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Spark-ITS: Indexing for Large-Scale Time Series Data on Spark with Liang Zhang

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The document discusses Spark-ITS, a distributed indexing framework designed for processing large-scale time series data. It highlights its new index tree that improves similarity query efficiency and describes the framework's overall architecture, including the index construction and query processing methods. Additionally, performance evaluations and comparisons to existing methodologies are presented, emphasizing the framework's effectiveness in handling billions of time series.

Data & Analytics
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Liang Zhang (lzhang6@wpi.edu) Data Science Dept., Worcester Polytechnic Institute Spark-ITS: Indexing for Large-Scale Time Series Data on Spark #SAISEco5
Prof. Elke A. Rundensteiner Prof. Mohamed Y. Eltabakh Liang Zhang Noura Alghamdi Data Science Research Group @ Worcester Polytechnic Institute Liang Zhang, Noura Alghamdi, Mohamed Y. Eltabakh, Elke A. Rundensteiner. TARDIS: Distributed Indexing Framework for Big Time Series Data. Proceedings of 35th IEEE International Conference on Data Engineering ICDE, 2019
Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 3
Time Series are Continuously Produced Everywhere • How to deal with billions of time series? 4 Climate data Web log Stock priceEEG
Almost all Time Series Data Mining Tasks rely on Similarity Query 5 Esling, Philippe, and Carlos Agon. "Time-series data mining." ACM (CSUR) 45.1 (2012): 12. Clustering Motif Discovery Classification çΩ Outlier Detection Whole Matching Subsequence Matching
Spark-ITS • A new Index Tree and an effective Signature to simplify the cardinality conversion and keep better similarity • A Distributed Index Framework to support large-scale time series dataset • Efficient algorithms for Exact Match and kNN Approximate queries process 6
Spark-ITS Overview 7 Global Index Indexed Data Local Index Query Partition 1. Sampling 2. Node Statistic 3. Build Index Tree 4. Assign Partition ID 1. Construct Local Structure 2. Construct Bloom Filter 1. Read and convert data 2. Shuffle data
Background: iSAX Representation 8 Shieh, Jin, and Eamonn Keogh. "iSAX: indexing and mining terabyte sized time series." SIGKDD ACM, 2008. Camerra, A., Palpanas, T., Shieh, J., & Keogh, E. "iSAX 2.0: Indexing and mining one billion time series." ICDM, 2010 A time series of length 16 PAA representation with 4 segments PAA: Piecewise Aggregate Approximation iSAX: indexable Symbolic Aggregate approXimation SAX representation with 4 segments and cardinality 4 [11,10,01,00] iSAX representation with 4 segments and variable cardinality [1", 1", 𝟎𝟏 𝟒, 0"]
Word-level Similarity 9 -2 -1 0 1 2 1 3 5 7 9 11 A B C 111 110 101 100 011 010 001 000 -2 -1 0 1 2 1 3 5 7 9 11 A B C 111 110 101 100 011 010 001 000 State-of-the-art: Character-level Similarity Proposed: Word-level Similarity B and C are similar A and C are similar A: [𝟎 𝟏, 𝟎 𝟏, 𝟎𝟏𝟏 𝟑, 𝟏 𝟏] B: [𝟎 𝟏, 𝟎 𝟏, 𝟎𝟏𝟎 𝟑, 𝟏 𝟏] C: [𝟎 𝟏, 𝟎 𝟏, 𝟎𝟏𝟎 𝟑, 𝟏 𝟏] A: [𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟏𝟎 𝟐] B: [𝟎𝟎 𝟐, 𝟎𝟎 𝟐, 𝟎𝟏 𝟐, 𝟏𝟏 𝟐] C: [𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟏𝟎 𝟐]
New Index Tree Supports Word-level Similarity 10 Proposed: iSAX-T K-ary TreeState-of-the-art: iSAX Binary Tree Root 0", 1",0" 1", 1", 1"0", 0", 0" 0", 11%,0" 0", 10%, 0" 0",11%, 01% 0", 11%,00% . . .. . . Leaf nodeInternal node 1st bit 2nd bit 3rd bit Root 1",1",0" 1",1",1"0",0",0" 01$, 00$, 10$ 01$, 01$, 11$ 010&,000&,100& . . . 0",0",1" . . . 00$, 00$, 10$ 011&, 001&, 101& . . . Leaf nodeInternal node
iSAX-T(Transpose) Signature 11 iSAX-T SAX(T,4,16) = {1100, 1101, 0110, 0001} = CE25 SAX(T,4,8) = {110, 110, 011, 000 } = CE2 SAX(T,4,4) = {11, 11, 01, 00 } = CE SAX(T,4,2) = {1, 1, 0, 0 } = C HexTranspose 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 C E 2 5 Time series: [1100, 1101, 0110, 0001]
Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 12
