CN108073695A - A kind of higher-dimension time-variable data method for visualizing of dimension reduction space visual perception enhancing - Google Patents
A kind of higher-dimension time-variable data method for visualizing of dimension reduction space visual perception enhancing Download PDFInfo
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Abstract
The invention discloses a kind of dimension reduction space visual perception enhancing higher-dimension time-variable data method for visualizing, including：Higher-dimension time-variable data is read, the two-dimensional space coordinate of higher-dimension time-variable data is obtained using multidimensional scaling algorithm, higher-dimension time-variable data is solved using formula (1) to obtain target orthogonal matrix in the coordinate of two-dimensional space,, in formula (1), Q represents target orthogonal matrix,Represent two-dimensional space coordinate of the higher-dimension time-variable data in i-th of data at current time,Represent two-dimensional space coordinate of the higher-dimension time-variable data in i-th of data of previous moment, N represents the number of higher-dimension time-variable data, Dt(Q) represent the higher-dimension time-variable data after orthogonal matrix converts at current time compared with the project migration of previous moment；Project migration of the higher-dimension time-variable data in two-dimensional space is minimized using target orthogonal matrix, obtains projection of the higher-dimension time-variable data at current time.The present invention can be obviously improved the visualization of higher-dimension time-variable data and analysis efficiency.
Description
Technical field
The present invention relates to a kind of higher-dimension time-variable data method for visualizing of dimension reduction space, belong to computer graphics and data
Visualization technique field.
Background technology
High dimensional data analysis usually considers the multidimensional property of data simultaneously, especially when there are stronger between the dimension of data
Correlation, when can not individually consider, the multidimensional property of effective display data and using multidimensional property analysis find in data dive
It is being characterized in the research hotspot in visual analysis field.Parallel coordinates (Mcdonnell K T, Mueller
K.Illustrative Parallel Coordi-nates [J] .Computer Graphics Forum, 2008,27 (3)：
1031-1038.) high dimensional data is represented using the broken line across one group of parallel vertical axis, wherein every parallel axes represents one
Dimension.The direction that user arranges along axis is supported to extract the implicit information of data, and then finds the correlation between dimension.However,
Unreasonable axis arrangement can bring serious data cable confounding issues, seriously reduce the readability of visible system, many
Person is to this progress in-depth study.The scholars such as Graham replace broken line to reduce blocking in same class data using free curve,
Realize data separation (Graham M, the Kennedy J.Using Curves to Enhance in same data set
Parallel Coordinate Visualisations[C]//International Conference on
Information Visualization.IEEE Computer Society, 2003：10).The scholars such as Peng pass through density point
Analysis to parallel coordinates carry out permutatation show it is less obscure, enhance data readability (Peng W, Ward M O,
Rundensteiner EA.Clutter Reduction in Multi-Dimensional Data Visualization
Using Dimension Reordering[C]//IEEE Symposium on Information Visual-
Ization.IEEE Computer Society, 2004：89-96.).Although parallel coordinates can show the distribution of multidimensional data
Feature, but the data hierarchy shown when data set is very big is chaotic, it is difficult to find the changing rule of data, hinders people couple
Understanding scatterplot matrices (Cleveland W C, the Mcgill M E.Dynamic graphics for statis- of information
Tics [J] .Journal ofthe Royal Statistical Society, 1990,153 (1)) by the different dimensions of data
Two-dimensional arrangements, the scatter diagram of the arbitrary 2 dimension combination producings of unique display, so as to which user be supported to solve are carried out in a certain order
Read raw data simultaneously analyzes the correlation between arbitrary 2 dimensions.But data have been the absence of in the case that more than two dimensions
Cluster displaying rotates and then finds although the scholars such as Elmqvist propose scatter diagram being put into three dimensions between multiple dimensions
Relation, but when handling more high-dimensional data, there are still limitation (Elmqvist N, Dragicevic P, Fekete J
D.Rolling the Dice：Multidimensional Visual Exploration using Scatterplot
Matrix Navigation [J] // .IEEE Transactions on Visualization＆Computer Graphics,
2008,14 (6)：1141.).
Dimensionality reduction mapping techniques can provide expression of the multidimensional data immanent structure in lower dimensional space, be a kind of effective multidimensional
Data visualization technique.It can help user that abstract multidimensional information and its knot are effectively explored and understood in lower dimensional space
Structure allows user rapidly and accurately to be excavated in data set impliedly during Knowledge Discovery, information cognition and information decision
Feature, relation, pattern, trend and clustering information etc..Principal Component Analysis is usually used in data being reduced to two or three dimensions
Degree is laid out to generate similitude.However this method has given up other dimensions of data, it is difficult to keep data in luv space
Higher-dimension is distributed.One classical method is locality preserving projections (locality preserving projection, LPP) (He
X, Niyogi P.Locality preserving projections [J] .Ad-vances in Neural Information
Processing Systems, 2004,16 (1)：186-197), this method linearly saves the local higher-dimension point of data
Cloth.As a kind of representative low-dimensional embedded mobile GIS, Isometric Maps (Isomap) (Tenenbaum J B, Silva V D,
Langford J C.A global geometric, for nonlinear dimensionality reduction [C] //
2000：It can 2319-23) preserve distribution of the data in original higher dimensional space.Compared to LPP, Isomap technologies are to calculate to own
Data to the distance between (otherness that data pair can be considered as), the global higher-dimension of data to be kept to be distributed.Wherein, multidimensional mark
Algorithm is spent as a kind of algorithms most in use in Isomap technologies, has been effectively combined the advantage of parallel coordinates and scatterplot matrices,
It supports to utilize the data distribution in lower dimensional space approximate expression hyperspace, illustrates the similitude of multidimensional data.In order to verify
Visual analysis ability with enhancing multidimensional scaling algorithm, domestic and foreign scholars have made intensive studies multidimensional scaling algorithm.Keim
Scholars is waited to devise the method for visualizing excavated for the large database based on multidimensional scaling, and compared parallel coordinates and dissipate
The bandwagon effect of point diagram matrix etc., present multidimensional scaling algorithm the visual high efficiency of high dimensional data (Keim D A,
Kriegel H P.Visualization Techniques for Mining Large Databases：A Comparison
[M] .IEEE Educational Activities Department, 1996).The scholars such as Vera are smoothly more using interpolation method
The two-dimensional map of scaling algorithm is tieed up as a result, time series data analysis ability (Vera J F, the Angulo J of enhancing multidimensional scaling algorithm
M, Rold á n J A.Stability analysis in nonstationary spatial covariance
Estimation [J] .Stochastic Environmental Research＆Risk Assessment, 2016：1-14).
