Extending Functional Dependency to Detect Abnormal Data in RDF Graphs
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1 Extending Functional Dependency to Detect Abnormal Data in RDF Graphs Yang Yu, Jeff Heflin SWAT Lab Department of Computer Science and Engineering Lehigh University PA, USA
2 Outline Semantic Web data and data model Functional Dependency (FD) Value-clustered Graph Functional Dependency (VGFD) System Clustering Pre-clustering Optimal k-means clustering Handling multi-valued properties Static pruning Runtime pruning Conclusion and future work 2
3 Semantic Web Data Linked Data 3
4 Semantic Web Data Model Mapping with DB model Record RDF node Column RDF property Cell RDF property value Advantages of Semantic Web data model No limit of number of properties No need to specify null values Schema evolution is inexpensive Machine processable 4
5 Functional Dependency in DB It is by far the most common integrity constraints for databases. It is devised to specify missing semantics in mere syntactic definitions of database relations. Definition Given a relation R, a set of attributes X in R is said to functionally determine another attribute Y, also in R, (written X Y) if, and only if, each X value is associated with precisely one Y value. E.g. {Course, Semester} Instructor {postalcode} province 5
6 Challenges RDF data can be viewed as extremely decomposed relational tables More forms of combinations of properties convey latent semantics E.g. advisorof studentof -, father brother Multi-valued properties make it harder to determine value correlations E.g. city and province Different syntactic values could be close in semantics E.g vs. 1.0; blue & red vs. red & blue 6
7 VGFD Definitions has-date Date_1 has-year Paper_1 article-of-journal Journal_A 1998 has-volume 6 An RDF graph: directed, labeled graph 7
8 VGFD Definitions has-date Date_1 has-year Paper_1 has-volume article-of-journal 6 Journal_A 1998 An example Composite Property: has-date has-year 8
9 VGFD Definitions has-date Date_1 has-year Paper_1 article-of-journal Journal_A 1998 has-volume 6 Value(Paper_1, has-date has-year) =
10 VGFD Definitions has-date Date_1 has-year Paper_1 article-of-journal Journal_A 1998 has-volume 6 An example Conjunctive Property: article-of-journal + has-volume 10
11 VGFD Definitions has-date Date_1 has-year Paper_1 article-of-journal Journal_A 1998 has-volume 6 Value(Paper_1, article-of-journal + has-volume) = <Journal_A, 6> 11
12 VGFD Definitions has-date Date_1 has-year 1998 has-date Date_2 has-year 1998 Paper_1 article-of-journal Journal_A Paper_2 article-of-journal Journal_A has-volume 6 has-volume 6 A possible example VGFD: article-of-journal + has-volume has-date has-year A value-clustered graph functional dependency (VGFD) in graph G is X Y, where X R +, Y R and i, j I, if V (i, X) = V (j, X) then V (i, Y ) = V (j, Y ). 12
13 System Overview 13
14 Handling Multi-valued Property 14
15 Handling Multi-valued Property 15
16 Handling Multi-valued Property 16
17 Handling Multi-valued Property 17
18 Handling Multi-valued Property Miss Match Confidence of VGFD deptno deptname = 4/5 =
19 Complexity Search space: O(2 n! n!) O(n!) possible composite properties O(2 n! ) possible conjunctive properties Static Pruning Without runtime investigation of values of two properties Runtime Pruning Investigate small portion of values of two properties
20 Static Pruning Heuristics Insufficient overlap between properties The discriminability of the LHS is less than that of the RHS Discriminability of a property = distinct property values / property extension The LHS or RHS has too high a discriminability The discriminability of a Composite Property (Conjunctive Property resp.) is no greater than (no less than resp.) that of each property involved 20
21 Level-wise Discovering Process Static pruning heuristics: 1. insufficient subject/object overlap between properties to be composed or between the LHS and the RHS, 2. the discriminability of the LHS is less than that of the RHS, 3. the LHS or RHS has too high a discriminability, 4. the discriminability of a Composite Property (Conjunctive Property resp.) is no greater than (no less than resp.) that of each property involved In this example, we suppose: a. A and B have few common subjects b. the discriminability of B is less then that of C c. D has a high discriminability 21
