Tools and Algorithms for Querying and Mining Large Graphs Hanghang Tong Machine Learning Department Carnegie Mellon University htong@cs.cmu.edu http://www.cs.cmu.edu/~htong 1 Thesis Committee • • • • Christos Faloutsos William Cohen Jeff Schneider Philip S. Yu 2 Graphs are everywhere! 3 Motivating Questions: (high level) • Given a large graph, we want to +Task A: Querying H.V. Jagadish 15 Laks V.S. Lakshmanan 10 R. Agrawal 13 Jiawei Han 10 1 2 Heikki Mannila Christos Faloutsos 1 1 Corinna Cortes 6 1 6 Padhraic Smyth 1 V. Vapnik 4 +Task B: Mining 3 1 1 M. Jordan Daryl Pregibon CePS on DBLP [Tong+ KDD 06] T3 on CIKM [Tong+ CIKM 08] Will return to this later… 4 Motivating Questions (in details) • Querying [Goal: query complex relationship] – Q.1. Find complex user-specific patterns; – Q.2. Link Prediction & Proximity Tracking; – Q.3. Answer all the above questions quickly. • Mining [Goal: find interesting patterns] – M.1. Spot Anomalies; – M.2. Mine time & space; – M.3. Detect communities. 5 Thesis Overview Q1 Q2 Q2 Q3 Q3 M1 M1 M2 M2 M3 M3 6 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 7 Thesis Overview: Impact Querying Mining Tasks Q1 Impact, Applications Identify master-mind criminal; money launder ring; interactive search & summarization Q2 Q3 Predict who-calls-whom; Trend analysis on graph level M1 M2 M3 Efficient anomaly detection in an intuitive, dynamic way Scale all the above app.s to large, disk resident, graphs Mine time/space in complex settings Detect community w/ optional constraints Footnote: Our work for Q1 has been transferred into IBM product (Cyano) 8 Roadmap • Introduction • Completed Work –Querying –Mining • Proposed Work • Preliminary • Q1 • Q2 • Q3 9 Preliminary: Proximity Measurement I 1 J 1 A 1 1 1 H 1 B 1 D 1 1 1 E G F a.k.a Relevance, Closeness, ‘Similarity’… 10 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 11 Competed work on Q1 • Goal: Find complex user-specific patterns, – Q1.1. Center-Piece Subgraph Discovery, – e.g., master-mind criminal given some suspects X, Y and Z? – Q1.2. Best Effort Pattern Match, – e.g., Money-laundry ring – Q1.3 Interactive querying (e.g. Negation) – e.g., find most similar conferences wrt KDD, but not like ICML? 12 Q1.1 Center-Piece Subgraph Discovery [Tong+ KDD 06] Input Output B B CePS Node A C Original Graph C A CePS Q: How to find hub for the black nodes? Red: Max (Prox(A, Red) x Prox(B, Red) x Prox(C, Red)) CePS: Example (AND Query) H.V. Jagadish 15 Laks V.S. Lakshmanan 10 R. Agrawal Jiawei Han 10 1 2 Heikki Mannila Christos Faloutsos 1 Corinna Cortes 6 1 6 1 Padhraic Smyth 1 1 V. Vapnik 4 13 3 1 M. Jordan Daryl Pregibon DBLP co-authorship network: - 400,000 authors, 2,000,000 edges 14 K_SoftAND: Relaxation of AND Noise Disconnected Communities Asking AND query? No Answer! 15 CePS: 2 SoftAND DB H.V. Jagadish 15 10 Laks V.S. Lakshmanan 13 R. Agrawal Jiawei Han Umeshwar Dayal 3 Stat. Bernhard Scholkopf 5 V. Vapnik 4 2 27 3 Peter L. Bartlett 3 2 M. Jordan Alex J. Smola 16 Q1.2. Best-Effort Pattern Match [Tong+ KDD 2007 b] Query Graph Interception Data Graph CEO SEC Matching Subgraph Accountant Manager Input Output Q: How to find matching subgraph? G-Ray: How to? details matching node matching node matching node matching node Goodness = Prox (12, 4) x Prox (4, 12) x Prox (7, 4) x Prox (4, 7) x Prox (11, 7) x Prox (7, 11) x Prox (12, 11) x Prox (11, 12) Observation: , etc. 18 Effectiveness: star-query Databases