CN104866615B - The method for visualizing that a kind of time series data sequential relationship develops - Google Patents

The method for visualizing that a kind of time series data sequential relationship develops Download PDF

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CN104866615B
CN104866615B CN201510307097.5A CN201510307097A CN104866615B CN 104866615 B CN104866615 B CN 104866615B CN 201510307097 A CN201510307097 A CN 201510307097A CN 104866615 B CN104866615 B CN 104866615B
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朱敏
贺庆来
谢昭阳
曾昂
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Sichuan University
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Abstract

The invention discloses the method for visualizing that a kind of time series data sequential relationship develops, time point upper entity total amount is corresponded to using the height mapping of transversely arranged time rectangle, using the total amount of the width mapping entity of the solid rectangular of longitudinal arrangement, using the quantity of radius and shade the mapping upper correspondent entity of corresponding time point of solid circle, using the intensity of the corresponding two inter-entity sequential relationships of width and shade mapping of details camber line, realize the multi-view analysis developed to sequential relationship and interactive exploration, the evolution of sequential relationship between time series data is expressed more simple and clearly, and there is stronger versatility, suitable for being more widely applied background and application demand.

Description

Visualization method for evolution of time sequence relation of time sequence data
Technical Field
The invention relates to the technical field of data time sequence relation analysis, in particular to a visualization method for time sequence data time sequence relation evolution.
Background
Time series data is widely existed in scientific research and daily life of people, and some time-related relation, namely time series relation, among different entities is often included. For example, the commodity purchase data includes a common purchase relationship between different commodities; the publication records contain the cooperation relationship among different organizations; the bank fund flow record contains the loan relation between different accounts. Meanwhile, the time sequence relationship can be divided into a single category relationship and a plurality of category relationships according to the relationship category. If the time sequence relations between different entities are the same category, the time sequence relations are single category time sequence relations (for example, the common purchasing relation between commodities only includes the correlation relation when the commodities are purchased); if the time sequence relationship includes different categories, the time sequence relationship is a multi-category time sequence relationship (for example, the cooperative relationship of the scientific research institutions includes the relationship of leadership, equal cooperation and following three categories).
The time sequence evolution means that the appearance, strength and other characteristics of the time sequence relationship are constantly changed along with the development of time, and a large amount of abundant information is contained in the time sequence evolution. The analysis of the evolution of the time sequence relationship can help to find the entities with the association and the characteristics of each entity, reveal the hidden relationship change trend among the entities and have profound significance for a plurality of applications and analysis requirements. Therefore, how to identify, display and explore the evolution of the time-series relationship in an intuitive and flexible manner to help users understand and extract useful knowledge from the evolution of the time-series relationship becomes a problem to be solved urgently.
Visualization technology is a technology for enhancing cognition by using a visual representation of data interaction with the perception capability of human eyes. The data is converted into sensible patterns, symbols, colors and the like to enhance the data identification efficiency and transmit effective information. Due to the intuition and high efficiency of visualization technology, the visualization technology is more and more widely applied to scientific research and practical application. At present, the visualization of the evolution of the time sequence relationship mainly focuses on two aspects of the visualization of the time sequence relationship and the visualization of the evolution of a time sequence event, and less work focuses on the evolution of the time sequence relationship. In the visualization of the time sequence relationship, the time sequence relationship is mainly displayed by establishing edges among the associated entities, and the visualization expression of the edges is enriched and strengthened by means of colors, directions, identifications and the like when the relationships of various categories are presented. However, the time sequence relationship information delivered by these methods is limited, and the evolution of the time sequence relationship cannot be shown intuitively and clearly. In the related research of the time-series event evolution visualization, most methods are based on the display mode of a time axis (timeline) and a river (river). The defects of the methods are that any one method provides limited display and exploration visual angles, and great cognitive burden is brought to a user to comprehensively analyze and understand the evolution of the time sequence relation. In addition, there are also few jobs focusing on the evolution of the time-series relationship, but these jobs are mostly concentrated on specific application fields, such as the evolution of popular vocabulary relationship, the evolution of entity relationship in stories, etc., and a visualization model with universality cannot be provided for displaying and analyzing the evolution of the time-series relationship, and cannot be applied to wider application background and application requirements.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a visualization method for representing evolution time series data time series relationship evolution of a time series relationship more intuitively and clearly, the technical solution is as follows:
