ERMO DG: Evolving Region Moving Object Dataset Generator. Authors: B. Aydin, R. Angryk, K. G. Pillai Presented by Micheal Schuh May 21, 2014

Transcription

1 ERMO DG: Evolving Region Moving Object Dataset Generator Authors: B. Aydin, R. Angryk, K. G. Pillai Presented by Micheal Schuh May 21, 2014

2 Introduction Spatiotemporal pattern mining algorithms Motivation from different scientific domains Real life datasets Synthetic dataset generator Instances of ERMO-DG have polygon representations their shapes evolve move Highly parametrized 2

3 Motivation Benchmark for spatiotemporal pattern mining algorithms creates co-occurrence patterns with foreseeable characteristics Verification purposes Different sized datasets can be created to test efficiency, scalability, correctness, and completeness of spatiotemporal pattern mining algorithms. 3

4 Concepts Spatial Framework Feature Type Instance Pattern 4

5 Concepts Spatial Framework Rectangle where instances are created, defined with D 1, D 2. (0,0) (D 1, D 2 ) 5

6 Concepts Feature Type List of attributes that will be utilized while creating the instances Attributes Min Vertex, Max Vertex Min Area, Max Area Min AreaEvol, Max AreaEvol Min Lifetime, Max Lifetime Min Velocity, Max Velocity Description Minimum and maximum number of vertices Minimum and maximum area Minimum and maximum factor of increase in area Minimum and maximum life duration Minimum and maximum velocity Min Acceleration, Max Acceleration Minimum and maximum acceleration 6

7 Concepts Instance Spatiotemporal instance, ordered list of timestamp, polygons. {(t i, polygon i ), (t i+1, polygon i+1 ),...} t i polygon i t j t k polygon j polygon k 7

8 Concepts Pattern A subset of distinct feature types Cardinality Core patterns: More frequently occurring patterns Overlap patterns: A superset of core patterns, created by adding one more feature type to core patterns. 8

9 Concepts Patterns ABCD BCD 3-cardinality overlap pattern ABC ABD ACD BCD AB AC AD BC BD CD BC 2-cardinality core pattern A B C D 9

10 Dataset Generation Input Parameters Parameter Name Description Parameter Name Description D 1 Horizontal dimension of spatial framework Base Acceleration Base acceleration parameter D 2 Vertical dimension of spatial framework F Count Total number of feature types GlobalMax Vertex Maximum number of vertices allowed N Core Number of core patterns Base Area Base area parameter S Overlap Number of overlap patterns for each core pattern Base AreaEvol Base areal evolution parameter S Inst Number of instances to be created for each pattern Base Lifetime Base lifetime parameter M SpN Number of spatial neighborhoods to be created for each pattern Base Velocity Base velocity parameter L Noise Ratio of noise instances 10

11 Creating Feature Types F Count feature types to create Base parameters for deciding minimum and maximum attribute values of a feature type Attribute values are generated using a procedure (described in next slides) that randomly picks those values Moreover, this procedure discretizes the attribute values 11

12 Creating Feature Types Feature Attributes How to find? Min Vertex - Max Vertex We generate two random numbers between 3 and GlobalMax Vertex. Min Area - Max Area Generate a random integer R Attr from {1,2,3,4,5} Generate a random integer r Attr from {0,1,,Base Attr } Min Velocity - Max Velocity Then, Min Attr = Base Attr * R Attr Min Lifetime - Max Lifetime Max Attr = Min Attr + r Attr (Attr stands for Area, Velocity, Lifetime and Acceleration and Min Acceleration - Max Acceleration each of them.) corresponding base parameters and random values R and r differ for 12

13 Creating Feature Types Feature Attributes How to find? Generate a random real number ev between [-2,2]. Next, ceil = ceiling(ev) floor = floor(ev) Min AreaEvol - Max AreaEvol Then, Min AreaEvol = (BaseAreaEvol) floor Max AreaEvol = (BaseAreaEvol) ceil 13

