sm(i) equal numberAnd with vector sum N-m-1 ratio, be denoted as
<mrow>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>:</mo>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>n</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
In formula；
<mrow>
<msup>
<mi>B</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</munderover>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
</mrow>
4) for m+1 point vectors, equally have
<mrow>
<msubsup>
<mi>A</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>n</mi>
<mi>i</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
In formula；
<mrow>
<msup>
<mi>A</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</munderover>
<msubsup>
<mi>A</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
</mrow>
5) entropy of this sequence is
<mrow>
<mi>S</mi>
<mi>a</mi>
<mi>m</mi>
<mi>p</mi>
<mi>E</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>,</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munder>
<mi>lim</mi>
<mrow>
<mi>N</mi>
<mo>&RightArrow;</mo>
<mi>&infin;</mi>
</mrow>
</munder>
<mo>{</mo>
<mo>-</mo>
<mi>ln</mi>
<mo>&lsqb;</mo>
<msup>
<mi>A</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>/</mo>
<msup>
<mi>B</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>}</mo>
</mrow>
But N can not possibly be ∞ in actually calculating, and when N takes finite value, be approximately equal to
SampEn (m, r, N)=- ln [Am(r)/Bm(r)]。
2. a kind of analysis of complexity method of non-linear EEG signals according to claim 1, i.e., made with matlab2016
For emulation tool, simulated timing diagrams signal is mapped with Logistic, Logistic mappings are the dynamical systems of a time discrete, i.e.,
Iterated according to equation below：
X (t+1)=μ x (t) (1-x (t))
Wherein, t walks for iteration time, and for arbitrary t, x (t) ∈ [0,1], μ are an adjustable parameter, in order to ensure that mapping obtains
X (t) be always positioned in [0,1], μ ∈ [0,4]；When different parameter μs are changed, the equation can show different move
Mechanics limiting behavior；When 0<μ<When 3, final x (t) is point of safes, as 3≤μ<When 3.58, x (t) is eventually at 2 or multiple
Jumped between numerical value, this stage is the phase of the cycles, as 3.5≤μ<When 4, the track of iteration operation will be in period type and chaos
Toggled between type；Until μ=4, system is in the state of Complete Chaos；Take sequence length for 2000, μ from 3.5 to 4 with
0.001 step-length respectively obtains 501 x (t) final form；
With sample rate 1000Hz, the signal of 7000 signaling points is simulated, 5000 are used as stabilization signal after taking；First to above-mentioned every
Bar time series signal carries out etc. dividing symbolism to handle, and then carries out the reconstruct of phase space and carries out the calculating of entropy, with tradition
Unlike Sample Entropy calculates, phase space vector similar Rule of judgment is changed to be substituted with the equal of symbolic vector；
Its specific algorithm is as follows:
1) for time series X={ x (i) }, i=1,2,3 ..., n；By sequence x (1), x (2) ..., x (N) are by suitable from small to large
Sequence is arranged：
x(k1)≤x(k2)≤x(k3)≤…≤x(kn)
Wherein x (k1) it is minimum value, x (kn) it is maximum, k1, k1, for the sequence number after sequence；L etc. is carried out to the sequence number after sequence
Point, use n1, n2, n3... represent sequence number corresponding to cut-point；
That is n1=0, nL=n
Then njTo meet the cut-point of condition 1, sequence may be unsatisfactory for above-mentioned second condition after segmentation, i.e. division points nearby have
Identical value, might not be equal after symbolism, need to do following processing；If the data equal with x (k) have m, i.e. identical data
First time series sequence number corresponding with last be respectively j1And jm；
<mrow>
<msub>
<mi>n</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>n</mi>
<msub>
<mi>j</mi>
<mn>1</mn>
</msub>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>j</mi>
<mo>&le;</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>n</mi>
<msub>
<mi>j</mi>
<mn>2</mn>
</msub>