Multidimensional data usually has the characteristics that timing variations, and the sequential evolution of data is often difficult to explore.Therefore, towards
Multidimensional data with notable Temporal Order carries out visual analysis and has great importance.Animation (Bender S, Mcfarland
D A.The art and science of dynamic network visualization[J].Journal of Social
Structure, 2006,7 (2)：1206-1241) because it can effectively preserve the mental map of user (mental map), and
The intuitive manner developed over time as demonstration data.But the scholars such as Archambault are experimentally confirmed：In animation
The mental map of middle acquisition may be engraved without too big help, moreover when multiple for the visual cognition of longer sequential
The acute variation of subpoint can not support changing pattern (the Archambault D, Purchase of fast track surrounding time node
H, Pinaud B.Animation, Small Multiples, and the Effect of Mental Map
Preservation in Dynamic Graphs[J].IEEE Transactions on Visualization&Computer
Graphics, 2011,17 (4)：539-552).Therefore, nearest method (Burch M, Fritz M, Beck F, et
al.TimeSpiderTrees：A Novel Visual Metaphor for Dynamic Compound Graphs[C]//
IEEE Symposium on Visual Languages and Human-Centric Computing.IEEE Computer
Society, 2010：168-175.Liu S, Wu Y, Wei E, Liu M, and Liu Y.Storyflow：Tracking the
evolution of stories[C]//IEEE Transactions on Visu-alization Computer
Graphics, 19 (12)：2436-45,2013) lay particular emphasis on more utilize static map displaying time series data.Time shaft and how small figure
(small multiples) is the two kinds of selections encoded in a manner of static map to time dimension.How small many scholar's uses are
Drawing method carries out the scholars such as visual analysis, Hadlak and proposes the method for visualizing based on how small figure, selects with allowing user interaction
Focal zone in multiple small figures is selected, and suitable layout (Hadlak S, Schulz H J, Schumann are established for selected data
H.In situ exploration of large dynamic networks[J].IEEE Trans Vis Comput
Graph, 2011,17 (12)：2334-2343).The advantages of spherical coordinate, is introduced into parallel coordinates by the scholars such as Walker, more directly
Temporal aspect ([18] Walker J, Geng Z, Jones M, the et al.Visualization for illustrating multidimensional data seen
Of Large, Time-Dependent, Abstract Data with Integrated Spherical and Parallel
Coordinates[C]//EuroVis-Short Papers.2012：43-47).However, when facing long-term sequence, how small figure
Method needs to show substantial amounts of perspective view, seriously reduces the readability of visual effect, increases vision clutter, and then limits
Tracking of the user to temporal aspect.
Method based on time shaft will be compressed to one-dimensional or two-dimensional space, pole the time as an axis, then by high dimensional information
The earth enhances readability, thus, it is a large amount of to show multidimensional time-varying by means of which using the research work of multidimensional scaling algorithm
Data, to enhance visual cognition of the user in lower dimensional space.The scholars such as Dwyer propose similar space-time cube (space-
Time is considered as the 3rd dimension after multidimensional scaling algorithm is projected in two-dimensional space by time-cube) technology, so as in three-dimensional
Spatially present variation (the Dwyer T.Gallagher D R.Visualising Changes in of data in time
Fund Manager Holdings in Two and a Half-Dimensions[J].In-formation
Visualization, 2004,3 (4)：227-244).Bernard is when scholars devise the displaying multidimensional based on time path
Become the method for data, connect data entity identical at different moments and form time path, single entities exist so that user to be helped to understand
Temporal patterns of change (Bernard J, Wilhelm N, Scherer M, et al.TimeSeriesPaths：
Projection-Based Explorative Analysis of Multivarate Time Series Data[C]//
Conference in Central Europe on Computer Graphics, Visualization and Computer
Vision.2012).Multidimensional scaling algorithm is more also utilized by method (the Hu Y, Wu of multidimensional data projection to two-dimensional space
S, Xia S, et al.Motion track：Visualizing variations of human motion data[C]//
Visualization Symposium.IEEE, 2010：153-160；Ward M O, Guo Z.Visual Exploration
Of Time-Series Data with Shape Space Projections [J] .Computer Graphics Forum,
2011,30 (3)：701-710；Mao Y, Dillon J, Lebanon G.Sequential document visual-
Ization. [J] .IEEE Transactions on Visualization＆Computer Graphics, 2007,13 (6)：
1208-1215.) etc., the movement in time of single data is focused on and path that they are generated in time.Although this
A little technologies allow to detect the circulation pattern of data in time, but since data item can be projected into arbitrary two-dimensional coordinate,
Serious visual disorders are resulted in, disturb the visual pursuit of user.The scholars such as Jackle are proposed based on the more of sliding window
Tie up scaling algorithm (Jackle D, Fischer F, Schreck T, and Keim D.A.Temporal mds plots for
analysis of multivariate data[C]//IEEE Transactions on Visualization Computer
Graphics, 22 (1)：141,2016), effectively by multi dimensional data compression to one-dimensional and be an axis in two-dimensional space using the time
Visual analysis network security data.However, after multidimensional data is mapped to the one-dimensional space, it is suppressed that the vision of feature difference is recognized
Know, and after the use of sliding window technique, although the effectively smooth mutability of multidimensional scaling algorithm, inhibits
Effective displaying of outlier.