14 Creating Feature Types Example F Count = 5 we will create 5 features {f 1, f 2, f 3, f 4, f 5 } For each f i Generate maximum and minimum attributes Global MaxVertex = 10 Base Velocity = 20 Base AreaEvol = 3 Min Vertex - Max Vertex Min Velocity - Max Velocity Min AreaEvol - Max AreaEvol Generate two random integers between 3 and Global MaxVertex. Suppose 5 and 9 generated Min Vertex 5 Max Vertex 9 Generate R velocity ϵ {1,2,3,4,5} Suppose 4 Min Velocity = 4 * Base Velocity = 80 Min Velocity 80 Generate r velocity ϵ [0,Base ] Velocity Suppose 11 Max Velocity = Min Velocity + r Velocity Max Velocity 91 Generate ev ϵ (-2,2) Suppose ev = ceil(ev) = 0 floor(ev) = -1 Min ArealEvol 3-1 Max ArealEvol

15 Creating Patterns Core Patterns More frequently occurring Overlap Patterns Each associated with a core pattern Used for achieving higher support for core patterns 15

16 Creating Patterns Core Patterns N Core patterns to be created One core pattern for each cardinality is created Starting from 2-cardinality Cardinality of last core pattern: N Core +1 For a k-cardinality core pattern, algorithm selects k distinct feature types, and adds them to pattern s feature set. 16

17 Creating Patterns Overlap Patterns Each overlap pattern is associated with a core pattern, specifically for the purpose of having core patterns more frequent. For each core pattern We generate S Overlap overlap patterns For a k-cardinality core pattern We generate S Overlap distinct overlap patterns by adding one more feature type to the associated core pattern s feature set. 17

18 Creating Patterns Example Features are {f 1, f 2, f 3, f 4, f 5 } Suppose N Core =2 and S Overlap =2 Then two core patterns 2-cardinality: Suppose {f 1, f 4 } 3-cardinality: Suppose {f 2, f 3, f 4 } After core patterns ({f 1, f 2 }, {f 2, f 3, f 4 }) created For each core pattern, create two overlap patterns For {f 1,f 2 }, overlap patterns {f 1, f 2, f 5 }, {f 1, f 2, f 4 } For {f 2, f 3, f 4 }, overlap patterns {f 1, f 2, f 3, f 4 }, {f 2, f 3, f 4, f 5 } 18

19 Creating Spatial Neighborhoods Related with a pattern, implemented as points S Inst / MSpN spatial neighborhoods created for each pattern Spatial Neighborhoods for pattern P={f 1, f 2 } Let M SpN = 2 Let S Inst = 4 19

20 Creating Spatial Neighborhoods The points are randomly selected within spatial framework. M SpN shows how many instances from each feature type will be created in that spatial neighborhood Spatial Neighborhoods for pattern P={f 1, f 2 } Let M SpN = 2 Let S Inst = 4 20

21 Instance Generation For each feature type in a pattern, S Inst instances are generated. Feature Type f 1 Feature Type f 2 Spatial Neighborhoods for pattern P={f 1, f 2 } Spatial Neighborhoods Let M SpN = 2 Let S Inst = 4 21

22 Instance Generation Instances are created using the attributes of their feature type. They have Number of vertices Area Areal Evolution Lifetime Velocity Acceleration We select a value for each instance attribute between related Min - Max attributes of associated pattern 22

23 Unit Polygon Generation After area and number of vertices (n) are decided for an instance, we start creating the instance using a unit polygon generation procedure. Create n vectors (each sources from point (0,0)) Randomly create an angle Randomly decide on the magnitude Enlarge the area Locate it into spatial neighborhoo d 23

24 Instance Movement After creating polygons, we select a random angle from 0 to 360, and use velocity and acceleration functions for displacement. Instance movement is linear with varying velocity constant acceleration 24

25 Noise Instance Generation Lastly, for each pattern (naturally for spatial neighborhoods), we create a particular amount of noise by selecting a random feature type (that is not present in pattern) selecting a random point (as in spatial neighborhood) Noise instances do not contribute to any pattern This decreases the ratio of instances that participates in a spatiotemporal pattern 25

26 Dataset Generation Summary 26

27 Conclusions ERMO-DG can be used for testing pattern mining algorithms Different sized datasets Small, checking correctness Large, estimating the behavior of algorithms Parameters can be used for tuning the general characteristics of dataset too. 27

28 Questions Thank you... 28