Ability Study of Proximity Measure for Big Data Mining Context on Clustering
- 1. Ability Study of Proximity Measure for Big Data Mining Context on Clustering Kamlesh Kumar Pandey Research Scholar Dept. of Computer Science & Applications Dr. HariSingh Gour Vishwavidyalaya (A Central University), Sagar, M.P. E-mail: kamleshamk@gmail.com 2nd International Conference on Communication and Computational Technologies (Paper ID : 16) Paper Presentation on
- 2. Content • Objectives • Big Data • Big Data Mining • Proximity Measures Enabled Clustering Taxonomy • Proximity Measure Taxonomy • Analysis of Proximity Measure for Big Data Mining
- 3. Objectives • The objective of this study is identifying a proximity measures for big data clustering respect to volume, variety, and velocity and presents how to create a cluster with the help of a proximity measure under the partition, hierarchical, density, grid, model, fuzzy and graph based cluster taxonomy.
- 4. Big Data • Present time technology is growing very fast. Every originations, industries or person moving towards Internet of things, cloud computing, warless sensor networks, social media, internet. These sources generated a data growing fast in per second, minutes or per hour in size of Terabytes or Petabytes . • Diebold et Al. (2000) is a first writer who discussed the word Big Data in his research paper. All of these authors define Big Data there means if the data set is large then gigabyte then these type of data set is known as Big Data. • Doug Laney et al (2001) was the first person who gave a proper definition for Big Data. He gave three characteristics Volume, Variety, and Velocity of Big Data and these characteristics known as 3 V’s of Big Data Management. If traditional data have met two basic characteristic at a time these data are come to under Big data. • Gartner (2012), “Big data is high-volume, high-velocity and high-variety information assets that demand cost-effective, innovative forms of information processing for enhanced insight and decision making”
- 5. Big Data V’s • In present time seven V’s used for Big Data where the first three V’s Volume, Variety, and Velocity are the main characteristics of big data. In addition to Veracity, Variability, Value, and Visualization are depending on the organization.
- 6. Big Data Mining • Big Data Mining fetching on the requested information, uncovering hidden relationship or patterns or extracting for the needed information or knowledge from a dataset these datasets have to meet three V’s of Big Data with higher complexity.
- 7. Clustering • Clustering is the one of the approaches for analysis and discovering the complex relation, pattern, and data in the form of underlying groups for the unlabeled object and Big Data perspective, the clustering algorithm must be deal high volume, high variety and high velocity with scalability.
- 8. Clustering Taxonomy • Partitioning based Clustering: These clustering methods constructs the clusters on the bases of center in the choice of k number of clusters. This clustering method used proximity measures as finding out the center of the cluster creation. • Hierarchical based Clustering: In this approach, large data are organized in a hierarchical manner based on the medium of proximity and its detect on easily relationship between data points. • Density Based Clustering: This clustering method scans the spatial databases and used for probability distribution based distance measure and distance measurements for creating core, border and noise point for density cluster. • Grid-Based Clustering: This clustering algorithm splits the data space into a grid structure, calculate the cell density, calculate the grid structure with the help of distance measure. • Model-Based Clustering: This clustering method optimizes the dataset into the mathematical model based on the mixing of probability distributions based distance measure and distance measure are also measuring the parameter of the selected model.
- 9. Proximity Measure Taxonomy In present time various proximity measure is available for cluster construction and these proximity measure categories under • Minkowski • L(1) • L(2) • Inner product • Shannon’s entropy • Combination • Intersection
- 10. Minkowski family Proximity Measures • 𝑑𝑖𝑠 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴𝑖 − 𝐵𝑖| 𝑃 1 𝑃 (Eq.1) • 𝑑𝑖𝑠manhattan 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴𝑖 − 𝐵𝑖| 𝑃 (Eq.2) p=1, construct hyper-rectangular shape cluster. • 𝑑𝑖𝑠euclidean 𝐴, 𝐵 = 2 𝑖=1 𝑛 |𝐴𝑖 − 𝐵𝑖|2 (Eq.3) p=2, construct compact or isolated cluster. • 𝑑𝑖𝑠minkowski 𝐴, 𝐵 = 𝑝 𝑖=1 𝑛 |𝐴𝑖 − 𝐵𝑖| 𝑝 (Eq.4) p= 2 to ∞, construct isolated or compacted cluster. • 𝑑𝑖𝑠chebyshev 𝐴, 𝐵 = ∞ 𝑖=1 𝑛 |𝐴𝑖 − 𝐵𝑖|∞ = 𝑚𝑎𝑥𝑖=1 𝑛 |𝐴𝑖 − 𝐵𝑖| 𝑃 (Eq.5) p= ∞ to maximum. This distance measure is used for when two data points are greatest of their absolute magnitude along with data dimension.