As can be seen that higher-dimension time-variable data method for visualizing can help domain expert quickly to analyze display data feature,
Enhance visual visual perception, improve the visualization of higher-dimension time-variable data and analysis efficiency to a certain extent.It is however existing
Parallel coordinates, the method for visualizing such as scatterplot matrices and dimensionality reduction mapping techniques still have certain limitation, it is difficult to display data
Temporal aspect, be unfavorable for user interaction formula analysis, hamper higher-dimension time-variable data visualization efficiency promotion.
The content of the invention
The object of the present invention is to provide a kind of higher-dimension time-variable data method for visualizing of dimension reduction space visual perception enhancing.
To achieve the above object, the technical solution adopted in the present invention is：
The higher-dimension time-variable data method for visualizing of dimension reduction space visual perception enhancing of the present invention includes：
Higher-dimension time-variable data is read, the two-dimensional space coordinate of higher-dimension time-variable data is obtained using multidimensional scaling algorithm, is used
Formula (1) solves higher-dimension time-variable data in the coordinate of two-dimensional space to obtain target orthogonal matrix,
In formula (1), Q represents target orthogonal matrix,Represent i-th data of the higher-dimension time-variable data at current time
Two-dimensional space coordinate,Represent two-dimensional space coordinate of the higher-dimension time-variable data in i-th of data of previous moment, N represents high
Tie up the number of time-variable data, Dt(Q) represent the higher-dimension time-variable data after orthogonal matrix converts at current time compared with preceding
The project migration at one moment；
Project migration of the higher-dimension time-variable data in two-dimensional space is minimized using target orthogonal matrix, obtains higher-dimension time-varying
Data are in the projection at current time.
Further, the present invention using formula (1) respectively by rotate, overturn two kinds of forms to higher-dimension time-variable data
The coordinate of two-dimensional space is solved, corresponding to obtain rotating orthogonal matrix, overturning orthogonal matrix, is calculated respectively through rotating orthogonal square
Battle array overturns the higher-dimension time-variable data after orthogonal matrix converts at current time compared with the project migration of previous moment, and selects
Wherein the orthogonal matrix with smaller project migration is as target orthogonal matrix.
Further, the present invention using target orthogonal matrix by higher-dimension time-variable data two-dimensional space project migration most
After smallization, projector space of the higher-dimension time-variable data at current time is divided into the subspace more than N number of, by different projections
Point is filled in different subspaces, obtains projection of the higher-dimension time-variable data at current time.
Further, subspace of the present invention is equilateral triangle, square or regular hexagon.
Further, the present invention is when the subspace is thrown to there are more than two targets in regular hexagon and target subspace
During shadow point, according to the traversal order of target projection point in target subspace, each target projection point is filled out one by one by the following method
It is charged in different regular hexagon subspaces：
If current goal subpoint is first subpoint, current goal subpoint is filled in target subspace；
Otherwise, following steps are performed：
If step a. current goal subpoints fall the central spot in current subspace, step b is performed, otherwise performs step
Rapid c；
Step b. is outwards successively searched for since the current subspace, until finding positive six side in periphery being not yet filled
Shape；Current goal subpoint is filled in the periphery regular hexagon, and is target subspace by current subspace update, and then
Judge whether the point of the target projection in target subspace fills to finish, if being not filled by finishing, using next target projection point as
Current goal subpoint, which returns, performs step a；
Step c. finds the regular hexagon of two angle minimums, the angle from the adjacent regular hexagon of current subspace
Minimum regular hexagon refers to：In all adjacent regular hexagons of current subspace, the central point of regular hexagon and current son
The line of the central point in space is minimum with the angle of current goal subpoint and the line of the central point of current subspace；
Step d. selected from the regular hexagon of two angle minimums the distance of its central point and current goal subpoint compared with
A small preferred regular hexagon of conduct；
If it is preferred that regular hexagon is not filled, current goal subpoint is filled in preferred regular hexagon by step e.,
And by current subspace update be target subspace, and then judge whether the point of the target projection in target subspace fills and finish,
If being not filled by finishing, returned using next target projection point as current goal subpoint and perform step a；If it is preferred that regular hexagon
It has been be filled that, then perform step f；
Step f. is selected from two adjacent regular hexagons for having common edge with preferred regular hexagon and current subspace
In small distance one of its central point and current goal subpoint is used as suboptimum regular hexagon；If suboptimum regular hexagon is not filled out
It fills, then current goal subpoint is filled in suboptimum regular hexagon, and be target subspace by current subspace update, and then
Judge whether the point of the target projection in target subspace fills to finish, if being not filled by finishing, using next target projection point as
Current goal subpoint, which returns, performs step a；If suboptimum regular hexagon has been filled, step g is performed；
Current subspace update is the preferred regular hexagon by step g., then current goal subpoint is empty from target
Between be transferred in current subspace, and make current goal subpoint in the position of current subspace with its shift before it is empty in target
Between position it is identical, be then back to and perform step c.
Compared with prior art, the beneficial effects of the invention are as follows：
(1) Dimension Time Series are obtained after the two-dimensional coordinate of dimension reduction space using multidimensional scaling algorithm, by iteration just
The project migration that transformation matrix minimizes adjacent time step is handed over to find target orthogonal matrix.And then using target orthogonal matrix to height
Dimension time-variable data is converted in the coordinate of two-dimensional space, and project migration of the higher-dimension time-variable data in two-dimensional space is minimized,
Reduce the offset of adjacent time node subpoint.Vision present invention decreases higher-dimension time-variable data in dimension reduction space as a result,
Disorder, the temporal aspect of data are quickly shown, facilitate the analysis of user interaction formula, hence it is evident that it is visual to promote higher-dimension time-variable data
Change and analysis efficiency can effectively meet the application demand of user.
(2) further, reduce solution rooms by rotating and turn over two kinds of forms can quickly to obtain target orthogonal
Matrix.
(3) better visual perception, the present invention are empty in the projection at current time by higher-dimension time-variable data in order to obtain
Between divided, it is minimum and apart from minimum factor to consider angle, different data item is projected in different subspaces, by
This further avoids due to subpoint increases that there are two or more subpoints to fall the institute on same regular hexagon
The visual disorders that may be brought.