Intelligent Agent Query Bio-medical Result 19 Effectiveness: line-query Theory Databases Learning Bio-medical Query Result 20 Q1.3: Interactive Querying User Feedback User Feedback User Feedback User Feedback 21 Q1.3 ProSIN for Interactive Querying [Tong+ ICDM 08] Initial Results No to `ICML’ Yes to `SIGIR’ 'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE' 'SIGMOD' 'NIPS' 'PKDD' 'IJCAI' 'PAKDD' 'ICDM' 'SDM' 'PKDD' 'ICDE' 'VLDB' 'SIGMOD' 'PAKDD' 'CIKM' 'SIGIR' 'WWW' 'SIGIR' 'TREC' 'CIKM' 'ECIR' 'CLEF' 'ICDM' 'JCDL' 'VLDB' 'ACL' 'ICDE' two main sub-communities in KDD: DBs (green) vs. Stat (Red) Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI) Positive feedback on SIGIR will bring more IR (brown) conferences. what are most related conferences wrt KDD? (DBLP author-conference bipartite graph) 22 Q1.3 ProSIN for Interactive Querying [Tong+ ICDM 08] Initial Results No to `ICML’ Yes to `SIGIR’ 'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE' 'SIGMOD' 'NIPS' 'PKDD' 'IJCAI' 'PAKDD' 'ICDM' 'SDM' 'PKDD' 'ICDE' 'VLDB' 'SIGMOD' 'PAKDD' 'CIKM' 'SIGIR' 'WWW' 'SIGIR' 'TREC' 'CIKM' 'ECIR' 'CLEF' 'ICDM' 'JCDL' 'VLDB' 'ACL' 'ICDE' two main sub-communities in KDD: DBs (green) vs. Stat (Red) Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI) Positive feedback on SIGIR will bring more IR (brown) conferences. what are most related conferences wrt KDD? (DBLP author-conference bipartite graph) 23 Q1.3 ProSIN for Interactive Querying [Tong+ ICDM 08] Initial Results No to `ICML’ Yes to `SIGIR’ 'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE' 'SIGMOD' 'NIPS' 'PKDD' 'IJCAI' 'PAKDD' 'ICDM' 'SDM' 'PKDD' 'ICDE' 'VLDB' 'SIGMOD' 'PAKDD' 'CIKM' 'SIGIR' 'WWW' 'SIGIR' 'TREC' 'CIKM' 'ECIR' 'CLEF' 'ICDM' 'JCDL' 'VLDB' 'ACL' 'ICDE' two main sub-communities in KDD: DBs (green) vs. Stat (Red) Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI) Positive feedback on SIGIR will bring more IR (brown) conferences. what are most related conferences wrt KDD? (DBLP author-conference bipartite graph) 24 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 25 Q2.1 Link Prediction: direction [Tong+ KDD 07 a] i i ? j i • Q: Given the existence of the link, i what is the direction of the link? • A: (DAP) Compare Prox(ij) and Prox(ji) density Web Link - 4, 000 nodes - 10, 000 edges >70% Prox (ij) - Prox (j26i) Q2.2 pTrack/cTrack: Challenge [Tong+ SDM 08] • Observations (CePS, GRay, ProSIN…) – All for static graphs – Proximity: main tool • Graphs are evolving over time! – New nodes/edges show up; – Existing nodes/edges die out; – Edge weights change… Q: How to make everything incremental? A: Track Proximity! 27 pTrack/cTrack: Trend analysis on graph level T. Sejnowski Rank of Influence C. Koch G.Hinton M. Jordan Year 28 pTrack: Problem Definitions • [Given] – (1) a large, skewed time-evolving bipartite graphs, – (2) the query nodes of interest • [Track] – (1) top-k most related nodes for each query node at each time step t; – (2) the proximity score (or rank of proximity) between any two query nodes at each time step t 29 pTrack: Philip S. Yu’s Top-5 conferences up to each year ICDE ICDCS SIGMETRICS PDIS VLDB CIKM ICDCS ICDE SIGMETRICS ICMCS KDD SIGMOD ICDM CIKM ICDCS ICDM KDD ICDE SDM VLDB 1992 1997 2002 2007 Databases Performance Distributed Sys. DBLP: (Au. x Conf.) - 400k aus, - 3.5k confs - 20 yrs Databases Data Mining 30 KDD’s Rank wrt. VLDB over years (Closer) Prox. Rank Data Mining and Databases are getting closer & closer Year 31 cTrack:10 most influential authors in NIPS community up to each year T. Sejnowski M. Jordan Author-paper bipartite graph from NIPS 1987-1999. 