22 Level-wise Discovering Process Static pruning heuristics: 1. insufficient subject/object overlap between properties to be composed or between the LHS and the RHS, 2. the discriminability of the LHS is less than that of the RHS, 3. the LHS or RHS has too high a discriminability, 4. the discriminability of a Composite Property (Conjunctive Property resp.) is no greater than (no less than resp.) that of each property involved In this example, we suppose: a. A and B have few common subjects b. the discriminability of B is less then that of C c. D has a high discriminability 22
23 Level-wise Discovering Process Static pruning heuristics: 1. insufficient subject/object overlap between properties to be composed or between the LHS and the RHS, 2. the discriminability of the LHS is less than that of the RHS, 3. the LHS or RHS has too high a discriminability, 4. the discriminability of a Composite Property (Conjunctive Property resp.) is no greater than (no less than resp.) that of each property involved In this example, we suppose: a. A and B have few common subjects b. the discriminability of B is less then that of C c. D has a high discriminability 23
24 Level-wise Discovering Process Static pruning heuristics: 1 1. insufficient subject/object overlap between properties to be composed or between the LHS and the RHS, 2. the discriminability of the LHS is less than that of the RHS, 3. the LHS or RHS has too high a discriminability, 4. the discriminability of a Composite Property (Conjunctive Property resp.) is no greater than (no less than resp.) that of each property involved In this example, we suppose: a. A and B have few common subjects b. the discriminability of B is less then that of C c. D has a high discriminability 24
25 Runtime Pruning Mutual Information of two properties Entropy coefficient (EC) of two properties Sampling a subset of instances (20%) for a VGFD to compute EC 25
26 Clustering Property Values Pre-clustering Light-weight computation provides two benefits for finer clustering The minimum number of clusters Reserves expensive distance calculation for pairs of points within the same pre-cluster Process Pick a point that is closest to the center Cluster points that are close to this center Repeat the above two steps until all points are clustered 26
27 Clustering Property Values Optimal k-means Clustering Improved from Gap Statistic [1] Without the input of k, automatically find the optimal number of clusters Variation of normal k-means clustering by restricting the distance calculation only on the pairs that within the same pre-cluster [1] Estimating the number of clusters in a data set via the gap statistic, R. Tibshirani, G. Walther, T. Hastie, Journal of the Royal Statistical Society, Vol. 63, No. 2. (2001), pp
28 Experimental Results Example VGFDs 28
29 Experimental Results Example Erroneous Data System Performance 29
30 Experimental Results Impact of pruning techniques Effect of # of properties on running time 30
31 Conclusion and Future Work Conclusion Finding corroboration patterns in the form of Value-clustered Graph Functional Dependency Detect abnormal data by checking conflicts with patterns Experiments on different real world data sets that validate the system Future work Further generalize the VGFDs Apply system on knowledge acquisition areas 31
32 Thank you Questions and comments? 32
33 Pre-clustering Pre-clustering on strings The weight of a word is based on its frequency in the values of the property The string that has the largest sum of weights divided by the number of words in it is the center Example pre-cluster results: {Coach, First Team Coach, Head coach, Senior Coach, Acting head coach, Reserve team coach, Chief Coach}, {Director, Sports Director, Technical Director, Director general} 33
34 Optimal k-means Clustering Initialize the estimated cluster center Find the closest center within the same pre-cluster Re-compute the center Check if the gain of this clustering is slower than the expected rate 34
Extending Functional Dependency to Detect Abnormal Data in RDF Graphs
Extending Functional Dependency to Detect Abnormal Data in RDF Graphs Yang Yu and Jeff Heflin Department of Computer Science and Engineering. Lehigh University 19 Memorial Drive West, Bethlehem, PA 18015
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