Description of the drawings
Fig. 1 is the present invention higher-dimension time-variable data is visual with afterwards before the project migration of two-dimensional space minimizes
Change effect contrast figure, wherein, (a) is projected high dimensional data to two-dimensional space using classical multidimensional scaling algorithm for current time
Result figure；(b) high dimensional data is projected to the result figure of two-dimensional space using classical multidimensional scaling algorithm for subsequent time；(c)
The result of orthogonal transformation is reused after high dimensional data is projected to two-dimensional space using classical multidimensional scaling algorithm for current time
Figure；(d) orthogonal transformation is reused after high dimensional data is projected to two-dimensional space using classical multidimensional scaling algorithm for subsequent time
Result figure.
Fig. 2 is the effect of visualization figure directly stacked on four subpoints to same regular hexagon；
Fig. 3 is the effect of visualization figure that the present invention fills subpoint using the scheme for considering angle and distance；
Fig. 4 is flow chart of the present invention using the scheme filling subpoint for considering angle and distance；
Fig. 5 is unobstructed drawing result comparison diagram, wherein, (a) is classical scatter diagram result images, and (b) is nothing of the present invention
Block drawing result image.
Specific embodiment
The higher-dimension time-variable data visualization side enhanced below with specific embodiment dimension reduction space visual perception of the present invention
Method is further described.Specific method is as follows：
Initial higher-dimension time-variable data is loaded, is projected higher-dimension time-variable data to two-dimensional space by classical multidimensional scaling algorithm
It is shown, obtains the two-dimensional space coordinate of higher-dimension time-variable data.Specific method is as follows：
First original higher-dimension time-variable data is normalized according to formula (2), to eliminate the shadow of different dimensions dimension
It rings.
In formula (2), xiRepresent the value of i-th of data in dimension x；xmin, xmaxThe maximum and most of dimension x is represented respectively
Small value；Represent i-th of data item in dimension x after normalizing.
Then distance matrix of the higher-dimension time-variable data in luv space after normalized is calculated.The present invention can adopt
With Euclidean distance battle array D, shown in calculation formula such as formula (3)：
In formula (3),The ith and jth data item in dimension x after normalizing is represented respectively, | | | | represent two
Norm computing,Represent the Euclidean distance of i-th of the data item and j-th of data item after normalizing in dimension x, n represents data
The number of item.
And then the centralization inner product battle array B of lower dimensional space expression is calculated according to distance matrix, as shown in formula (4)：
In formula (4),Represent the Euclidean distance of i-th of data item and j-th of data item, n represents the number of data item.
Orthogonal Decomposition is finally carried out to B, and chooses 2 maximum characteristic values and corresponding feature vector, obtains two dimension
Fitting composition under spaceShown in calculation formula such as formula (5)：
In formula (5), U, Λ, U ' are respectively the feature vector battle array, characteristic value battle array, the transposition with feature vector battle array of matrix B；For two of the maximum absolute value of matrix B characteristic value, U2It is feature vector corresponding with characteristic value；As higher-dimension time-varying
Data are in the expression of dimension reduction space (i.e. two-dimensional space).
In multidimensional scaling algorithm, due to only considering the consistency of the relative position between data, thus same data item exists
There are stronger arbitrariness, this species diversity is often as orthogonal transformation and either normalizes what is generated for projection at different moments,
Visual pursuit of the user to interested temporal aspect has been greatly interfered with, serious regard is brought to data analyst
Feel disorderly.Comparison diagram 1 (a) and Fig. 1 (b) understand that some data item are projected onto the upper right corner at the previous moment, and next
Moment then maps to the lower right corner suddenly, and compared to Fig. 1 (c) and Fig. 1 (d) there are serious visual disorders, this is making to a certain degree
The about promotion of higher-dimension time-variable data visualization efficiency.
For this purpose, the present invention proposes to improve visual cognition of the user to time varying characteristic on the basis of multidimensional scaling algorithm
Increase orthogonal transformation to correct the projection coordinate of data, so as to fulfill in the base of not change data relative position in lower dimensional space
On plinth, offset of the multidimensional time-variable data on lower dimensional space is minimized, enhances the ability of the time varying characteristic of heuristic data.
Orthogonal transformation can correct the coordinate of subpoint between not change data on the premise of the relation of mutual alignment, and then
Minimize the offset distance of neighbor mapping figure.For this purpose, the present invention utilizes the iterative solution mode shown in formula (1) to higher-dimension time-varying
Data are solved in the coordinate of two-dimensional space, obtain target orthogonal matrix, to obtain minimum project migration.
In formula (1), Q represents target orthogonal matrix,Represent i-th data of the higher-dimension time-variable data at current time
Two-dimensional space coordinate,Represent two-dimensional space coordinate of the higher-dimension time-variable data in i-th of data of previous moment, N represents high
Tie up the number of time-variable data, Dt(Q) represent the higher-dimension time-variable data after orthogonal matrix converts at current time compared with preceding
The project migration at one moment.
Further, project migration of the higher-dimension time-variable data in two-dimensional space is minimized using target orthogonal matrix, obtained
To higher-dimension time-variable data current time projection.The regarding in dimension reduction space present invention decreases higher-dimension time-variable data as a result,
Feel disorderly, the temporal aspect of data is quickly shown, facilitates the analysis of user interaction formula, hence it is evident that promoting higher-dimension time-variable data can
Depending on changing and analysis efficiency, it can effectively meet the application demand of user.
As the preferred embodiment of the present invention, quickly to obtain target orthogonal matrix, using the rotation in orthogonal transformation
The offset that sequence mapping graph is minimized with overturning reduces solution room.I.e. using formula (1) respectively by rotating, overturning two kinds of shapes
Formula to higher-dimension time-variable data the coordinate of two-dimensional space solve.Wherein, rotation transformation may be employed as shown in formula (6)
Matrix：
In formula (6), QRotationRepresenting the orthogonal matrix of rotation transformation, θ represents the anglec of rotation in rotation transformation, therefore most
The problem of smallization sequence mapping ensemblen deviates just is reduced to solve the optimal anglec of rotation.It is turning-over changed simultaneously to may be employed such as formula (7)
Shown matrix：
In formula (7), QOverturnRepresent turning-over changed orthogonal matrix, k represents the slope of turning-over changed middle symmetry axis.