a method for visualizing evolution of a time-series relationship of time-series data comprises the following steps:
1) the original time series data set D is represented as:
D＝{T,E,N,C}
wherein,
T＝{t1,t2,...,tpthe is the set of p time points in the original data;
E＝{e1,e2,...,emthe is the set of m entities in the original data;
N＝{N1,N2,...,Nmis the set of numbers in the raw data corresponding to each entity in E at p time points,
Ni＝{n1i,n2i,...,npii is more than or equal to 1 and less than or equal to m), wherein nji(1. ltoreq. j. ltoreq.p) as an entity eiAt a point in time tjThe amount of (a);
c ═ Con, Num } is the set of timing relationships between each pair of entities at each time point in the raw data, where
Con＝{Con1,Con2,...,Conm},Num＝{Num1,Num2,...,Numm}(1≤i≤m)，ConiIs a entity eiSet of all entities having a timing relationship, and ConiThe number of the elements is 0 or l (1 is more than or equal to l is less than or equal to m-1), when ConiWhen the number of the medium element is l, Numi＝{Num1i,Num2i,...,NumpiIs entity eiAnd set ConiThe set of strength values of the time sequence relation of the l entities at each time point, Numji＝{numji1,numji2,...,numjil}，numjiqAs entity eiAt a point in time tjAnd Con ofiThe strength value of the time sequence relation of the qth entity in the database, wherein q is more than or equal to 1 and less than or equal to l;
2) drawing a basic display view according to the original time sequence data set:
a) drawing a time overview view: drawing time rectangles with equal width (TW) corresponding to each time point in the set T one by one on the abscissa according to the time sequence, wherein the height TH of each time rectangle is in direct proportion to the sum of all the entity numbers at the corresponding time point, and any time point TjHigh TH of corresponding time rectanglejComprises the following steps:
THj＝k1(nj1+nj2+...+njm)；
b) and (3) drawing an entity overview view: drawing a rectangle of Equal Height (EH) entity corresponding to each entity in the set E one by one on the ordinate, wherein the width EW of the rectangle of entity is proportional to the sum of the number of corresponding entities at all time points, and any entity EiWide EW of corresponding solid rectangleiComprises the following steps:
EWi＝k2(n1i+n2i+...+npi)；
c) drawing an overall relation evolution view: drawing a solid circle and a detail arc line between the abscissa and the ordinate, wherein the center of the solid circle is located at the intersection of the longitudinal central axis of the time rectangle and the transverse central axis of the solid rectangle, the radius ER of the solid circle is in direct proportion to the number of corresponding entities at corresponding time points, and any entity eiAt any point in time tjRadius ER of upper corresponding solid circlejiComprises the following steps:
ERji＝k3nji；
the detail arc line is connected with each pair of entity circles corresponding to the same time point, the width DAW of the detail arc line is in direct proportion to the strength value of the time sequence relation existing between the two entities corresponding to the pair of entity circles at the time point, and at any time point tjTo connect any entity eiCorresponding entity circle and its timing relation set ConiWidth DAW of detail arc of solid circle corresponding to q-th solidjiqComprises the following steps:
DAWjiq＝k4numjiq；
wherein k is1、k2、k3、k4Is a scaling factor.
Furthermore, drawing a detail relation evolution view for showing the detail evolution of the time sequence relation between a certain pair of entities; firstly, drawing a horizontal axis representing a time point and a vertical axis representing a percentage scale (ranging from 0.0 to 1.0), and then drawing a color bar representing the evolution of the time sequence relation between the horizontal axis and the vertical axis; the drawing method of the color band comprises the following steps: calculating the percentage of the intensity value of each pair of time sequence relations at the corresponding time point to the sum of the intensity values of all the time sequence relations at the time point, sequencing the percentages from large to small, obtaining the arrangement position of the interested time sequence relation in the longitudinal axis according to the percentage value and the sequencing position, and determining the highest point and the lowest point of the color band at the corresponding time point according to the arrangement position; and connecting all the highest points on each time point in sequence by using a straight line, and then connecting all the lowest points on each time point in sequence to form the color band.
Further, the method also comprises the following steps: determining the width TW of the time rectangle according to the number p of time points in the original data, determining the height EH of the entity rectangle according to the number m of the entities:
wherein, w1、w2、w3And h1、h2、h3Is a preset number, and w1>w2>w3，h1＞h2＞h3；p1And p2Is a time number threshold, and p1＜p2；m1And m2Is a threshold of the number of entities, and m1＜m2。
Furthermore, the method comprises the following steps of highlighting the interested entity by adjusting the high EH of the entity rectangle and the radius ER of the entity circle in the basic display view, and comprises the following specific steps:
selecting an entity of interest eSFinding an entity e from said set ConSSet Con of all entities having a time-series relationshipSForming a new set Select, { e }S,ConS}; judging each entity E in the set EiWhether the entity belongs to the set Select or not, if so, adjusting the high EH of the entity rectangle corresponding to the entityiAnd the radius ER of the entity circle at all time points corresponding to the entityiIncreasing; otherwise, the above-mentioned value is adjusted to be reduced, i.e.