1.368099 2.713573 -4.851872 -2.710113 -5.577432 0.797747 -0.998534 0.535733 -2.244053 -0.298195 -5.040225 -0.093288 2.683385 -4.839688 5.617443 -0.087439 -0.857566 2.537812 -3.809641 0.638194 0.706312 -3.016157 -3.094813 4.975719 -3.664357 1.402586 0.444090 1.969943 1.282233 1.912557 2.277926 1.511366 0.945206 5.769843 0.406734 -4.205288 0.850925 -2.994073 1.270280 1.286681 -5.681450 3.137617 -4.996282 3.160174 -8.749059 2.648822 6.117611 3.109095 3.159747 0.442472 -1.482878 3.432288 0.960204 0.380183 -3.925308 -2.112708 -2.991460 -3.692369 4.508871 6.430551 -3.929611 -4.271633 0.268938 -1.756457 0.978831 0.783966 -1.982449 1.100825 -6.741050 0.882729 -3.098735 -0.330746 -0.659716 1.345305 -1.537599 -0.639539 2.028107 3.638267 0.211225 5.067515 -0.479032 2.713979 -2.921332 1.231413 -1.559693 -1.057173 -0.335133 -3.601023 -4.891684 -1.832524 -2.828772 0.257098 2.288298 -4.795566 -0.054114 1.991941 Global Index[1/4]: Sampling 1.368099 2.713573 -4.851872 -2.710113 -5.577432 0.797747 -0.998534 0.535733 -2.244053 -0.298195 -5.040225 -0.093288 2.683385 -4.839688 5.617443 -0.087439 -0.857566 2.537812 -3.809641 0.638194 0.706312 -3.016157 -3.094813 4.975719 0.594820 1.136821 0.163368 5.379237 -5.453637 -0.282540 0.572556 6.158454 -1.632961 -1.560935 2.514265 2.987787 -3.006184 0.965107 4.543610 0.614290 1.851868 -2.935539 -0.716928 2.357205 -3.126861 1.620514 -0.490122 -3.380533 -2.301087 -4.727099 6.885664 -5.210190 1.707254 -7.965270 -0.914942 0.622116 1.620520 -0.994487 -0.021151 -1.749576 -3.664357 1.402586 0.444090 1.969943 1.282233 1.912557 2.277926 1.511366 0.945206 5.769843 0.406734 -4.205288 0.850925 -2.994073 1.270280 1.286681 -5.681450 3.137617 -4.996282 3.160174 -8.749059 2.648822 6.117611 3.109095 -3.164684 0.884269 2.925519 -1.051656 -0.371788 -1.661374 0.041967 0.126226 -5.662528 -1.026395 -1.317764 2.268905 -2.998881 2.628193 -4.195228 2.261641 -1.676540 -1.646810 -0.056534 -1.551837 -5.098098 2.857196 -2.981121 -0.559482 -0.573813 2.996416 -2.567590 3.113241 2.385687 -1.195035 -4.255606 2.898200 -2.443996 1.196084 -0.759899 -2.065437 -0.709810 -2.848963 4.183200 -0.901386 3.303330 -2.852400 0.022771 1.184107 1.556879 1.825932 -2.375073 1.430655 -1.844884 0.074289 3.309890 1.141529 2.022026 0.552751 3.941867 -4.384278 -0.374243 1.231169 3.094143 1.208599 -1.893548 4.995226 -4.282130 -1.408826 4.439037 1.134620 3.159747 0.442472 -1.482878 3.432288 0.960204 0.380183 -3.925308 -2.112708 -2.991460 -3.692369 4.508871 6.430551 -3.929611 -4.271633 0.268938 -1.756457 0.978831 0.783966 -1.982449 1.100825 -6.741050 0.882729 -3.098735 -0.330746 1.041127 -3.140574 -1.436662 2.035271 0.203884 -0.821091 -0.659716 1.345305 -1.537599 -0.639539 2.028107 3.638267 0.211225 5.067515 -0.479032 2.713979 -2.921332 1.231413 -1.559693 -1.057173 -0.335133 -3.601023 -4.891684 -1.832524 -2.828772 0.257098 2.288298 -4.795566 -0.054114 1.991941 -3.091072 4.949271 -0.935447 3.327516 -3.299987 4.897994 -2.998881 2.628193 -4.195228 2.261641 -1.676540 -1.646810 -0.056534 -1.551837 -5.098098 2.857196 -2.981121 -0.559482 -0.573813 2.996416 -2.567590 3.113241 2.385687 -1.195035 -4.255606 2.898200 -2.443996 1.196084 -0.759899 -2.065437 -0.709810 -2.848963 4.183200 -0.901386 3.303330 -2.852400 0.022771 1.184107 1.556879 1.825932 -2.375073 1.430655 -1.844884 0.074289 3.309890 1.141529 2.022026 0.552751 3.941867 -4.384278 -0.374243 1.231169 3.094143 1.208599 -1.893548 4.995226 -4.282130 -1.408826 4.439037 1.134620 3.159747 0.442472 -1.482878 3.432288 0.960204 0.380183 13 Sampling Map Reduce iSAX-T(b bits), Freq:1Time series iSAX-T(b bits), Freq(b bits) 1256ae3e , 1 0134ef45 , 1 234567ae , 1 1256ae3e , 1 1256ae3e , 1 234567ae , 1 237867ae , 1 024567ae , 1 6243371e , 1 …… 452167ef , 1 1256ae3e , 23 0134ef45 , 2 234567ae , 20 024567ae , 4 237867ae , 10 …… 452167ef , 10 Segment Number: 8, so use 2 letters to represent 1 bit Initial cardinality: b bit level The data size is based on 1 billion time series with 256 length Word counting MapReduce process 1 Terabyte 100 G 0.9 G HDFS 0.1 G
Global Index[2/4]: Node Statistic 14 (iSAX-T(b),Freq(b)) (iSAX-T(1),Freq(b)) [(iSAX-T(1),Freq(1))] max(Freq(1)) Map Reduce Judge 1st layer: 2nd layer: Filter (iSAX-T(b),Freq(b)) (iSAX-T(2),Freq(b)) [(iSAX-T(2),Freq(2))] max(Freq(2)) Map Reduce Judge Filter 3rd layer: (iSAX-T(b),Freq(b)) (iSAX-T(3),Freq(b)) [(iSAX-T(3),Freq(3))] max(Freq(3)) Map Reduce Judge ……