</msub>
</mtd>
<mtd>
<mrow>
<mi>j</mi>
<mo>></mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Cut-point sequence number carries out symbolism processing after all determining：
S(ki)=s (j) j=1,2 ..., L；I=1,2 ..., n；nj-1+1≤i≤nj
2) symbol sebolic addressing S={ s (i) }, i=1,2,3 ..., n after converting；By sequence s (1), s (2) ..., s (N) group in order
Into m n dimensional vector ns, i.e.,
Sm(i)=[s (i), s (i+1) ... s (i+m-1)],
1≤i≤N-m+1
For each 1≤i≤N-m, count and Sm(i) equal numberAnd with vector sum N-m-1 ratio, be denoted as
<mrow>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>:</mo>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>n</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
In formula；
<mrow>
<msup>
<mi>B</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</munderover>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
</mrow>
For m+1 point vectors, equally have
<mrow>
<msubsup>
<mi>A</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>n</mi>
<mi>i</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
In formula；
<mrow>
<msup>
<mi>A</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</munderover>
<msubsup>
<mi>A</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
</mrow>
3) entropy of this sequence is
<mrow>
<mi>S</mi>
<mi>a</mi>
<mi>m</mi>
<mi>p</mi>
<mi>E</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>,</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munder>
<mi>lim</mi>
<mrow>
<mi>N</mi>
<mo>&RightArrow;</mo>
<mi>&infin;</mi>
</mrow>
</munder>
<mo>{</mo>
<mo>-</mo>
<mi>ln</mi>
<mo>&lsqb;</mo>
<msup>
<mi>A</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>/</mo>
<msup>
<mi>B</mi>
<mi>m</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>}</mo>
</mrow>
But N can not possibly be ∞ in actually calculating, and when N takes finite value, be approximately equal to SampEn (m, r, N)=- ln [Am(r)/
Bm(r)]。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710432360.2A CN107423682A (en) | 2017-06-09 | 2017-06-09 | A kind of analysis of complexity method of non-linear EEG signals |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710432360.2A CN107423682A (en) | 2017-06-09 | 2017-06-09 | A kind of analysis of complexity method of non-linear EEG signals |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107423682A true CN107423682A (en) | 2017-12-01 |
Family
ID=60429678
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710432360.2A Pending CN107423682A (en) | 2017-06-09 | 2017-06-09 | A kind of analysis of complexity method of non-linear EEG signals |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107423682A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108309238A (en) * | 2018-01-30 | 2018-07-24 | 陕西师范大学 | A kind of electrocardiosignal abnormality recognition method based on phase arrangement entropy |
| CN109144259A (en) * | 2018-08-23 | 2019-01-04 | 杭州电子科技大学 | It is a kind of based on it is multiple dimensioned arrangement transfer entropy brain area between synchronized relation analysis method |
| CN109464128A (en) * | 2019-01-09 | 2019-03-15 | 浙江强脑科技有限公司 | Sleep quality detection method, apparatus and computer readable storage medium |
| CN111950441A (en) * | 2020-08-10 | 2020-11-17 | 苏州大学 | FNIRS real-time decoding method and system for upper limb movement intention |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080021345A1 (en) * | 2006-06-28 | 2008-01-24 | Kern Steven E | Distinguishing different drug effects from the electroencephalogram |
| CN102178514A (en) * | 2011-05-09 | 2011-09-14 | 浙江大学 | Coma degree evaluating method based on multiple indexes of non-linearity and complexity |
| CN102488516A (en) * | 2011-12-13 | 2012-06-13 | 湖州康普医疗器械科技有限公司 | Nonlinear electroencephalogram signal analysis method and device |
| WO2014167460A1 (en) * | 2013-04-12 | 2014-10-16 | Commissariat A L'energie Atomique Et Aux Energies Alternatives | Methods to monitor consciousness |
-
2017
- 2017-06-09 CN CN201710432360.2A patent/CN107423682A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080021345A1 (en) * | 2006-06-28 | 2008-01-24 | Kern Steven E | Distinguishing different drug effects from the electroencephalogram |