It can be simplified to find optimal symmetry axis by turning-over changed minimum offset problem.The present invention can be by traveling through
Possible angle and symmetry axis obtain most accurate orthogonal transformation scheme.
As a kind of preferred embodiment, the present invention can be using the mean deviation angle of data item in neighbor mapping figure come anti-
The anglec of rotation is reflected, so as to obtain the optimal anglec of rotation, shown in calculation formula such as formula (8)：
In formula (8), θtRepresent the anglec of rotation of t moment；Represent i-th of subpoint in t moment and t-1 respectively
The projection coordinate at quarter；N is the number of subpoint.
As the preferred embodiment for calculating optimal symmetry axis, the offset maximum on neighbor mapping figure can be used in the present invention
The near symmetrical axis of m data item is as turning-over changed symmetry axis, shown in calculation formula such as formula (9)：
In formula (9),WithIt is that offset i-th is big on t moment and t-1 moment mapping graphs respectively
Subpoint .m is the number of the maximum data item of user-defined offset；ktRepresent the slope of t moment symmetry axis.Utilize slope kt
It can obtain the optimal symmetry axis of origin.
The optimal anglec of rotation is obtained with after symmetry axis, rotating by comparing and overturning by formula (8) and formula (9)
Bias size determines appropriate orthogonal transformation, and realization most preferably is rotated or turned over converting, and obtains minimizing the dimensionality reduction mapping knot of offset
Fruit makes user obtain preferably visual cognition.
When being projected using classical multidimensional scaling algorithm, scatter diagram is selected to carry out result displaying, however as data volume
The complex distributions of increase and multidimensional data cause mutually blocking for subpoint, easily trigger vision ambiguity and the interaction of user
Difficulty, and an appropriate subpoint size is difficult selection.Therefore present invention introduces space partitioning technology, by multidimensional scaling algorithm
Scatter diagram after projection is divided into multiple subspaces, a subpoint can be represented per sub-spaces, so as to remove subpoint
Mutually block.Detailed process is as follows：
The usable equilateral triangle of the present invention and both square simplest division Polygons carry out projector space
Division.As the preferred embodiment of the present invention, space projection division is carried out using regular hexagon, it not only can be with seamless segmentation
Plane further improves visual aesthetic feeling.By using man-to-man mapping method, each subpoint can be filled
In to corresponding regular hexagon subspace.The present invention can carry out space segmentation by using as far as possible small regular hexagon and make
At most only there are one subpoints on one regular hexagon subspace.If due to subpoint increases, there are two or more throwings
Shadow point falls the situation on same regular hexagon, can be further using shown in Fig. 4 as the preferred embodiment of the present invention
Scheme considers angle minimum, other subpoints is filled into other regular hexagons apart from shortest principle, so as to ensure
One regular hexagon is at most filled only with, there are one subpoint, effectively avoiding visual disorders.Detailed description below is using shown in Fig. 4
Scheme carries out projector space division and the method for filling subpoint：
When the subspace is has more than two target projection points in regular hexagon and target subspace, according to target
Each target projection point is filled into different positive six sides by the traversal order of target projection point in subspace one by one by the following method
In shape subspace：
If current goal subpoint is first subpoint, current goal subpoint is filled in target subspace；
Otherwise, following steps are performed：
If step a. current goal subpoints fall the central spot in current subspace, step b is performed, otherwise performs step
Rapid c；
Step b. is outwards successively searched for since the current subspace, until finding positive six side in periphery being not yet filled
Shape；Current goal subpoint is filled in the periphery regular hexagon, and is target subspace by current subspace update, and then
Judge whether the point of the target projection in target subspace fills to finish, if being not filled by finishing, using next target projection point as
Current goal subpoint, which returns, performs step a；
Step c. finds the regular hexagon of two angle minimums, the angle from the adjacent regular hexagon of current subspace
Minimum regular hexagon refers to：In all adjacent regular hexagons of current subspace, the central point of regular hexagon and current son
The line of the central point in space is minimum with the angle of current goal subpoint and the line of the central point of current subspace；
Step d. selected from the regular hexagon of two angle minimums the distance of its central point and current goal subpoint compared with
A small preferred regular hexagon of conduct；
If it is preferred that regular hexagon is not filled, current goal subpoint is filled in preferred regular hexagon by step e.,
And by current subspace update be target subspace, and then judge whether the point of the target projection in target subspace fills and finish,
If being not filled by finishing, returned using next target projection point as current goal subpoint and perform step a；If it is preferred that regular hexagon
It has been be filled that, then perform step f；
Step f. is selected from two adjacent regular hexagons for having common edge with preferred regular hexagon and current subspace
In small distance one of its central point and current goal subpoint is used as suboptimum regular hexagon；If suboptimum regular hexagon is not filled out
It fills, then current goal subpoint is filled in suboptimum regular hexagon, and be target subspace by current subspace update, and then
Judge whether the point of the target projection in target subspace fills to finish, if being not filled by finishing, using next target projection point as
Current goal subpoint, which returns, performs step a；If suboptimum regular hexagon has been filled, step g is performed；
Current subspace update is the preferred regular hexagon by step g., then current goal subpoint is empty from target
Between be transferred in current subspace, and make current goal subpoint in the position of current subspace with its shift before it is empty in target
Between position it is identical, be then back to and perform step c.
With specific example, the present invention will be described in detail considers angle and the preferred embodiment of distance further below.
As a comparison, Fig. 2 shows that directly stack tetra- subpoints of A, B, C, D (all falls within to same regular hexagon
Regular hexagon 1) in effect of visualization figure.