Global Index[3/4]: Build Tree 15 Root iSAX-T: 01 Freq: 512 . . . Segment number: 8 Partition Capacity: 100,000 iSAX-T: 02 Freq: 350,000 iSAX-T: 03 Freq: 4,352 iSAX-T: ff Freq: 270,520 iSAX-T: 0201 Freq: 5,012 iSAX-T: 0202 Freq: 100,550 iSAX-T: 02ff Freq: 620. . . iSAX-T: 020201 Freq: 12 iSAX-T: 020202 Freq: 550 iSAX-T: 0202ff Freq: 620 . . . • (“01”, 512) • (“02”, 355,000) • …. • (“ff”, 270,520) • (“0201”, 5,012) • (“0202”, 100,550) • …. • (“ffff”, 10,520) • (“020201”, 12) • (“020202”, 550) • …. • (“0202ff”, 620) 1st layer (iSAX-T, Freq) 2nd layer (iSAX-T, Freq) 3rd layer (iSAX-T, Freq)
Global Index[4/4]: Assign Partition Id to Leaf Nodes 16 Bin Packing Problem: How to fit a set of nodes in the smallest numbers of partitions? Partition capacity: 100,000 Partition ID: 1 Partition ID: 2 Partition ID: 3 iSAX-T: 02 Freq: 390,500 iSAX-T: 0201 Freq: 70,000 iSAX-T: 0202 Freq: 50,000 iSAX-T: 0203 Freq: 20,000 iSAX-T: 0204 Freq: 40,000 iSAX-T: 0205 Freq: 80,000 iSAX-T: 0206 Freq: 130,500 iSAX-T: 0202 Freq: 50,000 iSAX-T: 0204 Freq: 40,000 iSAX-T: 0201 Freq: 70,000 iSAX-T: 0203 Freq: 20,000 iSAX-T: 0205 Freq: 80,000
Repartition: Wrap Global Index as the Partitioner 17 Root iSAX-T: 01 Freq: 512 pid: 1 . . . iSAX-T: 02 Freq: 350,000 pid: 5,6,7 iSAX-T: 03 Freq: 4,352 pid:1 iSAX-T: ff Freq: 360,520 pid: 10,11,12 iSAX-T: 0201 Freq: 5,012 pid: 5 iSAX-T: 0202 Freq: 100,550 pid: 6,7 iSAX-T: 02ff Freq: 620 pid: 5 . . . iSAX-T: 020201 Freq: 12 pid: 6 iSAX-T: 020202 Freq: 550 pid:6 iSAX-T: 0202ff Freq: 620 . . . iSAX-T: 0202ff45 TS: [0.34, 0.31, 1.14…] iSAX-T: 0202ff45 A Time Series iSAX-T: 0202ff45 iSAX-T: 0202ff45
Local Index: Construction Within Each Partition 18 Partition capacity: 100,000 Node split threshold: 1000 Segment Number: 8 abcd Freq:5000 ab3c Freq: 450 Root Freq: 90,990 abcd12 Freq: 1010 abcd45 Freq: 96 … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid …… iSAX-T, ts, rid iSAX-T, ts, rid abcd12ff Freq: 30 abcd1201 Freq: 42 …… ab45 Freq:4000 …… … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T: abcd12ef34, …. +1 +1 +1 1.368099 2.713573 -4.851872 -2.710113 - 5.577432 0.797747 - 0.998534 0.535733 -2.244053 - 0.298195 -5.040225 -0.093288 2.683385 - 4.839688 5.617443 - 0.087439 - 0.857566 2.537812 - 3.809641 0.638194 0.706312 - 3.016157 - 3.094813 4.975719 0.594820 1.136821 0.163368 5.379237 - 5.453637 - 0.282540 0.572556 6.158454 - 1.632961 - 1.560935 2.514265 2.987787 -3.006184 0.965107 4.543610 0.614290 1.851868 - 2.935539 - 0.716928 2.357205 -3.126861 1.620514 -0.490122 - 3.380533 -2.301087 - 4.727099 6.885664 -5.210190 1.707254 - 7.965270 -0.914942 0.622116 1.620520 - 0.994487 - 0.021151 - 1.749576 - 3.664357 1.402586 0.444090 1.969943 1.282233 1.912557 2.277926 1.511366 0.945206 5.769843 0.406734 -4.205288 0.850925 - 2.994073 1.270280 1.286681 - 5.681450 3.137617 - 4.996282 3.160174 - 8.749059 2.648822 6.117611 3.109095 - 3.164684 0.884269 2.925519 - 1.051656 - 0.371788 - 1.661374 0.041967 0.126226 - 5.662528 -1.026395 - 1.317764 2.268905 - 2.998881 2.628193 - 4.195228 2.261641 - 1.676540 - 1.646810 - 0.056534 - 1.551837 - 5.098098 2.857196 -2.981121 - 0.559482 - 0.573813 2.996416 - 2.567590 3.113241 2.385687 - 1.195035 - 4.255606 2.898200 - 2.443996 1.196084 - 0.759899 - 2.065437 - 0.709810 - 2.848963 4.183200 - 0.901386 3.303330 - 2.852400 0.022771 1.184107 1.556879 1.825932 - 2.375073 1.430655 - 1.844884 0.074289 3.309890 1.141529 2.022026 0.552751 3.941867 -4.384278 - 0.374243 1.231169 3.094143 1.208599 - 1.893548 4.995226 -4.282130 - 1.408826 4.439037 1.134620 3.159747 0.442472 - 1.482878 3.432288 0.960204 0.380183 - 3.925308 - 2.112708 - 2.991460 - 3.692369 4.508871 6.430551 - 3.929611 - 4.271633 0.268938 - 1.756457 0.978831 0.783966 - 1.982449 1.100825 - 6.741050 0.882729 - 3.098735 - 0.330746 1.041127 - 3.140574 - 1.436662 2.035271 0.203884 - 0.821091 - 0.659716 1.345305 - 1.537599 - 0.639539 2.028107 3.638267 0.211225 5.067515 - 0.479032 2.713979 -2.921332 1.231413 - 1.559693 - 1.057173 - 0.335133 -3.601023 - 4.891684 - 1.832524 - 2.828772 0.257098 2.288298 - 4.795566 - 0.054114 1.991941 - 3.091072 4.949271 - 0.935447 3.327516 -3.299987 4.897994 1.306157 1.228019 -2.920305 0.710852 - 2.590932 - 3.644530 Time series in one partition Local Index Bloom Filter iSAX-T: abcd12ef34, ….
Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 19
000*,001*,001* Isax-t: 002 Exact Matching Query 20 Local Index Master Global Index Query Records in leaf node euDist = 0 Pid 6 Bloom Filter No Yes Exist? Pid:6 Worker Partition 6
KNN Approximate Query: One Partition Access 21 Worker 000*,001*,001* Isax-t: 002 Local Index Master iSAX-T Skeleton Query Pid Pid:6 (euDist, rid)1. euDist 2. sort 3. take Top(K)Records in leaf / internal node Partition 6 Records in leaf/internal node 1. euDist 2. sort 3. Top(K) dist as threshold
KNN Approximate Query: Multi-Partitions Access 22 000*,001*,001* iSAX-T: 002 Partition 6 Local Index Master Worker (euDist,rid) Local Index 1. euDist 2. sort 3. take Top(K) Sibling Pid List iSAX-T Skeleton Records in leaf/internal node 1. euDist 2. sort 3. Top(K) dist as threshold Records in leaf / internal node Query
Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 23
Experimental Setup 24 Dataset Size Length Random Walk 1 billion 256 Texmex 1 billion 128 DNA 200 million 192 Noaa Climate 200 million 64 HW&SW Configuration Spark 2.0.2, Standalone mode Hadoop 2.7.3 Platform Ubuntu 16.04. LTS HW 2 nodes, each node consist of 56 Xeon E5 processors, 500G RAM, 7TB SATA hard drive The dataset is normalized Each point is saved as float format Source: 1. http://corpus-texmex.irisa.fr/ 2. https://genmone.ucsc.edu 3. https://www.ncdc.gov/ 1 2 3 State-of-the-Art: Yagoubi, Djamel-Edine, et al. "DPiSAX: Massively Distributed Partitioned iSAX." ICDM 2017 The initial cardinality of the baseline system is the default value and it needs a large initial value to guarantee enough bit level for binary split. Baseline Spark-ITS Initial cardinality 512 64 Word length 8 8 Sampling percent 10% 10% Leaf node split threshold of Local index 1000 1000
Index Construction Time 25 0 500 1,000 1,500 2,000 200m 400m 600m 800m 1b 200m 400m 600m 800m 1b Spark-ITS Baseline (Minuts) #Time Series Global Index Local Index 2,323 334 Dataset: Random Walk Benchmark 80+% State-of-the-Art
0 10 20 30 40 Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline 200m 400m 600m 800m 1b (Minutes) sampling statistic build index assign Pid State-of-Art State-of-Art State-of-Art State-of-Art State-of-Art Sampling Statistic Build Index Assign Pid Index Construction Time: Breakdown 26 Global Index Time Breakdown Repartition and Local Index Time Breakdown Dataset: Random Walk Benchmark 0 500 1,000 1,500 2,000 Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline 200m 400m 600m 800m 1b (Minutes) iSAX read and convert Shuffle and build Local index Read and conversion State-of-Art State-of-Art State-of-Art State-of-Art State-of-Art Shuffle and Build Local Index
Exact Matching Query 27 State-of- the-Art State-of-the-Art
kNN-Approximate Query Performance 28 0% 15% 30% 45% 60% RandomWalk Texmex DNA Noaa ✕30 ✕ 35 ✕ 28 ✕ 72 1.0 1.3 1.6 1.9 2.2 RandomWalk Texmex DNA Noaa 27% 26% 48% 34% Recall Error Ratio Dataset (#Time series) Dataset (#Time series) (400m) (400m) (200m) (200m) (400m) (400m) (200m) (200m) State-of-the-Art
Conclusion • Index Tree – Large fan-out decreases the depth of leaf nodes – Keeps better similarity at Word-level – The signature simplifies the conversion of cardinality • Spark-ITS: Index Construction – Block-sampling and node statistic collection to fast build global index – Synchronously build local indices within a partition – Constructs Index faster 80+%. • Spark-ITS: Query – Exact Matching: the time decreases by 50%. – kNN approximate: the accuracy increases more than 10 fold. 29
Acknowledge Funding from... Xianjin Tech Co., Ltd. Saudi Arabian Cultural Mission WPI Computer Science Dept., NSF CNS: 305258 II-EN NSF CRI: 0551584

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Spark-ITS: Indexing for Large-Scale Time Series Data on Spark with Liang Zhang

  • 1. Liang Zhang (lzhang6@wpi.edu) Data Science Dept., Worcester Polytechnic Institute Spark-ITS: Indexing for Large-Scale Time Series Data on Spark #SAISEco5