Wherein, EH'iAnd ER'iTo optimize the presentation of the values, f1And f2Is a scaling factor, and f1＞1,f2＞1。
Further, the method also comprises the following steps: and (3) optimally calculating the numerical values of the following elements by adopting a logarithm mapping method: height TH of time rectangle, width EW of solid rectangle, radius ER of solid circle, and width DAW of detail arc:
TH′＝a1log(TH)+b1
EW′＝a2log(EW)+b2
ER′＝a3log(ER)+b3
DAW′＝a4log(DAW)+b4
wherein, TH, EW, ER and DAW are basic values, and TH ', EW', ER 'and DAW' are display values displayed in the view after mapping; a is1、a2、a3、a4、b1、b2、b3、b4To correct the parameters.
Further, the method also comprises the following steps: mapping the number of corresponding entities at corresponding time points by the color depth of the entity circle, specifically: dividing the whole numerical range of the corresponding entity number at the corresponding time point into x1Dividing into equal parts, selecting x with different shade of same color system1And determining the color of the entity circle according to the corresponding color from light to dark from small to large of the number of the entities.
Further, the method also comprises the following steps: mapping the intensity of the corresponding time sequence relation by the color depth of the detail arc, specifically: dividing the whole numerical range of the time sequence relation strength numerical value of the corresponding entity at the corresponding time point into x2Dividing into equal parts, selecting x with different shade of same color system2And determining the color of the detail arc according to the fact that the number of the entities is from small to large and the corresponding color is from light to dark.
Further, the method includes drawing a general arc in the entity overview view, the general arc connecting the entity rectangles corresponding to each pair of entities having a general relationship, the width GAW of the general arc being proportional to the strength value of the general relationship existing between the pair of entities, and connecting the entities eiWith its set of timing relationships ConiTotal arc of two entity rectangles corresponding to the q-th entityWidth GAW ofiqComprises the following steps:
GAWiq＝k5(num1iq+num2iq+...+nmupiq)
wherein k is5Is a scaling factor.
Further, the method also comprises the following steps: and (3) optimally calculating the width GAW of the overall arc by adopting a logarithmic mapping method:
GAW′＝a5log(GAW)+b5
wherein, GAW is an original numerical value, and GAW' is a basic display numerical value displayed in the view after mapping; a is5And b5To correct the parameters.
Further, the method also comprises the following steps: mapping the size of the corresponding overall relationship strength by the color depth of the overall arc line, specifically: dividing the overall numerical range of the overall relationship strength numerical values of the corresponding entities into x3Dividing into equal parts, selecting x with different shade of same color system3And determining the color of the general arc according to the relationship strength value from small to large and the corresponding color from light to dark.
The invention has the beneficial effects that: the invention adopts the height of the transversely arranged time rectangles to map the total amount of the entities on the corresponding time points, adopts the width of the longitudinally arranged entity rectangles to map the total amount of the entities, adopts the radius of the entity circle and the color depth to map the number of the corresponding entities on the corresponding time points, adopts the width of the detail arc line and the color depth to map the strength of the time sequence relation between the two entities, realizes the multi-view analysis and interactive exploration on the evolution of the time sequence relation, expresses the evolution situation of the time sequence relation between the time sequence data more intuitively and clearly, has stronger universality and is suitable for wider application background and application requirements.
Drawings
FIG. 1 is a schematic view of a visual interface of time series data according to the present invention.
Fig. 2 is a visualization effect diagram of shopping record data of a supermarket for 12 days.
FIG. 3 is a comparison diagram of the time sequence evolution of the common purchasing relationship of different commodities in the supermarket: (a) "snack (snack)"; (b) "seasoning".
Detailed Description
The invention is further illustrated by the following specific examples: the system prototype Revoler interface of the visual view realized by the invention is shown in FIG. 1:
(1) time overview view, fig. 1 (a): the time points can be arranged from left to right in a time sequence from large to small or from small to large, the height of the rectangle corresponding to each time point corresponds to the total amount of the related entities at the time point, and the larger the total amount, the higher the rectangle.
Entity overview view, fig. 1 (B): for representing the distribution of the total amount of entities in the data set, each rectangle corresponding to each entity, the width of the rectangle representing the total amount of the corresponding entity, the larger the total amount the wider the rectangle.
Overall relationship evolution view, fig. 1 (C): the system is used for displaying the overall relationship evolution situation, and mainly observing and analyzing the relationship distribution and the rough change situation of the entities interested by the user in the whole time period, wherein each circle corresponds to the number of each entity at each time point, and the larger the number is, the larger the circle radius is.
