Support Data Sampling Using Bitmap Indices over Scientific Dataset

Yu Su*, Gagan Agrawal*, Jon Woodring†

*The Ohio State University†Los Alamos National Lab

Outline

• Motivation and Introduction• Background• System Overview• Index Sampling and Optimizations• Experiment Results• Conclusion

Motivation• Science becomes increasingly data driven;• Strong requirement for efficient data analysis;• Challenges:

– Fast data generation speed– Slow disk IO and network speed – Some number from road-runner EC3 simulation

• 40003 particles, 36 bytes per particle => 2.3 TB/time• 10GB/s • 230 times different, and bigger in future

• Extremely hard to analyze or visualize entire data

Existing Data Management Methods

SimpleRequest

AdvancedRequest

Challenges?

No subsetting request?

Data subset still big?

Server-side SubsettingClient-side Subsetting

Server-side Data Sampling• Statistic Sampling Techniques:

– sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.

• Examples: – Simple Random Sampling– Stratified Random Sampling

• Information Loss is Unavoidable• Error Metrics:

– Mean, Variance – Histogram– QQPlot

Data Sampling Challenges• Challenges in Scientific Data Management:

– Data Accuracy. Fail to consider data features.• Data Value Distribution• Data Spatial Locality

– Error Calculation is time-consuming.– Can’t support sampling over flexible data subset– Data has to be reorganized

• Bitmap indexing has been widely used– Support efficient subsetting over values– Fastbit, FastQuery, our ICPP work

Our Solution• A server-side subsetting and sampling framework.

– Standard SQL interface– Data Subsetting: Dimensions, Values

• TEMP(longitude, latitude, depth) ;– Flexible sampling mechanism

• Support Data Sampling over Bitmap Indices– No data reorganization is needed– Generate an accurate error metrics result– Support Error Prediction before sampling the data– Support data sampling over flexible data subset

Background: Bitmap Indexing• Widely used in Scientific Data Management

• Suitable for float value for binning small ranges• Run Length Compression(WAH, BBC)

– Compress bitvector based on continuous 0s or 1s

System Architecture

Data Sampling Using Bitmap Indices

• Features: – Different bitvectors reflect the value distribution;– Each bitvector keep the data locality;

• Row major, Column major• Hilbert Curve, Z-order Curve

• Method:– Perform stratified sampling within each bitvector;– Multi-level indexing generates multi-level samples;

Stratified Sampling over Bitvectors

S1: Index Generation

S2: Divide Bitvector into Equal Strides

S3: Random Select certain % of 1’s out of

each stride

Error Prediction

• Calculate errors based on bins instead of samples– Indices classifies the data into bins;– Each bin corresponds to one value or value range;– Find a represent value for each bin: Vi;– Equal probability is forced for each bin;– Compute number of samples within each bin: Ci;– Predict error metrics based on Vi and Ci;

• Represent Value: – Small Bin: mean or median value– Big Bin: lower-bound, upper-bound, mean value

Error Prediction Metadata

MeanVarianceHistogramQQPlot

Mean, Variance over Strides

Error Prediction Formula (1)• Mean, Variance:

• Histogram:

Error Prediction Formula (2)• QQPlot

Data Subsetting + Sampling

S3: Perform Sampling on Subset

S2: Find Spatial ID subset

S1: Find value subset Val = 1.2

ID = (11, 21)

Multi-attributes Subsetting and Sampling Support

S3: Generate Bitmap Indices based on mbins

S2: Combine Single Value Intervals to mbins

S1: Generate Value Interval for each attribute

Experiment Setup• Environment:

– Darwin Cluster: 120 nodes, 48 cores, 64 GB memory• Dataset:

– Ocean Data – Regular Multi-dimensional Dataset– Cosmos Data – Discrete Points with 7 attributes

• Sampling Method: – Simple Random Method– Simple Stratified Random Method– KDTree Stratified Random Method– Big Bin Index Random Method– Small Bin Index Random Method

Experiment Goals

• Two Applications after Sampling: – Data Visualization - Paraview– Data Mining - K-means in MATE

• Goals: – Efficiency and Accuracy with and without sampling– Accuracy between different sampling methods– Efficiency between different sampling methods– Compare Predicted Error with Actual Error – Speedup for sampling over data subset

Efficiency and Accuracy of Sampling over Ocean Data

• Data size: 11.2 GB TEMP• Network Transfer Speed: 20 MB/s• Speedup compared to original dataset: 25% - 1.87; 12.5% - 3.72; 1% - 10.97; 0.1% - 31.62;

• Error Metrics: Variances over Strides• Value diffs between original and samples• Information Loss Percent: 25% - 0.39%; 12.5% - 0.56%; 1% - 0.91%; 0.1% - 1.18%;

Efficiency and Accuracy of Sampling over Cosmos Data

• Data size: 16 GB (VX, VY, VZ)• Network Transfer Speed: 20 MB/s• Speedup compared to original dataset: 25% - 2.11; 12.5% - 4.30; 1% - 21.02; 0.1% - 60.14;

• Kmeans: 20 clusters, 3 dims, 50 iterations• MATE: 16 threads • Error Metrics: Means of cluster centers• Much better than other methods

Absolute Mean Value Differences over Strides – 0.1%

Absolute Histogram Value Differences – 0.1%

Absolute QQPlot Value Differences – 0.1%

Data Sampling Time

• Data size: 1.4 GB• Our method: extra

striding cost• Compare: small bin

random cost 1.19 – 3.98 most time compared with KDTree random method

Error Calculation Time

• Error Prediction: O(m)• Error Calculation

• QQPlot: O(slogs)• Others: O(s)

• Compare: Error Prediction achieved >28 times speedup compared with error calculation

Total Time based on sampling times

• Depends on sampling times

• Comparison: Small bin methods achieved a 0.37 – 5.29 times speedup compared with KDTree random method

Predicted Error vs. Actual Error

Predicted Error vs. Actual Error

Subsetting OptimizationSubset over Spatial IDsSubset over values

• Smaller Index Loading Time• Smaller Sampling Time• Speedup: 2.28 - 21.54 for small bin 2.25 - 13.56 for big bin

• Smaller Sampling Time• Speedup: 1.37 - 2.48 for small bin 1.67 - 3.02 for big bin

Conclusion

• ‘Big Data’ issue brings challenges ;• Data sampling is necessary for data analysis;• Perform server-side sampling over bitmap indices;• Error Prediction and Sampling based on subset;• Achieve a good accuracy and efficiency.

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