  • 2. Prof. Elke A. Rundensteiner Prof. Mohamed Y. Eltabakh Liang Zhang Noura Alghamdi Data Science Research Group @ Worcester Polytechnic Institute Liang Zhang, Noura Alghamdi, Mohamed Y. Eltabakh, Elke A. Rundensteiner. TARDIS: Distributed Indexing Framework for Big Time Series Data. Proceedings of 35th IEEE International Conference on Data Engineering ICDE, 2019
  • 3. Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 3
  • 4. Time Series are Continuously Produced Everywhere • How to deal with billions of time series? 4 Climate data Web log Stock priceEEG
  • 5. Almost all Time Series Data Mining Tasks rely on Similarity Query 5 Esling, Philippe, and Carlos Agon. "Time-series data mining." ACM (CSUR) 45.1 (2012): 12. Clustering Motif Discovery Classification çΩ Outlier Detection Whole Matching Subsequence Matching
  • 6. Spark-ITS • A new Index Tree and an effective Signature to simplify the cardinality conversion and keep better similarity • A Distributed Index Framework to support large-scale time series dataset • Efficient algorithms for Exact Match and kNN Approximate queries process 6
  • 7. Spark-ITS Overview 7 Global Index Indexed Data Local Index Query Partition 1. Sampling 2. Node Statistic 3. Build Index Tree 4. Assign Partition ID 1. Construct Local Structure 2. Construct Bloom Filter 1. Read and convert data 2. Shuffle data
  • 8. Background: iSAX Representation 8 Shieh, Jin, and Eamonn Keogh. "iSAX: indexing and mining terabyte sized time series." SIGKDD ACM, 2008. Camerra, A., Palpanas, T., Shieh, J., & Keogh, E. "iSAX 2.0: Indexing and mining one billion time series." ICDM, 2010 A time series of length 16 PAA representation with 4 segments PAA: Piecewise Aggregate Approximation iSAX: indexable Symbolic Aggregate approXimation SAX representation with 4 segments and cardinality 4 [11,10,01,00] iSAX representation with 4 segments and variable cardinality [1", 1", 𝟎𝟏 𝟒, 0"]
  • 9. Word-level Similarity 9 -2 -1 0 1 2 1 3 5 7 9 11 A B C 111 110 101 100 011 010 001 000 -2 -1 0 1 2 1 3 5 7 9 11 A B C 111 110 101 100 011 010 001 000 State-of-the-art: Character-level Similarity Proposed: Word-level Similarity B and C are similar A and C are similar A: [𝟎 𝟏, 𝟎 𝟏, 𝟎𝟏𝟏 𝟑, 𝟏 𝟏] B: [𝟎 𝟏, 𝟎 𝟏, 𝟎𝟏𝟎 𝟑, 𝟏 𝟏] C: [𝟎 𝟏, 𝟎 𝟏, 𝟎𝟏𝟎 𝟑, 𝟏 𝟏] A: [𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟏𝟎 𝟐] B: [𝟎𝟎 𝟐, 𝟎𝟎 𝟐, 𝟎𝟏 𝟐, 𝟏𝟏 𝟐] C: [𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟎𝟏 𝟐, 𝟏𝟎 𝟐]
  • 10. New Index Tree Supports Word-level Similarity 10 Proposed: iSAX-T K-ary TreeState-of-the-art: iSAX Binary Tree Root 0", 1",0" 1", 1", 1"0", 0", 0" 0", 11%,0" 0", 10%, 0" 0",11%, 01% 0", 11%,00% . . .. . . Leaf nodeInternal node 1st bit 2nd bit 3rd bit Root 1",1",0" 1",1",1"0",0",0" 01$, 00$, 10$ 01$, 01$, 11$ 010&,000&,100& . . . 0",0",1" . . . 00$, 00$, 10$ 011&, 001&, 101& . . . Leaf nodeInternal node
  • 11. iSAX-T(Transpose) Signature 11 iSAX-T SAX(T,4,16) = {1100, 1101, 0110, 0001} = CE25 SAX(T,4,8) = {110, 110, 011, 000 } = CE2 SAX(T,4,4) = {11, 11, 01, 00 } = CE SAX(T,4,2) = {1, 1, 0, 0 } = C HexTranspose 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 C E 2 5 Time series: [1100, 1101, 0110, 0001]
  • 12. Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 12
  • 13. 1.368099 2.713573 -4.851872 -2.710113 -5.577432 0.797747 -0.998534 0.535733 -2.244053 -0.298195 -5.040225 -0.093288 2.683385 -4.839688 5.617443 -0.087439 -0.857566 2.537812 -3.809641 0.638194 0.706312 -3.016157 -3.094813 4.975719 -3.664357 1.402586 0.444090 1.969943 1.282233 1.912557 2.277926 1.511366 0.945206 5.769843 0.406734 -4.205288 0.850925 -2.994073 1.270280 1.286681 -5.681450 3.137617 -4.996282 3.160174 -8.749059 2.648822 6.117611 3.109095 3.159747 0.442472 -1.482878 3.432288 0.960204 0.380183 -3.925308 -2.112708 -2.991460 -3.692369 4.508871 6.430551 -3.929611 -4.271633 0.268938 -1.756457 0.978831 0.783966 -1.982449 1.100825 -6.741050 0.882729 -3.098735 -0.330746 -0.659716 1.345305 -1.537599 -0.639539 2.028107 3.638267 0.211225 5.067515 -0.479032 2.713979 -2.921332 1.231413 -1.559693 -1.057173 -0.335133 -3.601023 -4.891684 -1.832524 -2.828772 0.257098 2.288298 -4.795566 -0.054114 1.991941 Global Index[1/4]: Sampling 1.368099 2.713573 -4.851872 -2.710113 -5.577432 0.797747 -0.998534 0.535733 -2.244053 -0.298195 -5.040225 -0.093288 2.683385 -4.839688 5.617443 -0.087439 -0.857566 2.537812 -3.809641 0.638194 0.706312 -3.016157 -3.094813 4.975719 0.594820 1.136821 0.163368 5.379237 -5.453637 -0.282540 0.572556 6.158454 -1.632961 -1.560935 2.514265 2.987787 -3.006184 0.965107 4.543610 0.614290 1.851868 -2.935539 -0.716928 2.357205 -3.126861 1.620514 -0.490122 -3.380533 -2.301087 -4.727099 6.885664 -5.210190 1.707254 -7.965270 -0.914942 0.622116 1.620520 -0.994487 -0.021151 -1.749576 -3.664357 1.402586 0.444090 1.969943 1.282233 1.912557 2.277926 1.511366 0.945206 5.769843 0.406734 -4.205288 0.850925 -2.994073 1.270280 1.286681 -5.681450 3.137617 -4.996282 3.160174 -8.749059 2.648822 6.117611 3.109095 -3.164684 0.884269 2.925519 -1.051656 -0.371788 -1.661374 0.041967 0.126226 -5.662528 -1.026395 -1.317764 2.268905 -2.998881 2.628193 -4.195228 2.261641 -1.676540 -1.646810 -0.056534 -1.551837 -5.098098 2.857196 -2.981121 -0.559482 -0.573813 2.996416 -2.567590 3.113241 2.385687 -1.195035 -4.255606 2.898200 -2.443996 1.196084 -0.759899 -2.065437 -0.709810 -2.848963 4.183200 -0.901386 3.303330 -2.852400 0.022771 1.184107 1.556879 1.825932 -2.375073 1.430655 -1.844884 0.074289 3.309890 1.141529 2.022026 0.552751 3.941867 -4.384278 -0.374243 1.231169 3.094143 1.208599 -1.893548 4.995226 -4.282130 -1.408826 4.439037 1.134620 3.159747 0.442472 -1.482878 3.432288 0.960204 0.380183 -3.925308 -2.112708 -2.991460 -3.692369 4.508871 6.430551 -3.929611 -4.271633 0.268938 -1.756457 0.978831 0.783966 -1.982449 1.100825 -6.741050 0.882729 -3.098735 -0.330746 1.041127 -3.140574 -1.436662 2.035271 0.203884 -0.821091 -0.659716 1.345305 -1.537599 -0.639539 2.028107 3.638267 0.211225 5.067515 -0.479032 2.713979 -2.921332 1.231413 -1.559693 -1.057173 -0.335133 -3.601023 -4.891684 -1.832524 -2.828772 0.257098 2.288298 -4.795566 -0.054114 1.991941 -3.091072 4.949271 -0.935447 3.327516 -3.299987 4.897994 -2.998881 2.628193 -4.195228 2.261641 -1.676540 -1.646810 -0.056534 -1.551837 -5.098098 2.857196 -2.981121 -0.559482 -0.573813 2.996416 -2.567590 3.113241 2.385687 -1.195035 -4.255606 2.898200 -2.443996 1.196084 -0.759899 -2.065437 -0.709810 -2.848963 4.183200 -0.901386 3.303330 -2.852400 0.022771 1.184107 1.556879 1.825932 -2.375073 1.430655 -1.844884 0.074289 3.309890 1.141529 2.022026 0.552751 3.941867 -4.384278 -0.374243 1.231169 3.094143 1.208599 -1.893548 4.995226 -4.282130 -1.408826 4.439037 1.134620 3.159747 0.442472 -1.482878 3.432288 0.960204 0.380183 13 Sampling Map Reduce iSAX-T(b bits), Freq:1Time series iSAX-T(b bits), Freq(b bits) 1256ae3e , 1 0134ef45 , 1 234567ae , 1 1256ae3e , 1 1256ae3e , 1 234567ae , 1 237867ae , 1 024567ae , 1 6243371e , 1 …… 452167ef , 1 1256ae3e , 23 0134ef45 , 2 234567ae , 20 024567ae , 4 237867ae , 10 …… 452167ef , 10 Segment Number: 8, so use 2 letters to represent 1 bit Initial cardinality: b bit level The data size is based on 1 billion time series with 256 length Word counting MapReduce process 1 Terabyte 100 G 0.9 G HDFS 0.1 G
  • 14. Global Index[2/4]: Node Statistic 14 (iSAX-T(b),Freq(b)) (iSAX-T(1),Freq(b)) [(iSAX-T(1),Freq(1))] max(Freq(1)) Map Reduce Judge 1st layer: 2nd layer: Filter (iSAX-T(b),Freq(b)) (iSAX-T(2),Freq(b)) [(iSAX-T(2),Freq(2))] max(Freq(2)) Map Reduce Judge Filter 3rd layer: (iSAX-T(b),Freq(b)) (iSAX-T(3),Freq(b)) [(iSAX-T(3),Freq(3))] max(Freq(3)) Map Reduce Judge ……
  • 15. Global Index[3/4]: Build Tree 15 Root iSAX-T: 01 Freq: 512 . . . Segment number: 8 Partition Capacity: 100,000 iSAX-T: 02 Freq: 350,000 iSAX-T: 03 Freq: 4,352 iSAX-T: ff Freq: 270,520 iSAX-T: 0201 Freq: 5,012 iSAX-T: 0202 Freq: 100,550 iSAX-T: 02ff Freq: 620. . . iSAX-T: 020201 Freq: 12 iSAX-T: 020202 Freq: 550 iSAX-T: 0202ff Freq: 620 . . . • (“01”, 512) • (“02”, 355,000) • …. • (“ff”, 270,520) • (“0201”, 5,012) • (“0202”, 100,550) • …. • (“ffff”, 10,520) • (“020201”, 12) • (“020202”, 550) • …. • (“0202ff”, 620) 1st layer (iSAX-T, Freq) 2nd layer (iSAX-T, Freq) 3rd layer (iSAX-T, Freq)