Detail relationship evolution view, fig. 1 (D): the method is used for displaying the detail evolution of the relationship between two selected entities, and the percentage, the ranking and the variation trend of the relationship in all the relationships displayed in the overall relationship evolution view can be accurately analyzed. The wider the color bar, the higher the percentage of the color bar in all the relations, and the higher the highest point of the color bar, the more forward the rank.
Relationship legend, fig. 1 (E): and explaining the relationship category represented by each color in the visual view and the corresponding relationship strength of the relationship category.
The specific method for displaying the original time sequence data according to the model comprises the following steps:
1) the original time series data set D is represented as:
D＝{T,E,N,C}
wherein,
T＝{t1,t2,...,tpthe is the set of p time points in the original data;
E＝{e1,e2,...,emthe is the set of m entities in the original data;
N＝{N1,N2,...,Nmis the set of numbers in the raw data corresponding to each entity in E at p time points,
Ni＝{n1i,n2i,...,npii is more than or equal to 1 and less than or equal to m), wherein nji(1. ltoreq. j. ltoreq.p) as an entity eiAt a point in time tjThe amount of (a);
c ═ Con, Num } is the set of timing relationships between each pair of entities at each time point in the raw data, where
Con＝{Con1,Con2,...,Conm},Num＝{Num1,Num2,...,Numm}(1≤i≤m)，ConiIs a entity eiSet of all entities having a timing relationship, and ConiThe number of the elements is 0 or l (1 is more than or equal to l is less than or equal to m-1), when ConiWhen the number of the medium element is l, Numi＝{Num1i,Num2i,...,NumpiIs entity eiAnd set ConiThe set of strength values of the time sequence relation of the l entities at each time point, Numji＝{numji1,numji2,...,numjil}，numjiqAs entity eiAt a point in time tjAnd Con ofiThe strength value of the time sequence relation of the qth entity in the database, wherein q is more than or equal to 1 and less than or equal to l;
2) drawing a basic display view according to the original time sequence data set:
a) drawing a time overview view: drawing time rectangles with equal width (TW) corresponding to each time point in the set T one by one on the abscissa according to the time sequence, wherein the height TH of each time rectangle is in direct proportion to the sum of all the entity numbers at the corresponding time point, and any time point TjHigh TH of corresponding time rectanglejComprises the following steps:
THj＝k1(nj1+nj2+...+njm)；
b) and (3) drawing an entity overview view: drawing a rectangle of Equal Height (EH) entity corresponding to each entity in the set E one by one on the ordinate, wherein the width EW of the rectangle of entity is proportional to the sum of the number of corresponding entities at all time points, and any entity EiWide EW of corresponding solid rectangleiComprises the following steps:
EWi＝k2(n1i+n2i+...+npi)；
c) drawing an overall relation evolution view: drawing a solid circle and a detail arc line between the abscissa and the ordinate, wherein the center of the solid circle is located at the intersection of the longitudinal central axis of the time rectangle and the transverse central axis of the solid rectangle, the radius ER of the solid circle is in direct proportion to the number of corresponding entities at corresponding time points, and any entity eiAt any point in time tjRadius ER of upper corresponding solid circlejiComprises the following steps:
ERji＝k3nji；
the detail arc line is connected with each pair of entity circles corresponding to the same time point, the width DAW of the detail arc line is in direct proportion to the strength value of the time sequence relation existing between the two entities corresponding to the pair of entity circles at the time point, and at any time point tjTo connect any entity eiCorresponding entityCircle and its timing relation set ConiWidth DAW of detail arc of solid circle corresponding to q-th solidjiqComprises the following steps:
DAWjiq＝k4numjiq；
wherein k is1、k2、k3、k4Is a scaling factor.
