CN106533742A - Time sequence mode representation-based weighted directed complicated network construction method - Google Patents
Time sequence mode representation-based weighted directed complicated network construction method Download PDFInfo
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Abstract
A time sequence mode representation-based weighted directed complicated network construction method comprises the steps of adopting a zero-mean normalization method to normalize an original time sequence; dividing a new time sequence into n sections in an equal probability manner, using the characters in a set character string to represent the sections, and representing the new time sequence into a character string sequence; moving a sliding window of which the length is 1 from left to right from the first character of the character string sequence, every time the sliding window moves one step, dividing the character string sequence into ((n-1)+1) fragments of which the lengths are all 1, and regarding each fragment as a mode; taking the different modes as the nodes of a complicated network, determining the connection edge weights and directions between the nodes of the complicated network according to the conversion frequency and the conversion directions between the nodes, and mapping the character string sequence into the weighted directed complicated network; and calculating the network topology statistical characteristics of the weighted directed complicated network. The method of the present invention enables the classification or identification precision of the time sequence signals to be improved remarkably.
Description
Technical field
The present invention relates to a kind of complex network networking method.More particularly to a kind of adding based on time sequence model sign
Power directed complex networks networking method.
Background technology
Complex Networks Analysis method is the relation between complication system internal primitives abstract node and Lian Bian for network
Form, then by the topological structure and dynamic behavior of quantitative analysis network, discloses inherent attribute and the operation of complication system
The important informations such as rule.Complex Networks Analysis method is different types of complex system study (such as bio-networks, cranial nerve net
Network, WWW, social networks etc.) there is provided brand-new visual angle, the extensive concern of different subject scientific research personnel is therefore suffered from, and
Achieve a series of gratifying progress.But with research deepen continuously and application sharp increase, existing complex network side
The defect of method and deficiency are also gradually highlighted, thus seek the new relevance grade wider and more excellent complex network networking method of performance into
For one of field difficult problem urgently to be resolved hurrily.
In the last few years, scientific research personnel's research finds that Complex Networks Analysis method can not only excavate the weight in time series
Information is wanted, and is easy to study the Complex Nonlinear System that theoretical model is difficult to accurate description, therefore, it is developing progressively as a class
Brand-new (non-linear) seasonal effect in time series analysis tool.At present, (Nonlinear Time Series are mapped as the most classical side of complex network
Method has：Based on phase space reconfiguration networking method and Visual Graph networking method.Phase space reconfiguration networking method is by Embedded dimensions
One group of multi-C vector is extracted from original time series with time delay estimating techniques, using these vectors as complex network section
Point, then according to vector between similitude determine network node company side (similarity measurements between node be more than a certain given threshold
Value), so as to construct the corresponding complex network of original time series, the method is in Embedded dimensions and time delay estimation process
There is destabilizing factor, and the optimal threshold that even frontier juncture system judges also is difficult to determine, causes the robustness of the method application poor.
Visual Graph networking method be using the data point in original time series as network node, by the visible relation between data point
Used as the company side of network, wherein visible relation is determined by the size of data between node and visual rule.Compare mutually empty
Between reconstruct networking method, Visual Graph networking method parameter is less, algorithm robustness preferably, but this networking method network size with
Length of time series is directly related, and when the length of time series of analysis is longer, correspondence complex network nodes are more, after causing
The extraction computation complexity of continuous complex network characteristic is larger.Additionally, above two networking method can only build have no right, undirected complexity
Network.
Having no right, in undirected complex network, " relevant with do not associate " this simple relation between each primitive, is only existed,
If the company of there is side between relevant two nodes for representing primitive, otherwise just there is no even side.But in many actual complex
In system, the difference between each primitive on correlation degree amount, therefore can not simply use " 0 " or " 1 " to represent.Additionally, very
Associate between many primitives and also there is certain directional difference, such as primitive A can affect primitive B, but primitive B may be to primitive
The state of A does not affect, i.e., primitive A has unidirectional delivery to primitive B.It is therefore seen that, have no right, undirected complex network cannot essence
The really association between reaction node (or primitive).
The content of the invention
The technical problem to be solved is to provide a kind of reflection original time series that can be finer and is respectively segmented
Between relation based on time sequence model characterize weighting directed complex networks networking method.