  • 16. Global Index[4/4]: Assign Partition Id to Leaf Nodes 16 Bin Packing Problem: How to fit a set of nodes in the smallest numbers of partitions? Partition capacity: 100,000 Partition ID: 1 Partition ID: 2 Partition ID: 3 iSAX-T: 02 Freq: 390,500 iSAX-T: 0201 Freq: 70,000 iSAX-T: 0202 Freq: 50,000 iSAX-T: 0203 Freq: 20,000 iSAX-T: 0204 Freq: 40,000 iSAX-T: 0205 Freq: 80,000 iSAX-T: 0206 Freq: 130,500 iSAX-T: 0202 Freq: 50,000 iSAX-T: 0204 Freq: 40,000 iSAX-T: 0201 Freq: 70,000 iSAX-T: 0203 Freq: 20,000 iSAX-T: 0205 Freq: 80,000
  • 17. Repartition: Wrap Global Index as the Partitioner 17 Root iSAX-T: 01 Freq: 512 pid: 1 . . . iSAX-T: 02 Freq: 350,000 pid: 5,6,7 iSAX-T: 03 Freq: 4,352 pid:1 iSAX-T: ff Freq: 360,520 pid: 10,11,12 iSAX-T: 0201 Freq: 5,012 pid: 5 iSAX-T: 0202 Freq: 100,550 pid: 6,7 iSAX-T: 02ff Freq: 620 pid: 5 . . . iSAX-T: 020201 Freq: 12 pid: 6 iSAX-T: 020202 Freq: 550 pid:6 iSAX-T: 0202ff Freq: 620 . . . iSAX-T: 0202ff45 TS: [0.34, 0.31, 1.14…] iSAX-T: 0202ff45 A Time Series iSAX-T: 0202ff45 iSAX-T: 0202ff45
  • 18. Local Index: Construction Within Each Partition 18 Partition capacity: 100,000 Node split threshold: 1000 Segment Number: 8 abcd Freq:5000 ab3c Freq: 450 Root Freq: 90,990 abcd12 Freq: 1010 abcd45 Freq: 96 … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid …… iSAX-T, ts, rid iSAX-T, ts, rid abcd12ff Freq: 30 abcd1201 Freq: 42 …… ab45 Freq:4000 …… … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid … iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T, ts, rid iSAX-T: abcd12ef34, …. +1 +1 +1 1.368099 2.713573 -4.851872 -2.710113 - 5.577432 0.797747 - 0.998534 0.535733 -2.244053 - 0.298195 -5.040225 -0.093288 2.683385 - 4.839688 5.617443 - 0.087439 - 0.857566 2.537812 - 3.809641 0.638194 0.706312 - 3.016157 - 3.094813 4.975719 0.594820 1.136821 0.163368 5.379237 - 5.453637 - 0.282540 0.572556 6.158454 - 1.632961 - 1.560935 2.514265 2.987787 -3.006184 0.965107 4.543610 0.614290 1.851868 - 2.935539 - 0.716928 2.357205 -3.126861 1.620514 -0.490122 - 3.380533 -2.301087 - 4.727099 6.885664 -5.210190 1.707254 - 7.965270 -0.914942 0.622116 1.620520 - 0.994487 - 0.021151 - 1.749576 - 3.664357 1.402586 0.444090 1.969943 1.282233 1.912557 2.277926 1.511366 0.945206 5.769843 0.406734 -4.205288 0.850925 - 2.994073 1.270280 1.286681 - 5.681450 3.137617 - 4.996282 3.160174 - 8.749059 2.648822 6.117611 3.109095 - 3.164684 0.884269 2.925519 - 1.051656 - 0.371788 - 1.661374 0.041967 0.126226 - 5.662528 -1.026395 - 1.317764 2.268905 - 2.998881 2.628193 - 4.195228 2.261641 - 1.676540 - 1.646810 - 0.056534 - 1.551837 - 5.098098 2.857196 -2.981121 - 0.559482 - 0.573813 2.996416 - 2.567590 3.113241 2.385687 - 1.195035 - 4.255606 2.898200 - 2.443996 1.196084 - 0.759899 - 2.065437 - 0.709810 - 2.848963 4.183200 - 0.901386 3.303330 - 2.852400 0.022771 1.184107 1.556879 1.825932 - 2.375073 1.430655 - 1.844884 0.074289 3.309890 1.141529 2.022026 0.552751 3.941867 -4.384278 - 0.374243 1.231169 3.094143 1.208599 - 1.893548 4.995226 -4.282130 - 1.408826 4.439037 1.134620 3.159747 0.442472 - 1.482878 3.432288 0.960204 0.380183 - 3.925308 - 2.112708 - 2.991460 - 3.692369 4.508871 6.430551 - 3.929611 - 4.271633 0.268938 - 1.756457 0.978831 0.783966 - 1.982449 1.100825 - 6.741050 0.882729 - 3.098735 - 0.330746 1.041127 - 3.140574 - 1.436662 2.035271 0.203884 - 0.821091 - 0.659716 1.345305 - 1.537599 - 0.639539 2.028107 3.638267 0.211225 5.067515 - 0.479032 2.713979 -2.921332 1.231413 - 1.559693 - 1.057173 - 0.335133 -3.601023 - 4.891684 - 1.832524 - 2.828772 0.257098 2.288298 - 4.795566 - 0.054114 1.991941 - 3.091072 4.949271 - 0.935447 3.327516 -3.299987 4.897994 1.306157 1.228019 -2.920305 0.710852 - 2.590932 - 3.644530 Time series in one partition Local Index Bloom Filter iSAX-T: abcd12ef34, ….