On the basis of the above embodiment, the method further comprises the following steps: drawing a detail relation evolution view for showing the detail evolution of the time sequence relation between a certain pair of entities; firstly, drawing a horizontal axis representing a time point and a vertical axis representing a percentage scale (ranging from 0.0 to 1.0), and then drawing a color bar representing the evolution of the time sequence relation between the horizontal axis and the vertical axis; the drawing method of the color band comprises the following steps: calculating the percentage of the intensity value of each pair of time sequence relations at the corresponding time point to the sum of the intensity values of all the time sequence relations at the time point, sequencing the percentages from large to small, obtaining the arrangement position of the interested time sequence relation in the longitudinal axis according to the percentage value and the sequencing position, and determining the highest point and the lowest point of the color band at the corresponding time point according to the arrangement position; and connecting all the highest points on each time point in sequence by using a straight line, and then connecting all the lowest points on each time point in sequence to form the color band. Wherein, the percentage of the intensity value of the interested time sequence relation at each time point corresponds to the width of the color band; the percentage sorting position determines the longitudinal highest point of the color strip, and the higher the highest point is, the more forward the sorting position is; the straight lines between the time points represent the trend of the relationship. For example, there are 3 time-series relationships at a certain point in time: re1、Re2And Re3The percentage of the intensity value of each pair of time sequence relations to the sum of the intensity values of all the time sequence relations at the time point is respectively as follows: 50%, 30%, 20%; if Re1For the interesting time sequence relationship, the highest point of the color band at the time point is 1, and the lowest point of the color band is 0.5, because the percentage of the color band is named as 1 st and the width of the color band is 0.5; if Re2For the timing relationship of interest, since the percentage is named 2 nd and the width of the color bar is 0.3, the highest point of the color bar at this time point is 0.5 and the lowest point is 0.2.
When the time sequence relation is a single-type time sequence relation, displaying a single color bar on the interface; when the time sequence relationship is a multi-category time sequence relationship, the stacked color bands with different colors are displayed in the interface according to the change of each relationship, wherein each color band corresponds to one time sequence relationship, and the whole color band represents the detail evolution of the multi-category time sequence relationship.
On the basis of the above embodiment, the method further comprises the following steps: determining the width TW of a time rectangle according to the number p of time points in the original data, determining the height EH of an entity rectangle according to the number m of entities, and obtaining proper display dimensions and reasonably utilizing drawing space under different data sets:
wherein, w1、w2、w3And h1、h2、h3Is a preset number, and w1>w2>w3，h1＞h2＞h3；p1And p2Is a time number threshold, and p1＜p2；m1And m2Is a threshold of the number of entities, and m1＜m2The intermediate number threshold and the entity number threshold may be set differently according to different data sets. When the number m of entities or the number p of time points exceeds the display range of the drawing space, the "data overview" can be selected, and the height EH of the entity rectangle or the width TW of the time rectangle is correspondingly adjusted to the minimum value, so as to help the user to see more data information.
On the basis of the above embodiment, the method further comprises the following steps: when a user selects an entity to observe the evolution of the time sequence relationship between the entity and the related entity, the entity in the basic display view can be adjustedThe high EH of the entity rectangle corresponding to the body and the semi-ER diameter of the entity circle highlight the interested entity, so that the time sequence relationship is more convenient and clear to analyze and explore. The specific method comprises the following steps: selecting an entity of interest eSFinding an entity e from said set ConSSet Con of all entities having a time-series relationshipSForming a new set Select, { e }S,ConS}; judging each entity E in the set EiWhether the entity belongs to the set Select or not, if so, adjusting the high EH of the entity rectangle corresponding to the entityiAnd the radius ER of the entity circle at all time points corresponding to the entityiIncreasing; otherwise, the above-mentioned value is adjusted to be reduced, i.e.
Wherein, EH'iAnd ER'iTo optimize the presentation of the values, f1And f2Is a scaling factor, and f1＞1,f2＞1。
On the basis of the above embodiment, the method further comprises the following steps: and (3) optimally calculating the numerical values of the following elements by adopting a logarithm mapping method: the height TH of the time rectangle, the width EW of the solid rectangle, the radius ER of the solid circle, and the width DAW of the detail arc. Because of the ubiquitous large data difference in the original data set, the method adopts logarithmic mapping for better visual effect on the basis of keeping the original data difference. The expression is as follows:
TH′＝a1log(TH)+b1
EW′＝a2log(EW)+b2
ER′＝a3log(ER)+b3
DAW′＝a4log(DAW)+b4
wherein, TH, EW, ER and DAW are basic values, and TH ', EW', ER 'and DAW' are display values displayed in the view after mapping; a is1、a2、a3、a4、b1、b2、b3、b4For correcting the parameters, different mapping data are correspondingly adjusted by adopting different correction parameters.
On the basis of the above embodiment, the method further comprises the following steps: mapping the number of corresponding entities at corresponding time points by the color depth of the entity circle, specifically: dividing the whole numerical range of the corresponding entity number at the corresponding time point into x1Dividing into equal parts, selecting x with different shade of same color system1And determining the color of the entity circle according to the corresponding color from light to dark from small to large of the number of the entities. On the basis of the above embodiment, the method further comprises the following steps: mapping the intensity of the corresponding time sequence relation by the color depth of the detail arc, specifically: dividing the whole numerical range of the time sequence relation strength numerical value of the corresponding entity at the corresponding time point into x2Dividing into equal parts, selecting x with different shade of same color system2And determining the color of the detail arc according to the fact that the number of the entities is from small to large and the corresponding color is from light to dark. If there are multiple categories of timing relationships, each timing relationship can be distinguished by a different color family of colors.