1740 papers, 2037 authors, spreading over 13 years 32 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 33 Proximity is the main tool • Q.1: CePS, G-Ray, ProSIN • Q.2: DAP, pTrack/cTrack I 1 J 1 A 1 1 1 H 1 1 D 1 1 1 E B a.k.a Relevance, Closeness, ‘Similarity’… G F Q: What is a `good’ Score? 34 Random walk with restart [Pan+ KDD 2004] 0.04 9 0.10 2 0.13 1 0.03 10 12 0.02 0.08 3 8 0.13 11 0.04 4 0.13 6 5 7 Node 4 0.05 Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 Node 11 Node 12 0.13 0.10 0.13 0.22 0.13 0.05 0.05 0.08 0.04 0.03 0.04 0.02 0.05 Nearby nodes, higher scores More red, more relevant Ranking vector r4 Why RWR is a good score? Q(i, j ) ri , j j 1 Q ( I cW ) i W: adjacency matrix. c: damping factor Qc W all paths from i to j with length 1 2 c W 2 c 3 all paths from i to j with length 2 W 3 ... all paths from i to j with length 3 RWR summarizes all the weighted paths from i to j Computing RWR • OntheFly ri [t 1] cWri [t ] (1 c)ei – No Pre-Computation; ~ – Light Storage Cost (W) – Slow On-Line Response: O(mE) • Pre-Compute Q ( I cW ) 1 – Fast On-Line Response – Prohibitive Pre-Compute Cost: O(n3) – Prohibitive Storage Cost: O(n2) 37 Q: How to Balance? On-line Off-line Goal: Efficiently Get (elements) of Q ( I cW )1 38 B_Lin: Basic Idea [Tong+ ICDM 2006] 10 9 12 2 Find Community 1 8 3 11 4 9 0.04 7 12 2 8 1 6 5 10 3 9 0.10 0.13 8 3 0.13 5 6 0.05 5 6 0.02 11 0.04 4 4 12 0.08 2 1 11 0.03 10 0.13 7 0.05 7 9 10 10 12 12 2 8 1 3 Combine 11 11 4 Fix the remaining 6 5 7 39 B_Lin: details ~ W details + = ~ ~ + ~ W 1: within community Cross community 40 B_Lin: details details -1 -1 ~ ~ ~ I – c W1 – cUSV I – cW ~ Easy to be inverted LRA difference Sherman–Morrison Lemma! If Then 41 B_Lin: summary • Pre-Compute Stage • Q: Efficiently compute and store Q • A: A few small, instead of ONE BIG, matrices inversions • On-Line Stage • Q: Efficiently recover one column of Q • A: A few, instead of MANY, matrix-vector multiplications 42 Query Time vs. Pre-Compute Time Log Query Time Our Results •Quality: 90%+ •On-line: •Up to 150x speedup •Pre-computation: •Two orders saving Log Pre-compute Time 43 More on Scalability Issues for Querying (the spectrum of ``FastProx’’) • B_Lin: one large linear system – [Tong+ ICDM06, KAIS08] • BB_Lin: the intrinsic complexity is small – [Tong+ KAIS08] • FastUpdate: time-evolving linear system – [Tong+ SDM08, SAM08] • FastAllDAP: multiple linear systems – [Tong+ KDD07 a] • Fast-ProSIN: dealing w/ on-line feedback – [Tong+ ICDM 2008] 44 Roadmap • Introduction • Completed Work –Querying –Mining • Proposed Work • M1: Spotting Anomalies • M2: Mining Time 45 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 46 Motivation [Tong+ KDD 08 b] • Q: How to find patterns? – e.g., communities, anomalies, etc. • A: Low-Rank Approximation (LRA) for Adjacency Matrix of the Graph. X M X A ~ R L 47 LRA for Graph Mining: Example Adj. matrix: A John ICDM KDD Carl ISMB M X Tom Bob L ~ R X Conf. Cluster Interaction Van Roy Author RECOMB Conf. Au. clusters Recon. error is high ‘Carl’ is abnormal 48 Challenges: How to get (L, M, R)? • Efficiently • both time and space • Intuitively • easy for interpretation • Dynamically • track patterns over time None of Existing Methods Fully Meets Our Wish List! 49 Why Not