  • 19. Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 19
  • 20. 000*,001*,001* Isax-t: 002 Exact Matching Query 20 Local Index Master Global Index Query Records in leaf node euDist = 0 Pid 6 Bloom Filter No Yes Exist? Pid:6 Worker Partition 6
  • 21. KNN Approximate Query: One Partition Access 21 Worker 000*,001*,001* Isax-t: 002 Local Index Master iSAX-T Skeleton Query Pid Pid:6 (euDist, rid)1. euDist 2. sort 3. take Top(K)Records in leaf / internal node Partition 6 Records in leaf/internal node 1. euDist 2. sort 3. Top(K) dist as threshold
  • 22. KNN Approximate Query: Multi-Partitions Access 22 000*,001*,001* iSAX-T: 002 Partition 6 Local Index Master Worker (euDist,rid) Local Index 1. euDist 2. sort 3. take Top(K) Sibling Pid List iSAX-T Skeleton Records in leaf/internal node 1. euDist 2. sort 3. Top(K) dist as threshold Records in leaf / internal node Query
  • 23. Outline • Motivation • Background • Spark-ITS Framework – Overview – Index Construction – Query Processing • Performance Evaluation 23
  • 24. Experimental Setup 24 Dataset Size Length Random Walk 1 billion 256 Texmex 1 billion 128 DNA 200 million 192 Noaa Climate 200 million 64 HW&SW Configuration Spark 2.0.2, Standalone mode Hadoop 2.7.3 Platform Ubuntu 16.04. LTS HW 2 nodes, each node consist of 56 Xeon E5 processors, 500G RAM, 7TB SATA hard drive The dataset is normalized Each point is saved as float format Source: 1. http://corpus-texmex.irisa.fr/ 2. https://genmone.ucsc.edu 3. https://www.ncdc.gov/ 1 2 3 State-of-the-Art: Yagoubi, Djamel-Edine, et al. "DPiSAX: Massively Distributed Partitioned iSAX." ICDM 2017 The initial cardinality of the baseline system is the default value and it needs a large initial value to guarantee enough bit level for binary split. Baseline Spark-ITS Initial cardinality 512 64 Word length 8 8 Sampling percent 10% 10% Leaf node split threshold of Local index 1000 1000
  • 25. Index Construction Time 25 0 500 1,000 1,500 2,000 200m 400m 600m 800m 1b 200m 400m 600m 800m 1b Spark-ITS Baseline (Minuts) #Time Series Global Index Local Index 2,323 334 Dataset: Random Walk Benchmark 80+% State-of-the-Art
  • 26. 0 10 20 30 40 Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline 200m 400m 600m 800m 1b (Minutes) sampling statistic build index assign Pid State-of-Art State-of-Art State-of-Art State-of-Art State-of-Art Sampling Statistic Build Index Assign Pid Index Construction Time: Breakdown 26 Global Index Time Breakdown Repartition and Local Index Time Breakdown Dataset: Random Walk Benchmark 0 500 1,000 1,500 2,000 Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline Spark-ITS Baseline 200m 400m 600m 800m 1b (Minutes) iSAX read and convert Shuffle and build Local index Read and conversion State-of-Art State-of-Art State-of-Art State-of-Art State-of-Art Shuffle and Build Local Index
  • 28. kNN-Approximate Query Performance 28 0% 15% 30% 45% 60% RandomWalk Texmex DNA Noaa ✕30 ✕ 35 ✕ 28 ✕ 72 1.0 1.3 1.6 1.9 2.2 RandomWalk Texmex DNA Noaa 27% 26% 48% 34% Recall Error Ratio Dataset (#Time series) Dataset (#Time series) (400m) (400m) (200m) (200m) (400m) (400m) (200m) (200m) State-of-the-Art
  • 29. Conclusion • Index Tree – Large fan-out decreases the depth of leaf nodes – Keeps better similarity at Word-level – The signature simplifies the conversion of cardinality • Spark-ITS: Index Construction – Block-sampling and node statistic collection to fast build global index – Synchronously build local indices within a partition – Constructs Index faster 80+%. • Spark-ITS: Query – Exact Matching: the time decreases by 50%. – kNN approximate: the accuracy increases more than 10 fold. 29
  • 30. Acknowledge Funding from... Xianjin Tech Co., Ltd. Saudi Arabian Cultural Mission WPI Computer Science Dept., NSF CNS: 305258 II-EN NSF CRI: 0551584