On the basis of the above embodiment, the method further comprises the following steps: drawing a general arc line in the entity overview view, wherein the general arc line is connected with the entity rectangle corresponding to each pair of entities with general relation, the width GAW of the general arc line is in direct proportion to the strength value of the general relation existing between the pair of entities, and the general arc line is connected with an entity eiWith its set of timing relationships ConiWidth GAW of overall arc of two entity rectangles corresponding to the q-th entityiqComprises the following steps:
GAWiq＝k5(num1iq+num2iq+...+nmupiq)
wherein k is5Is a scaling factor.
On the basis of the above embodiment, the method further comprises the following steps: and (3) optimally calculating the width GAW of the overall arc by adopting a logarithmic mapping method:
GAW′＝a5log(GAW)+b5
wherein, GAW is an original numerical value, and GAW' is a basic display numerical value displayed in the view after mapping; a is5And b5To correct the parameters.
On the basis of the above embodiment, the method further comprises the following steps: mapping the size of the corresponding overall relationship strength by the color depth of the overall arc line, specifically: dividing the overall numerical range of the overall relationship strength numerical values of the corresponding entities into x3Dividing into equal parts, selecting x with different shade of same color system3And determining the color of the general arc according to the relationship strength value from small to large and the corresponding color from light to dark.
For example: four different colors c1，c2，c3，c4When a solid circle, a detail arc or a general arc is displayed, the mapping can be performed according to the following method:
(1) acquiring a maximum value Max, a minimum value Min and a numerical range extension of data to be mapped;
(2) the original data value is divided according to the following segmentation functionxMapping to color c for presentationx：
In order to verify the usefulness and the effectiveness of the invention, a time sequence relationship evolution visualization method in the invention of supermarket shopping record data is selected for verification. The shopping record data of 12 days in a supermarket selected in the embodiment includes 7694 shopping records, and relates to 33 commodity categories, and the shopping record data is used for analyzing the evolution of the common purchasing relationship of commodities when the commodities are purchased. The data is processed and visually displayed by the method provided by the invention, and the visual result is obtained as shown in fig. 2.
From fig. 2, basic information about this data can be acquired as follows:
(1) total daily sales in the supermarket: from the comparison of the heights of the transverse rectangles, it can be seen that the pin count is highest at "20060420" and lowest at "20060425".
(2) The sale condition of each commodity class in the supermarket is as follows: from the comparison of the widths of the longitudinal rectangles, it can be seen that the sales of the items "drink", "biscuit", "snack" are high.
(3) Distribution of sales for each commodity class on a daily basis: for example, for the category "biscuit", it can be seen that the variation thereof is approximately consistent with the overall sales represented by the horizontal rectangle according to the size and the color depth of the entity diagram corresponding thereto, the sales are higher at "200060415" and "20060420", and the sales are the lowest at "20060425".
(4) Overall association of goods: according to the arc line connecting the entity rectangles on the left side of the view, each pair of entities with a time sequence relationship can be seen. For example, in fig. 2, "snack" is associated with "sweet", "drink", and "biscuit". Meanwhile, according to the color depth and thickness of the arc line, the strongest correlation between the snack and the biscuit can be seen.
Then, selecting a solid rectangle marked as "snack" on the left, and analyzing the evolution of the overall relationship, wherein the result is shown in the overall relationship evolution view in fig. 3 (a): it can be seen that:
(1) appearance of time sequence relation and evolution of intensity: in general, the relationship of "snack" to the other three associated entities persists during this time period. The relationship between 20060415 and 20060420 is very obvious, and the relationship between 20060413 and 20060425 is weaker. This is largely related to the sales volume of the current commodity, and it is presumed that the common purchasing relationship due to the common purchasing behavior changes accordingly, depending on the influence of the sales volume.
(2) The timing relationship preference evolves: "snack" has no strongest or weakest relationship with a commodity that is stable at all times, and the relative timing relationship strength changes. For example, at "20060414", "snack" and "bisguit" are the most relevant; but the relationship between "20060419", "snack" and "drink" is strongest.