As shown in Fig. 3 (a), tetra- subpoints of A, B, C, D sequentially fall in target subspace (to all fall within successively
In regular hexagon 1).Projector space of the higher-dimension time-variable data at current time is then divided into regular hexagon of no less than four
Space.In Fig. 3 (a), regular hexagon 2,3,4,5,6,7 is to have adjacent positive the six of common edge with current subspace (regular hexagon 1)
Side shape, they are the peripheral regular hexagon of the first level for current subspace (regular hexagon 1)；Regular hexagon 8-
19 for current subspace (regular hexagon 1), then is the peripheral regular hexagon of the second level.
During preferred embodiment shown in Fig. 4 using the present invention, according to the traversal order of target projection point, successively to first
Target projection point A, second target subpoint B, the 3rd target projection point C, the 4th target projection point D are filled.Tool
Body method is as follows：
(1) first aim subpoint A is filled first.As shown in Fig. 3 (a), since A is that first aim is thrown
Shadow point, therefore target projection point A is filled in current subspace, at this point, current subspace is target subspace (regular hexagon
1)。
(2) next second target subpoint B is filled.Since current goal subpoint B does not fall within current son
The central spot in space, therefore perform according to the following steps；
For step a. through judging, current goal subpoint B does not fall within the central point O of current subspace regular hexagon 11Place, because
This performs step c.
Step c. is by the central point O of current goal subpoint B and current subspace regular hexagon 11Connection, obtains line
O1B.By the central point of all adjacent regular hexagon 2-7 of the current subspace central point O with current subspace respectively1Connection, than
Compared with these lines and line O1The size of the angle of B.Wherein, it is minimum with angle α and β (α=β).As shown in Fig. 3 (a), α is
The central point O of regular hexagon 11With the central point O of regular hexagon 22Line (line O1O2) and line O1The angle of B, β are positive six
The central point O of side shape 11With the central point O of regular hexagon 55Line (line O1O5) and line O1The angle of B.Due to angle α and
β is minimum, therefore regular hexagon 2 and regular hexagon 5 are described " regular hexagon of angle minimum ".Perform step d.
Step d. is due to the regular hexagon that regular hexagon 2 and regular hexagon 5 are angle minimum, and therefore, it is necessary to from positive six
The conduct in small distance that its central point and current goal subpoint B are further selected in side shape 2 and regular hexagon 5 is preferred
Regular hexagon.As shown in Fig. 3 (a), due to current goal subpoint B and central point O2The distance between be less than B and central point O5It
Between distance, therefore, according to apart from shortest principle, regular hexagon 2 is selected to be filled as current goal subpoint B excellent
Select regular hexagon.
Current goal subpoint B is filled in by step e. since preferred regular hexagon (regular hexagon 2) is not filled
It is preferred that in regular hexagon (regular hexagon 2), and be target subspace (i.e. regular hexagon 1) by current subspace update.【Referring to figure
3(b)】。
(3) next the 3rd subpoint C is filled.
For step a. through judging, current goal subpoint C does not fall within the central spot of current subspace, therefore performs following step
Suddenly：
Wherein, step c to step d can refer to the filling process of above-mentioned target projection point B, according to angle minimum and apart from most
Short principle, regular hexagon 2 are the alternative preferred regular hexagon for being used to fill target projection point C.Next step e is performed.Tool
Body is as follows：
Step e., cannot be again by target since preferred regular hexagon (regular hexagon 2) has been filled by target projection point B
Subpoint C is filled in regular hexagon 2, thus continues to execute step f.
Step f. has common edge from preferred regular hexagon (regular hexagon 2) and current subspace (regular hexagon 1)
Selected in two adjacent regular hexagons (regular hexagon 3 and regular hexagon 4) distance of its central point and current goal subpoint compared with
Small one is used as suboptimum regular hexagon.Due to the central point O of regular hexagon 33With the line O of target projection point C3The length of C is small
In the central point O of regular hexagon 44With the line O of subpoint C4The length of C, thus using regular hexagon 3 as suboptimum regular hexagon.
Since suboptimum regular hexagon (regular hexagon 3) is not filled, current goal subpoint C is being filled in suboptimum just
In hexagon (regular hexagon 3), and it is target subspace (regular hexagon 1) by current subspace update.【Referring to Fig. 3 (c)】.
(4) the 4th subpoint D is filled.
For step a. through judging, current goal subpoint D does not fall within the central spot of current subspace, therefore performs following step
Suddenly：
Similarly, step b to step f can refer to the filling process of above-mentioned target projection point C, according to angle minimum and apart from most
Short principle, regular hexagon 2 are the alternative preferred regular hexagon for being used to fill target projection point D.However, due to preferred positive six side
Shape (regular hexagon 2) is filled by target projection point B, therefore target projection point D cannot be filled in regular hexagon 2 again.And
Suboptimum regular hexagon (regular hexagon 3) due to by target projection point C fill, target projection point D can not be filled in
In regular hexagon 3.Step g is continued to execute as a result,.
Step g. by current subspace update be preferred regular hexagon (i.e. regular hexagon 2), using regular hexagon 2 as newly
Current subspace.Then current goal subpoint D is being transferred to current subspace (just from target subspace (regular hexagon 1)
Hexagon 2) in, and it is preceding in target that current goal subpoint D is made to be shifted in the position of current subspace (regular hexagon 2) with it
The position in space (regular hexagon 1) is identical, and step h is continued to execute then according to the method for step c.
Shown in step h. such as Fig. 3 (c), regular hexagon 1,3,4,8,9,10 is adjacent for current subspace (regular hexagon 2)
Regular hexagon.By the central point of all adjacent regular hexagons 1,3,4,8,9,10 of current subspace (regular hexagon 2) respectively with
The central point O of current subspace (regular hexagon 2)2Connection, compares these lines and line O2The size of the angle of D.Wherein, with
Angle γ and δ are minimum (γ=δ).As shown in Fig. 3 (c), the central point O of regular hexagon 99With current subspace (regular hexagon
2) central point O2Line O9O2With line O2The angle of D is γ, the central point O of current subspace (regular hexagon 2)2With positive six
The central point O of side shape 11Line O2O1With line O2The angle of D is δ, and γ=δ.Therefore, two positive six sides of angle minimum
Shape is regular hexagon 1 and regular hexagon 9.