SVD and CUR/CX? • SVD: Optimal in L2 and LF • CUR: Example-based – Efficiency 2 2 O (min( n m , nm )) • Time: • Space: (L, R) are dense – Interpretation • Linear Combination of many columns – Dynamic: Not Easy – Efficiency • Better than SVD • Redundancy in L – Interpretation • Actual Columns from A xxxx – Dynamic: Not Easy 50 Solutions: Colibri [Tong+ KDD 08 b] detail s • Colibri-S: for static graph – Basic idea: remove linear redundancy – Same accuracy as CUR/CX – Significant savings in both time & space • Up to 53x speed-up • Colibri-D: for dynamic graph – Basic idea: leverage smoothness between time – Same accuracy as CUR/CMD • Up to 112x speed-up 51 A Pictorial Comparison (for static graphs) detail s 1st singular vector SVD CUR 2nd singular vector CMD Colibri-S 52 Comparison SVD, CUR vs. Colibri s Wish List SVD CUR/CX detail s Colibri [Golub+ 1989] [Drineas+ 2005] [Tong+ 2008] Efficiency Interpretation Dynamics 53 Performance of Colibri-S CUR CUR CMD Ours CMD Time Ours • Accuracy • Same 91%+ • Time • 12x of CMD • 28x of CUR • Space • ~1/3 of CMD • ~10% of CUR Space Data set: Network traffic - 21,837 sources/destinations, 158,805 edges 54 Performance of Colibri-D Time CMD Network traffic - 21,837 nodes - 1,220 hours - 22,800 edge/hr Colibri-S Colibri-D # of changed cols Colibri-D achieves up to 112x speedups 55 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 56 M2: How to mine time in some complex context? [Tong+ CIKM 08] 57 A Motivating Example: Inputs Time Event(e.g., Session) Entity Oct. 26 Link Analysis Clustering Classification Anomaly Detection Party Web Search Advertising Enterprise Search Q&A Tom, Bob Bob, Alan Bob, Alan Alan, Beck Beck, Dan Dan, Jack Jack, Peter Jack, Peter Peter, Smith Oct. 27 Oct. 28 Oct. 29 Oct. 30 Oct. 31 58 Time Cluster, rep. entities: b7,b6, b8 A Motivating Example: Outputs Oct. 30 Jack Oct. 29 Time Cluster Oct. 30 Rep. Entities: ``Jack’’, ``Peter’’, ``Smith’’ Abnormal Time Oct. 28 Rep. Entities: ``Beck’’ , ``Dan’’ Oct. 26 Oct. 27 Time Cluster Rep. Entities: ``Tom’’, ``Bob’’, ``Alan’’ Problem Definitions (How to mine time in such complex context) • Given data sets collected at different time stamps; • We want to find Our Solutions +1: Time Clusters +2: Abnormal Time stamps +3: Interpretations +4: Right time granularity T3 MT3 60 Data Sets • CIKM: from CIKM proceedings • Time: Publication year (1993-2007, 15) • Event: Paper-published (952) • Entities: Author (1895) & Session (279) • Attribute: Keyword (158) • DeviceScan: from MIT Reality Mining • Time: the day scanning happened (1/1/20045/5/2005, 294) • Event: blue tooth device scanning person (114, 046) • Entities: Device (103) & Person (97) • Attribute: NA 61 T3 on `CIKM’ Data Set Rep. Authors Rep. Keywords James. P. Callan W. Bruce Croft James Allan Philip S. Yu George Karypis Charles Clarke Web Cluster Classification XML Language Stream Rep. Authors Rep. Keywords Elke Rundensteiner Daniel Miranker Andreas Henrich Il-Yeol Song Scott B Huffman Robert J. Hall Knowledge System Unstructured Rule Object-oriented Deductive 62 MT3 on `DeviceScan’ Data Set Work day Semester Break & Holiday Apr. 2004 is anomaly Aggregate by Day Aggregate by Month 63 Roadmap • Introduction • Completed Work –Querying –Mining • Proposed Work –P1: Community detection –P2: Mining Space –P3: Diffusion Wavelets 64 Questions That We Ask Thesis Overview Completed CePS, G-Ray, ProSIN Q1 (KDD06, KDD07 a, ICDM08) Q2 Q3 DAP Proposed Q2 pTrack/cTrack Q3 FastProx (SDM08, SAM08) (KDD07 b) FastProx (ICDM06, KAIS07, KDD07 b, ICDM08) P3 M1 Colibri-S M2 P2 P3 M2 M3 P1 P3 M3 (KDD08 b) P3 M1 (SDM08, SAM08) Colibri-D (KDD08 b) T3/MT3 (CIKM08) P1 65 P1 Detecting Communities • Observations: two seemingly opposite efforts in community detection – E1: parameter-free (no user intervention) – E2: cluster w/ constraints (listen to users) • Challenge: How to fill the gap? • Idea: MDL-based method, encoding the constraints in descriptions. 