The technical solution adopted in the present invention is：A kind of weighting directed complex networks characterized based on time sequence model are built
Network method, comprises the steps：
1) original time series is standardized using zero-mean normalization method, by formula is calculated as below：
Wherein,It is seasonal effect in time series average, a is the standard deviation of original time series,
For original time series { xi, i=1 ..., t obtain new time series { y after being standardizedi, i=
1,…,t；
2) by new time series { yi, i=1 ..., t equiprobability is divided into n interval, the character string that then use sets
In character it is interval to represent each, each interval one character of correspondence, so as to by new time series { yi, i=1 ..., t
It is expressed as character string sequence { sk, k=1 ..., t, wherein skBe setting character string in character, the character string of the setting is
Front n letter in by English alphabet is constituted；
3) with the sliding window that length is l, the default value of l is 4, from character string sequence { sk, k=1 ..., first of n
Character starts to move from left to right, and sliding window moves 1 step every time, just by character string sequence { skIt is divided into (the n-l+ that length is l
1) each fragment is considered as a mode by individual fragment；
4) different modalities are determined into complexity by the conversion frequency and conversion direction between node as the node of complex network
Company side right weight and direction between network node, so as to by character string sequence { skIt is mapped as weighting directed complex networks；
5) the network topology statistical property of calculating weighting directed complex networks, including network size SN, weighting are oriented average
Path WPL and betweenness center BC；
SN=N (4)
Wherein,
Wherein,
Node total numbers of the wherein N for network；Weighting oriented shortest path lengths of the Pl (p, q) for node p to node q, wpq
For the weight path of node p to node q；Betweenness centers of the Bc (p) for node p, LmqBe from node m to node q it is all most
The total number of short path, LmqP () is from node m to node q and through all shortest path numbers of node p.
Step 4) it is that company's side right weight and the direction between complex network node is determined according to following rule：If present node
Identical with subsequent time node, i.e., node keeps constant；If the node from present node to subsequent time has sent out change, then
There is a company side between the two nodes, direction is to point between next node, and the two nodes from present node
Even side right increases by 1 again.
Step 4) also include that the connection state that oriented weighted network is drawn by the NETDRAW kits of UCINET softwares can
View.
The weighting directed complex networks networking method characterized based on time sequence model of the present invention, is accorded with by time series
Number change characterization technique and sliding window technology, obtain series of sign pattern as network node, then analyze symbolism pattern it
Between association determine network weight and direction.Reflection original time series that can be finer of the invention pass respectively between segmentation
System, therefore its network structure and characteristic can sensitiveer, more accurately embody the difference of unlike signal, so as to be obviously improved time sequence
The classification of column signal or accuracy of identification.The main advantages of the present invention and characteristic be embodied in following aspects：
1st, it is proposed by the present invention weighting directed complex networks due to the association that more subtly can reflect between primitive, therefore its
Network topology structure and characteristic can sensitiveer, more accurately embody seasonal effect in time series difference, be obviously improved time series classification and
Recognition performance.
2nd, the inventive method determines network node using time series symbolism modeling technology, then by calculating symbol
Number change pattern the conversion frequency determine network weight, the conversion direction of symbolism pattern determines the closure between node.It is above-mentioned
Processing method is less by seasonal effect in time series effect length, is applicable to that length is longer or even the time series analysis of overlength, and Jing
Allusion quotation time series Complex Networks Analysis method (such as visual drawing method and Phase Space Method) cannot be realized.
3rd, time series proposed by the present invention is oriented, the Weighted Complex Networks networking method scope of application is very wide, analysis letter
Number can be linear signal can also be nonlinear properties.The method is different types of analysis of complex system, such as meteorological number
A brand-new deciphering instrument is provided according to the analysis of, data such as stock certificate data, heart and brain electricity.
Description of the drawings
Fig. 1 is the flow chart of the weighting directed complex networks networking method that the present invention is characterized based on time sequence model；
Fig. 2 is that the Logistics that present example is chosen is mapped in corresponding time series chart under different parameters；
Fig. 3 is that the Logistics that present example is chosen is mapped under different parameters after corresponding time series standardization
The sequence chart for obtaining；
Fig. 4 is the schematic diagram that standardization sequence when Logistics is mapped in parameter μ=3.8 carries out symbolism sign；
Fig. 5 a are the oriented complexity of weighting that Logistics maps that corresponding periodic state time series is set up under different parameters
The network size SN variation diagram of network；
Fig. 5 b are the oriented complexity of weighting that Logistics maps that corresponding chaos state time series is set up under different parameters
The network size SN variation diagram of network；
Fig. 6 a are the oriented complexity of weighting that Logistics maps that corresponding chaos state time series is set up under different parameters
The oriented average path length WDPL variation diagrams of weighting of network；
Fig. 6 b are the oriented complexity of weighting that Logistics maps that corresponding chaos state time series is set up under different parameters
The betweenness center BC variation diagram of network.