Step i. according to step d method, due to current goal subpoint D and central point O9The distance between be less than D with
Central point O1The distance between, therefore, according to apart from shortest principle, regular hexagon 9 is selected as current goal subpoint D institutes
The preferred regular hexagon to be filled.
Current goal subpoint D is filled in regular hexagon 9 by step j. since regular hexagon 9 is not yet filled.
After projection by current subspace update be target subspace (i.e. regular hexagon 1).
If also having more target projection points in current regular hexagon 1, return and perform step a, select according to the method described above
It selects corresponding regular hexagon and fills target projection point.
As the preferred embodiment of the present invention, each target projection point is filled into one by one according to method as shown in Figure 4
In each regular hexagon, high dimensional data can be removed and degraded to lower dimensional space, subpoint mutually blocks the vision ambiguity of initiation, uses
Family can obtain the high dimensional data not blocked and project displaying in lower dimensional space, enhance visual cognition of the user to multidimensional data.
Fig. 1 shows that the higher-dimension time-variable data shown using scatter diagram is using classical multidimensional scaling algorithm and side of the present invention
The result images comparison that method obtains, wherein, Fig. 1 (a), Fig. 1 (b) they are using shown in formula (3), formula (4) and formula (5)
The drawing result that classical multidimensional scaling algorithm obtains, due to only considering the consistency of the relative position between data, thus same number
There is very strong arbitrariness in projection at different moments according to item, very big obstacle is caused to the visual perception of user, to data
Time series pattern be difficult carry out visual pursuit；Fig. 1 (c), Fig. 1 (d) are the dimension reduction spaces shown in using formula (8) and formula (9)
Enhance the visual drawing result image of higher-dimension time-variable data of visual perception, orthogonal transform matrix is calculated, when minimizing adjacent
The subpoint offset of spacer step, enhances visual perception of the user to the temporal aspect of higher-dimension time-variable data, comparison diagram 1 (b) and Fig. 1
(d) it can be found that using inventive algorithm, the subpoint of higher-dimension time-variable data adjacent time step can be tracked clearly.
Fig. 5, which is illustrated, is using revised multidimensional scaling algorithm, and in the case of using formula (1), high dimensional data utilizes
The result images comparison that scatter diagram is shown and hexagon division space obtains.Wherein, Fig. 5 (a) is obtained using common scatter diagram
Drawing result, due in scatter diagram subpoint size be difficult definition, often there are serious eclipse phenomenas.Fig. 5 (b) is to adopt
The drawing result image obtained with regular hexagon division space, when multiple points are projected in same regular hexagon, in use
It states and considers the preferred embodiment of angle and distance and eliminate mutually blocking for subpoint.
It, can be so as to there is no the eclipse phenomena in scatter diagram as can be seen that the result images obtained using the method for the present invention
Analysis is interacted sharply, improves the visualization of higher-dimension time-variable data and analysis efficiency.
Compared with traditional higher-dimension time-variable data visualization process, sharpest edges of the invention are to obtain higher-dimension time-variable data to exist
The expression of lower dimensional space on the basis of multidimensional scaling algorithm, makes higher-dimension time-variable data in two-dimensional space by orthogonal transformation
Project migration minimizes, and user to be helped to carry out effective visual perception and tracking to interested temporal mode, enhances use
Family to higher-dimension time-variable data dimension reduction space visual perception.In addition, to avoid mutually blocking between subpoint, further draw
Enter regular hexagon to divide the projector space of higher-dimension time-variable data, it is special in dimension reduction space to high dimensional data to enhance user
The visual cognition of sign and interaction, can quick impliedly time series pattern in display data, it is visual to improve higher-dimension time-variable data
Change and analysis efficiency.It can enhance vision of the user to high dimensional data time varying characteristic in lower dimensional space using the method for the present invention
It perceives, calculates orthogonal matrix to realize and minimize higher-dimension time-variable data in the project migration of two-dimensional space, reduce multidimensional scaling
The visual disorders that algorithm is brought when analyzing time-variable data, and projector space is divided by hexagon, it eliminates between subpoint
It mutually blocks, improves the visualization of higher-dimension time-variable data and analysis efficiency.
Claims (5)
1. a kind of higher-dimension time-variable data method for visualizing of dimension reduction space visual perception enhancing, which is characterized in that including：
Higher-dimension time-variable data is read, the two-dimensional space coordinate of higher-dimension time-variable data is obtained using multidimensional scaling algorithm, uses formula
(1) higher-dimension time-variable data is solved to obtain target orthogonal matrix in the coordinate of two-dimensional space,
<mrow>
<munder>
<mrow>
<mi>arg</mi>
<mi>min</mi>
</mrow>
<mi>Q</mi>
</munder>
<msup>
<mi>D</mi>
<mi>t</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>Q</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mo>|</mo>
<msubsup>
<mi>Qv</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>v</mi>
<mi>i</mi>
<mrow>
<mi>t</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>|</mo>
<mo>|</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (1), Q represents target orthogonal matrix,Represent two dimension of the higher-dimension time-variable data in i-th of data at current time
Space coordinates,Two-dimensional space coordinate of the higher-dimension time-variable data in i-th of data of previous moment is represented, when N represents higher-dimension
Become the number of data, Dt(Q) represent higher-dimension time-variable data after orthogonal matrix converts current time compared with it is previous when
The project migration at quarter；
Project migration of the higher-dimension time-variable data in two-dimensional space is minimized using target orthogonal matrix, obtains higher-dimension time-variable data
In the projection at current time.
2. higher-dimension time-variable data method for visualizing according to claim 1, it is characterised in that：Led to respectively using formula (1)
Cross rotation, two kinds of forms of overturning to higher-dimension time-variable data the coordinate of two-dimensional space solve, correspondence obtains rotating orthogonal
Matrix, overturning orthogonal matrix calculate the higher-dimension time-variable data after rotating orthogonal matrix, overturning orthogonal matrix conversion and are working as respectively
The preceding moment compared with previous moment project migration, and select wherein with smaller project migration orthogonal matrix as target just
Hand over matrix.