66 P2 Mining Space • Given the data sets collected at different locations • We want to – Find similar locations – Spot Abnormal locations – Provide Interpretations • Idea: extend T3/MT3 to 2-d case 67 P3 Diffusion Wavelets • Observation #1: Graph Laplacian is basis – For many querying and mining techniques • Observation #2: Diffusion wavelets focus on local spectrum in multi-scales • Conjecture: Diffusion wavelets (might) provide an alternative/better way for – Querying – Mining 68 Time Line • Dec. ‘08: Thesis Proposal P1• Jan. – Feb., ‘09: – Research on Community Detection P2• Mar. – Apr. ‘09: – Research on Mining Space P3• May – Jul. ‘09: – Research on Diffusion Wavelets • Aug. ‘09: Thesis Write-up • Sep. ‘09: Defense 69 Selected References • H. Tong & C. Faloutsos. (2006) Center-piece subgraphs: problem definition and fast solutions. In KDD, 404-413, 2006. • H. Tong, C. Faloutsos, & J.Y. Pan. (2006) Fast Random Walk with Restart and Its Applications. In ICDM, 613-622, 2006. (b.p. award) • H. Tong, Y. Koren, & C. Faloutsos. (2007) Fast direction-aware proximity for graph mining. In KDD, 747-756, 2007. • H. Tong, B. Gallagher, C. Faloutsos, & T. Eliassi-Rad. (2007) Fast best-effort pattern matching in large attributed graphs. In KDD, 737-746, 2007. • H. Tong, S. Papadimitriou, P.S. Yu & C. Faloutsos. (2008) Proximity Tracking on Time-Evolving Bipartite Graphs. in SDM 2008. (b.p. award) • H. Tong, S. Papadimitriou, J. Sun, P.S. Yu & C. Faloutsos. (2008) Fast Mining of Static and Dynamic Graphs. KDD 2008 • H. Tong, Y. Sakurai, T. Eliassi-Rad, and C. Faloutsos. Fast Mining of Complex Time-Stamped Events CIKM 08 • H. Tong, H. Qu, and H. Jamjoom. Measuring Proximity on Graphs with Side Information. ICDM 2008 70 My other work during Ph.D study • GhostEdge (w/ Brian, Christos and Tina, in KDD 08) – Classification in Sparsely Labeled Network • GMine (w/ Junio, Agma, Christos and Jure, in VLDB 06) – Interactive Graph Visualization and Mining • Graphite (w/ Polo, Christos, Jason, Brian and Tina, in ICDM 08) – Visual Query System for Attributed Graphs • TANGENT (w/ Kensuke and Christos) – ``surprise-me’’ recommendation • PaCK (w/ Jingrui, Spiros, Tina, Jaime and Christos) – Community detection for heterogonous graphs 71 Acknowledgements (the old way) • Christos Faloutsos, Jia-Yu Pan, Yehuda Koren, Spiros Papadimitriou, Philip S. Yu, Jimeng Sun, Huiming Qu, Hani Jamjoom, Tina Eliassi-Rad, Brian Gallagher, Yasushi Sakurai, • Kensuke Oonuma, Duen Horng (Polo) Chau, Jason I. Hong, Jingrui He, Jaime Carbonell, José Fernando Rodrigues Jr., Jure Leskovec Agma J. M. Traina, • Charalampos (Babis) Tsourakakis, Meng Su 72 A Graph Miner’s Way: My Collaboration Graph Legends: Green: Querying Blue: Mining Purple: Others : Completed : Proposed (During Ph.D Study) P1 Q1 CePS ProSIN M3 Gray DAP T3/MT3 P2 M2 P3 M1 Colibri Q2 pTrack cTrack GhostEdge Graphite FastDAP Q3 Fast-ProSIN BLin GMine BBLin Pack TANGENT Q&A Thank you! 74