Specific embodiment
With reference to the weighting directed complex networks characterized based on time sequence model of embodiment and accompanying drawing to the present invention
Networking method is described in detail.
The weighting directed complex networks networking method characterized based on time sequence model of the present invention, is comprised the steps：
1) original time series is standardized using zero-mean normalization method, zero-mean normalization method be by sometimes
Between sequence data be converted into average for 0, variance is 1 normalized temporal sequence.By formula is calculated as below：
Wherein,It is seasonal effect in time series average, a is the standard deviation of original time series,
For original time series { xi, i=1 ..., t obtain new time series { y after being standardizedi, i=
1,…,t；
2) by new time series { yi, i=1 ..., t equiprobability is divided into n interval, the character string that then use sets
In character it is interval to represent each, each interval one character of correspondence, so as to by new time series { yi, i=1 ..., t
It is expressed as character string sequence { sk, k=1 ..., t, wherein skBe setting character string in character, the character string of the setting is
Front n letter in by English alphabet is constituted；
3) with the sliding window that length is l, the default value of l is 4, from character string sequence { sk, k=1 ..., first of n
Character starts to move from left to right, and sliding window moves 1 step every time, just by character string sequence { skIt is divided into (the n-l+ that length is l
1) each fragment is considered as a mode by individual fragment；
4) different modalities are determined into complexity by the conversion frequency and conversion direction between node as the node of complex network
Company side right weight and direction between network node, so as to by character string sequence { skIt is mapped as weighting directed complex networks；
Company's side right weight and the direction between complex network node is specifically determined according to following rule：If present node and subsequent time
Node is identical, i.e., node keeps constant；If the node from present node to subsequent time has sent out change, then the two nodes
Between there is a company side, direction is to point to company's side right between next node, and the two nodes from present node to increase again
Plus 1；
The step also includes that the connection state that oriented weighted network is drawn by the NETDRAW kits of UCINET softwares can
View.
5) the network topology statistical property of calculating weighting directed complex networks, including network size SN, weighting are oriented average
Path WDPL and betweenness center BC；
SN=N (4)
Wherein,
Wherein,
Node total numbers of the wherein N for network；Weighting oriented shortest path lengths of the Pl (p, q) for node p to node q, wpq
For the weight path of node p to node q；Betweenness centers of the Bc (p) for node p, LmqBe from node m to node q it is all most
The total number of short path, LmqP () is from node m to node q and through all shortest path numbers of node p.
Had based on the weighting that time sequence model is characterized with reference to Logistics map examples and accompanying drawing detailed description
It is as follows to complex network networking method：
Logistics mappings are typical one-dimensional chaos time sequence models, and it is to enter chaos by double period bifurcation
's.Logistics mapping models are with reference to equation below：
xn+1=μ xn(1-xn) (8)
The value of parameter μ is different, that is, correspond to different states.In this example, we set the first of Logistics systems
Initial value is 0.5, and step-length is 0.01, and the time is 100s.Parameter μ takes 3.5,3.6,3.628,3.7,3.74,3.8,3.84 respectively,
During 3.9,3.99 this 9 values, the Logistics time serieses that length is 10000 different conditions can be obtained, such as Fig. 2 institutes
Show.State under parameters is with reference to table 1.
State of the 1 Logistics systems of table under parameters
1) by each Logistics time series { xn, n=1 ..., 10000 standardize, and we are equal using zero here
Value normalization method.The method is that all time series datas are converted into average for 0, and variance is 1 normalized temporal sequence.
For original time series { xn, n=1 ..., 10000, it is standardized for after and is obtained new time series { yn, i=
1 ..., 10000, as shown in Figure 3.Its computing formula is：
Wherein,It is seasonal effect in time series average, a is the standard deviation of original time series.
2) by the standardized time series { y for obtainingi, i=1 ..., 10000 equiprobability be divided into 12 it is interval, then
With the character representation regional in the character string of setting, each region one character of correspondence, as shown in Figure 4.Thus by number
According to sequence { yi, i=1 ..., 10000 are converted into character string sequence { sk, k=1 ..., 10000, wherein skIt is the character of setting
Character in string, the character string of the setting by English alphabet in front 12 letters constitute
3) with the sliding window that length is 4, from from character string sequence { sk, k=1 ..., 10000 first character is opened
Start from left-hand to move right, divide character string sequence { sk, k=1 ..., 10000 be each sub-piece, sliding window every time move 1 step.
So, character string sequence is divided into into 9997 fragments that length is 4 just, each fragment is considered as into a mode.