3. higher-dimension time-variable data method for visualizing according to claim 1 or 2, it is characterised in that：Orthogonal using target
Matrix by higher-dimension time-variable data two-dimensional space project migration minimize after, by higher-dimension time-variable data current time throwing
Shadow space is divided into N number of above subspace, different subpoints is filled in different subspaces, obtains parameter during higher-dimension
According to the projection at current time.
4. higher-dimension time-variable data method for visualizing according to claim 3, it is characterised in that：The subspace is positive triangle
Shape, square or regular hexagon.
5. higher-dimension time-variable data method for visualizing according to claim 4, which is characterized in that when the subspace is positive six
When there is more than two target projection points in side shape and target subspace, the traversal according to target projection point in target subspace is suitable
Each target projection point is filled into different regular hexagon subspaces by sequence one by one by the following method：
If current goal subpoint is first subpoint, current goal subpoint is filled in target subspace；Otherwise,
Perform following steps：
If step a. current goal subpoints fall the central spot in current subspace, step b is performed, otherwise performs step c；
Step b. is outwards successively searched for since the current subspace, until finding a peripheral regular hexagon being not yet filled；
Current goal subpoint is filled in the periphery regular hexagon, and is target subspace by current subspace update, and then is sentenced
Whether the target projection point in disconnected target subspace, which fills, finishes, if being not filled by finishing, using next target projection point for ought
Preceding target projection point, which returns, performs step a；
Step c. finds the regular hexagon of two angle minimums from the adjacent regular hexagon of current subspace, and the angle is minimum
Regular hexagon refer to：In all adjacent regular hexagons of current subspace, the central point of regular hexagon and current subspace
Central point line and current goal subpoint and current subspace central point line angle it is minimum；
Step d. selects the in small distance of its central point and current goal subpoint from the regular hexagon of two angle minimums
One preferred regular hexagon of conduct；
If it is preferred that regular hexagon is not filled, current goal subpoint is filled in preferred regular hexagon by step e., and will
Current subspace update is target subspace, and then judges whether the point of the target projection in target subspace fills and finish, if not
Filling finishes, then is returned using next target projection point as current goal subpoint and perform step a；If it is preferred that regular hexagon by
Filling, then perform step f；
Step f. is selected wherein from two adjacent regular hexagons for having common edge with preferred regular hexagon and current subspace
Heart point and in small distance one of current goal subpoint are used as suboptimum regular hexagon；If suboptimum regular hexagon is not filled,
Then current goal subpoint is filled in suboptimum regular hexagon, and is target subspace by current subspace update, and then is sentenced
Whether the target projection point in disconnected target subspace, which fills, finishes, if being not filled by finishing, using next target projection point for ought
Preceding target projection point, which returns, performs step a；If suboptimum regular hexagon has been filled, step g is performed；
Current subspace update is the preferred regular hexagon by step g., then current goal subpoint is turned from target subspace
Move on in current subspace, and make current goal subpoint in the position of current subspace with its shift before in target subspace
Position is identical, is then back to and performs step c.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109656662A (en) * | 2018-12-14 | 2019-04-19 | 浙江财经大学 | The visualization aligning method of parallel coordinate axes based on cluster correlation |
| CN109753547A (en) * | 2018-11-19 | 2019-05-14 | 浙江财经大学 | Geographical Spatial Multi-Dimensional data visualization analysis method is arranged based on parallel coordinate axes |
| CN109763814A (en) * | 2019-01-09 | 2019-05-17 | 浙江财经大学 | Stratum matching visual analysis method based on multi-dimensional logging data |
| CN111509846A (en) * | 2020-04-17 | 2020-08-07 | 贵州电网有限责任公司 | Method and system for efficiently collecting big data of power grid |
| EP4432136A1 (en) * | 2023-03-15 | 2024-09-18 | Rohde & Schwarz GmbH & Co. KG | Computer-implemented data processing method, and measurement system |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101609510A (en) * | 2009-07-15 | 2009-12-23 | 北京交通大学 | A kind of method that image, video are carried out the dimension yojan |
| CN103942753A (en) * | 2014-05-04 | 2014-07-23 | 华东交通大学 | Multi-dimensional quantum colored image geometric transformation design and achieving method |
| CN106204625A (en) * | 2016-07-27 | 2016-12-07 | 大连理工大学 | A kind of variable focal length flexibility pose vision measuring method |
-
2017
- 2017-12-10 CN CN201711304971.5A patent/CN108073695B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101609510A (en) * | 2009-07-15 | 2009-12-23 | 北京交通大学 | A kind of method that image, video are carried out the dimension yojan |
| CN103942753A (en) * | 2014-05-04 | 2014-07-23 | 华东交通大学 | Multi-dimensional quantum colored image geometric transformation design and achieving method |
| CN106204625A (en) * | 2016-07-27 | 2016-12-07 | 大连理工大学 | A kind of variable focal length flexibility pose vision measuring method |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109753547A (en) * | 2018-11-19 | 2019-05-14 | 浙江财经大学 | Geographical Spatial Multi-Dimensional data visualization analysis method is arranged based on parallel coordinate axes |
| CN109753547B (en) * | 2018-11-19 | 2020-09-11 | 浙江财经大学 | Geographic space multi-dimensional data visual analysis method based on parallel coordinate axis arrangement |
| CN109656662A (en) * | 2018-12-14 | 2019-04-19 | 浙江财经大学 | The visualization aligning method of parallel coordinate axes based on cluster correlation |
| CN109763814A (en) * | 2019-01-09 | 2019-05-17 | 浙江财经大学 | Stratum matching visual analysis method based on multi-dimensional logging data |
| CN111509846A (en) * | 2020-04-17 | 2020-08-07 | 贵州电网有限责任公司 | Method and system for efficiently collecting big data of power grid |
| EP4432136A1 (en) * | 2023-03-15 | 2024-09-18 | Rohde & Schwarz GmbH & Co. KG | Computer-implemented data processing method, and measurement system |
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