Next, any detail arc representing the relationship between "snap" and "biscure" is selected, and the evolution of the detail time series relationship is further analyzed, and the result is shown in the detail relationship evolution view in fig. 3 (a):
from "20060413" to "20060425", the strength of the time series relationship is 0.6, 0.5,0.3, 0.5, 0.5,0.3,0.3,0.6, 0.4,0.2, 0.8,0.3 in all the relationships relating to "snack", respectively. From the ranking, at several time points of "20060413", "20060414", "20060416", "20060417", "20060421", "20060424", it is the dominant relationship; at "20060419" and "20060423", the ranking is last compared to other correlations. Trending, the relationship strength is weak in the time periods from "20060414" to "20060415", "20060417" to "20060419", "20060421" to "20060423", and "20060424" to "20060425"; the ranking trend is enhanced from "20060415" to "20060416", "20060419" to "20060421", "20060423" to "20060424"; the relationship ranking remains for the remaining time periods.
In addition, different attributes of different entities can be found through comparison of time sequence relations and evolution thereof of the different entities. The timing relationship between the two entities "snack" and "seasoning" is shown in fig. 3(a) and (b), and the comparison shows that the timing relationship between "snack" is more stable and obvious, indicating that it belongs to hot goods in the common purchase. In contrast, "seasoning" has an insignificant and variable chronological relationship with other entities, indicating that it belongs to a more "independent" commodity and is not distinguished from the characteristics of other commodities purchased together.

Claims (10)

1. A method for visualizing evolution of a time-series relationship of time-series data is characterized by comprising the following steps:
1) the original time series data set D is represented as:
D＝{T,E,N,C}
wherein,
T＝{t1,t2,...,tpthe is the set of p time points in the original data;
E＝{e1,e2,...,emthe is the set of m entities in the original data;
N＝{N1,N2,...,Nmis the set of numbers in the raw data corresponding to each entity in E at p time points,
Ni＝{n1i,n2i,...,npi1 is more than or equal to i and less than or equal to m, wherein njiAs entity eiAt a point in time tjJ is more than or equal to 1 and less than or equal to p;
c ═ Con, Num } is the set of timing relationships between each pair of entities at each time point in the raw data, where
Con＝{Con1,Con2,...,Conm},Num＝{Num1,Num2,...,Numm}，1≤i≤m，ConiIs a entity eiSet of all entities having a timing relationship, and ConiThe number of the medium elements is 0 or l, l is more than or equal to 1 and less than or equal to m-1, when ConiWhen the number of the medium element is l, Numi＝{Num1i,Num2i,...,NumpiIs entity eiAnd set ConiThe set of strength values of the time sequence relation of the l entities at each time point, Numji＝{numji1,numji2,...,numjil}，numjiqAs entity eiAt a point in time tjAnd Con ofiThe strength value of the time sequence relation of the qth entity in the database, wherein q is more than or equal to 1 and less than or equal to l;
2) drawing a basic display view according to the original time sequence data set:
a) drawing a time overview view: drawing time rectangles with equal width (TW) corresponding to each time point in the set T one by one on the abscissa according to the time sequence, wherein the height TH of each time rectangle is in direct proportion to the sum of all the entity numbers at the corresponding time point, and any time point TjHigh TH of corresponding time rectanglejComprises the following steps:
THj＝k1(nj1+nj2+...+njm)；
b) and (3) drawing an entity overview view: drawing a rectangle of Equal Height (EH) entity corresponding to each entity in the set E one by one on the ordinate, wherein the width EW of the rectangle of entity is proportional to the sum of the number of corresponding entities at all time points, and any entity EiCorresponding entityWide EW of rectangleiComprises the following steps:
EWi＝k2(n1i+n2i+...+npi)；
c) drawing an overall relation evolution view: drawing a solid circle and a detail arc line between the abscissa and the ordinate, wherein the center of the solid circle is located at the intersection of the longitudinal central axis of the time rectangle and the transverse central axis of the solid rectangle, the radius ER of the solid circle is in direct proportion to the number of corresponding entities at corresponding time points, and any entity eiAt any point in time tjRadius of upper corresponding solid circle
ERjiComprises the following steps:
ERji＝k3nji；
the detail arc line is connected with each pair of entity circles corresponding to the same time point, the width DAW of the detail arc line is in direct proportion to the strength value of the time sequence relation existing between the two entities corresponding to the pair of entity circles at the time point, and at any time point tjTo connect any entity eiCorresponding entity circle and its timing relation set ConiWidth DAW of detail arc of solid circle corresponding to q-th solidjiqComprises the following steps:
DAWjiq＝k4numjiq；
wherein k is1、k2、k3、k4Is a scaling factor.