4) different modalities are determined into complexity by the conversion frequency and conversion direction between node as the node of complex network
Company side right weight and direction between network node, so as to by character string sequence { skIt is mapped as weighting directed complex networks.
Company's side right weight and the direction between complex network node is specifically determined according to following rule：If present node and subsequent time
Node is identical, i.e., node keeps constant；If the node from present node to subsequent time has sent out change, then the two nodes
Between there is a company side, direction is to point to company's side right between next node, and the two nodes from present node to increase again
Plus 1.
5) the connection state Visual Graph of oriented weighted network is drawn by the NETDRAW kits of UCINET softwares；
6) the network topology statistical property of calculated weighting vector network chart, including network size SN, weighting are oriented
Average path length WDPL and betweenness center BC；
SN=N (4)
Wherein,
Wherein,
Node total numbers of the wherein N for network；Weighting oriented shortest path lengths of the Pl (p, q) for node p to node q, wpq
For the weight path of node p to node q；Betweenness centers of the Bc (p) for node p, LmqBe from node m to node q it is all most
The total number of short path, LmqP () is from node m to node q and through all shortest path numbers of node p.
As shown in Figure 5 a, the weighting that the corresponding cycle time sequence of Logistics mappings is set up under different parameters is oriented multiple
The network size of miscellaneous network is exactly equal to the number of cycle disaggregation, as shown in Figure 5 b, Logistics mappings correspondence under different parameters
Chaos time sequence set up weighting directed complex networks network size increase with the increase of chaos degree.Such as Fig. 6 a institutes
Show, under different parameters, the weighting of the weighting directed complex networks that the corresponding chaos time sequence of Logistics mappings is set up is oriented
The value of average path length WDPL, increases with the increase of chaos degree, as shown in Figure 6 b, Logistics under different parameters
Betweenness center BC of the weighting directed complex networks that corresponding chaos time sequence is set up is mapped with the increase of chaos degree
And constantly reduce.
Claims (3)
1. it is a kind of based on time sequence model characterize weighting directed complex networks networking method, it is characterised in that including as follows
Step：
1) original time series is standardized using zero-mean normalization method, by formula is calculated as below：
Wherein,It is seasonal effect in time series average, a is the standard deviation of original time series,
For original time series { xi, i=1 ..., t obtain new time series { y after being standardizedi, i=1 ...,
t；
2) by new time series { yi, i=1 ..., t equiprobability is divided into n interval, the word in the character string that then use sets
Symbol is interval to represent each, each interval one character of correspondence, so as to by new time series { yi, i=1 ..., t are expressed as
Character string sequence { sk, k=1 ..., t, wherein skBe setting character string in character, the character string of the setting is by English
Front n letter composition in letter；
3) with the sliding window that length is l, the default value of l is 4, from character string sequence { sk, k=1 ..., the first character of n
Beginning is moved from left to right, and sliding window moves 1 step every time, just by character string sequence { skBe divided into length be l (n-l+1) it is individual
Each fragment is considered as a mode by fragment；
4) different modalities are determined into complex network by the conversion frequency and conversion direction between node as the node of complex network
Company side right weight and direction between node, so as to by character string sequence { skIt is mapped as weighting directed complex networks；
5) the network topology statistical property of weighting directed complex networks, including network size SN, the oriented average path of weighting are calculated
Length WPL and betweenness center BC；
SN=N (4)
Wherein,
Wherein,
Node total numbers of the wherein N for network；Weighting oriented shortest path lengths of the Pl (p, q) for node p to node q, wpqFor section
Weight paths of the point p to node q；Betweenness centers of the Bc (p) for node p, LmqIt is all shortest paths from node m to node q
The total number in footpath, LmqP () is from node m to node q and through all shortest path numbers of node p.
2. the weighting directed complex networks networking method characterized based on time sequence model according to claim 1, which is special
Levy and be, step 4) it is that company's side right weight and the direction between complex network node is determined according to following rule：If present node
Identical with subsequent time node, i.e., node keeps constant；If the node from present node to subsequent time has sent out change, then
There is a company side between the two nodes, direction is to point between next node, and the two nodes from present node
Even side right increases by 1 again.
3. the weighting directed complex networks networking method characterized based on time sequence model according to claim 1, which is special
Levy and be, step 4) also include that the connection state that oriented weighted network is drawn by the NETDRAW kits of UCINET softwares can
View.
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| CN107665276A (en) * | 2017-09-18 | 2018-02-06 | 天津大学 | Time series complexity measuring method based on symbolism mode and the conversion frequency |
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