| CN102178514A (en) * | 2011-05-09 | 2011-09-14 | 浙江大学 | Coma degree evaluating method based on multiple indexes of non-linearity and complexity |
| CN102488516A (en) * | 2011-12-13 | 2012-06-13 | 湖州康普医疗器械科技有限公司 | Nonlinear electroencephalogram signal analysis method and device |
| WO2014167460A1 (en) * | 2013-04-12 | 2014-10-16 | Commissariat A L'energie Atomique Et Aux Energies Alternatives | Methods to monitor consciousness |
Non-Patent Citations (2)
| Title |
|---|
| 侯凤贞: "心率变异性的时间不可逆性研究", 《中国博士学位论文全文数据库医药卫生科技辑》 * |
| 黄晓林等: "等概率符号化样本熵应用于脑电分析", 《物理学报》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108309238A (en) * | 2018-01-30 | 2018-07-24 | 陕西师范大学 | A kind of electrocardiosignal abnormality recognition method based on phase arrangement entropy |
| CN108309238B (en) * | 2018-01-30 | 2020-10-16 | 陕西师范大学 | Electrocardiosignal abnormity identification method based on phase permutation entropy |
| CN109144259A (en) * | 2018-08-23 | 2019-01-04 | 杭州电子科技大学 | It is a kind of based on it is multiple dimensioned arrangement transfer entropy brain area between synchronized relation analysis method |
| CN109464128A (en) * | 2019-01-09 | 2019-03-15 | 浙江强脑科技有限公司 | Sleep quality detection method, apparatus and computer readable storage medium |
| CN111950441A (en) * | 2020-08-10 | 2020-11-17 | 苏州大学 | FNIRS real-time decoding method and system for upper limb movement intention |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107423682A (en) | A kind of analysis of complexity method of non-linear EEG signals | |
| CN104807534B (en) | Equipment eigentone self study recognition methods based on on-line vibration data | |
| Grant et al. | Comparison of matrix pencil and prony methods for power system modal analysis of noisy signals | |
| Liu et al. | Sparse-gev: Sparse latent space model for multivariate extreme value time serie modeling | |
| Kitić et al. | Physics-driven inverse problems made tractable with cosparse regularization | |
| Sang et al. | Wavelet-based hydrological time series forecasting | |
| D'Urso et al. | Wavelet‐based self‐organizing maps for classifying multivariate time series | |
| He et al. | Feature extraction of analogue circuit fault signals via cross‐wavelet transform and variational Bayesian matrix factorisation | |
| CN103176946A (en) | Sparse decomposition and denoising method facing block sparse signals | |
| Obuchowski et al. | ORNSTEIN--UHLENBECK PROCESS WITH NON-GAUSSIAN STRUCTURE. | |
| Zbilut | Use of recurrence quantification analysis in economic time series | |
| CN109904878B (en) | Multi-wind-field power generation time sequence simulation scene construction method | |
| Paynabar et al. | Informative sensor and feature selection via hierarchical nonnegative garrote | |
| He et al. | Separation and analyzing of harmonics and inter‐harmonics based on single channel independent component analysis | |
| CN117076171A (en) | Abnormality detection and positioning method and device for multi-element time sequence data | |
| Buzzard | Efficient basis change for sparse-grid interpolating polynomials with application to T-cell sensitivity analysis | |
| Sexton et al. | Relaxed multirate infinitesimal step methods | |
| CN110188407B (en) | Method and device for determining liquid flow parameters in porous medium | |
| CN104268217A (en) | User behavior time relativity determining method and device | |
| CN109447512B (en) | Large power grid reliability assessment method based on uniform design | |
| Sahlberg | Ensemble for Deterministic Sampling with positive weights: Uncertainty quantification with deterministically chosen samples | |
| CN103279592B (en) | A kind of out-of-limit emulation mode of distribution network voltage | |
| Ke et al. | Discogen: Learning to discover gene regulatory networks | |
| Cai et al. | Application of IWO-SVM approach in fault diagnosis of analog circuits | |
| Lauwers | Time Series Clustering |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20171201 |
|
| RJ01 | Rejection of invention patent application after publication |