2. The method for visualizing evolution of time series relationship of time series data according to claim 1, wherein a detail relationship evolution view is drawn for showing detail evolution of time series relationship between a pair of entities; firstly, drawing a horizontal axis representing a time point and a vertical axis representing a percentage scale in a range of 0.0-1.0, and then drawing a color band representing the evolution of the time sequence relation between the horizontal axis and the vertical axis; the drawing method of the color band comprises the following steps: calculating the percentage of the intensity value of each pair of time sequence relations at the corresponding time point to the sum of the intensity values of all the time sequence relations at the time point, sequencing the percentages from large to small, obtaining the arrangement position of the interested time sequence relation in the longitudinal axis according to the percentage value and the sequencing position, and determining the highest point and the lowest point of the color band at the corresponding time point according to the arrangement position; and connecting all the highest points on each time point in sequence by using a straight line, and then connecting all the lowest points on each time point in sequence to form the color band.
3. The method for visualizing evolution of time-series data time-series relationship according to claim 1, further comprising: determining the width TW of the time rectangle according to the number p of time points in the original data, determining the height EH of the entity rectangle according to the number m of the entities:
wherein, w1、w2、w3And h1、h2、h3Is a preset number, and w1>w2>w3，h1＞h2＞h3；p1And p2Is a time number threshold, and p1＜p2；m1And m2Is a threshold of the number of entities, and m1＜m2。
4. The method for visualizing evolution of time series data time series relationship according to claim 1, further comprising highlighting the entity of interest by adjusting high EH of entity rectangle and radius ER of entity circle in the base presentation view by:
selecting an entity of interest eSFinding an entity e from said set ConSSet Con of all entities having a time-series relationshipSForming a new set Select, { e }S,ConS}; judging each entity E in the set EiWhether the entity belongs to the set Select or not, if so, adjusting the high EH of the entity rectangle corresponding to the entityiAnd the radius ER of the entity circle at all time points corresponding to the entityiIncreasing; otherwise, the above-mentioned value is adjusted to be reduced, i.e.
Wherein, EHi' and ERi' to optimize the display of the values, f1And f2Is a scaling factor, and f1＞1,f2＞1。
5. The method for visualizing evolution of time-series data time-series relationship according to claim 1, further comprising: and (3) optimally calculating the numerical values of the following elements by adopting a logarithm mapping method: height TH of time rectangle, width EW of solid rectangle, radius ER of solid circle, and width DAW of detail arc:
TH′＝a1log(TH)+b1
EW′＝a2log(EW)+b2
ER′＝a3log(ER)+b3
DAW′＝a4log(DAW)+b4
wherein, TH, EW, ER and DAW are basic values, and TH ', EW', ER 'and DAW' are display values displayed in the view after mapping; a is1、a2、a3、a4、b1、b2、b3、b4To correct the parameters.
6. The method for visualizing evolution of time-series data time-series relationship according to claim 1, further comprising: mapping the number of corresponding entities at corresponding time points by the color depth of the entity circle, specifically: dividing the whole numerical range of the corresponding entity number at the corresponding time point into x1Equally dividing, selecting depth of same color systemShallow difference x1And determining the color of the entity circle according to the corresponding color from light to dark from small to large of the number of the entities.
7. The method for visualizing evolution of time-series data time-series relationship according to claim 1, further comprising: mapping the intensity of the corresponding time sequence relation by the color depth of the detail arc, specifically: dividing the whole numerical range of the time sequence relation strength numerical value of the corresponding entity at the corresponding time point into x2Dividing into equal parts, selecting x with different shade of same color system2And determining the color of the detail arc according to the fact that the number of the entities is from small to large and the corresponding color is from light to dark.
8. The method of visualizing evolution of a time-series relationship of data as claimed in any of claims 1 to 7, further comprising drawing a general arc in said entity overview view, said general arc connecting the entity rectangles corresponding to each pair of entities having a general relationship, the width GAW of said general arc being proportional to the magnitude of the general relationship existing between said pair of entities, connecting the entities eiWith its set of timing relationships ConiWidth GAW of overall arc of two entity rectangles corresponding to the q-th entityiqComprises the following steps:
GAWiq＝k5(num1iq+num2iq+...+nmupiq)
wherein k is5Is a scaling factor.
9. The method for visualizing evolution of time-series data time-series relationship according to claim 8, further comprising: and (3) optimally calculating the width GAW of the overall arc by adopting a logarithmic mapping method:
GAW′＝a5log(GAW)+b5
wherein, GAW is an original numerical value, and GAW' is a basic display numerical value displayed in the view after mapping; a is5And b5To correct the parameters.
10. The method for visualizing evolution of time-series data time-series relationship according to claim 8, further comprising: mapping the size of the corresponding overall relationship strength by the color depth of the overall arc line, specifically: dividing the overall numerical range of the overall relationship strength numerical values of the corresponding entities into x3Dividing into equal parts, selecting x with different shade of same color system3And determining the color of the general arc according to the relationship strength value from small to large and the corresponding color from light to dark.
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