- 11. L(1) family, Manhattan family Proximity Measures The Manhattan distance measure faces two difficulties in the respects of distance value. First one is normalization of a distance value and second is related to figure out of small and large distance. • 𝑑𝑖𝑠sorensen 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴 𝑖−𝐵 𝑖| 𝑖=1 𝑛 |𝐴 𝑖+𝐵 𝑖| (Eq.6) Normalized dis value between 0 and 1. • 𝑑𝑖𝑠soergel 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴 𝑖−𝐵 𝑖| 𝑖=1 𝑛 max 𝐴 𝑖 𝐵 𝑖 (Eq.7) choosing the max coefficient data point. • 𝑑𝑖𝑠kulczynski 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴 𝑖−𝐵 𝑖| 𝑖=1 𝑛 min 𝐴 𝑖 𝐵 𝑖 (Eq.8) choosing the min coefficient data point. • 𝑑𝑖𝑠motyka 𝐴, 𝐵 = 𝑖=1 𝑛 max 𝐴 𝑖 𝐵 𝑖 𝑖=1 𝑛 |𝐴 𝑖+𝐵 𝑖| (Eq.9) takes the max data point of the data set. • 𝑑𝑖𝑠canberra 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴 𝑖−𝐵𝑖| |𝐴 𝑖+𝐵𝑖| (Eq.10) absolute difference of the individual data. • 𝑑𝑖𝑠lorentzian 𝐴, 𝐵 = i=1 n ln(1 + |𝐴𝑖 − 𝐵𝑖| (Eq.11) Normalized dis value natural logarithm • 𝑑𝑖𝑠wavehedge 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴 𝑖−𝐵 𝑖| max 𝐴 𝑖 𝐵 𝑖 (Eq.12) normalizes the difference of each data pair with its max value
- 12. L(2) or χ 2, Euclidian family Proximity Measures The L(2) family member based on the Euclidian distance and gives the distance value after normalization. • 𝑑𝑖𝑠matusita 𝐴, 𝐵 = 𝑖=1 𝑛 ( 𝐴𝑖 − 𝐵𝑖)2 (Eq. 13) • 𝑑𝑖𝑠clark 𝐴, 𝐵 = 𝑖=1 𝑛 ( |𝐴 𝑖−𝐵 𝑖| (𝐴 𝑖+𝐵 𝑖) )2 (Eq. 14) • 𝑑𝑖𝑠divergence 𝐴, 𝐵 = 2 𝑖=1 𝑛 (𝐴 𝑖−𝐵 𝑖)2 (𝐴 𝑖+𝐵 𝑖)2 (Eq. 15) • 𝑑𝑖𝑠squared_euclidean 𝐴, 𝐵 = 𝑖=1 𝑛 (𝐴𝑖 − 𝐵𝑖)2 (Eq.16) • 𝑑𝑖𝑠squared_chi 𝐴, 𝐵 = 𝑖=1 𝑛 (𝐴 𝑖−𝐵 𝑖)2 (𝐴 𝑖+𝐵 𝑖) (Eq. 17) • 𝑑𝑖𝑠pearson_chi 𝐴, 𝐵 = 𝑖=1 𝑛 (𝐴 𝑖−𝐵 𝑖)2 𝐵 𝑖 (Eq. 18) • 𝑑𝑖𝑠neyman_chi 𝐴, 𝐵 = 𝑖=1 𝑛 (𝐴 𝑖−𝐵 𝑖)2 𝐴 𝑖 (Eq. 19)
- 13. Inner product family Proximity Measures Inner product distance measure gives the distance on the basis of multiplication of real data. Their formulation shows as Eq. 20 and normalized distances shown as Eq. 21 to Eq. 24 respectively on the basis of Eq. 20. • 𝑑𝑖𝑠inner_product 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴𝑖 𝐵𝑖 (Eq. 20) • 𝑑𝑖𝑠cosine 𝐴, 𝐵 = 𝒊=𝟏 𝒏 𝐴 𝑖 𝐵 𝑖 𝒊=𝟏 𝒏 𝐴 𝑖 𝟐 𝒊=𝟏 𝒏 𝐵 𝑖 𝟐 (Eq. 21) • 𝑑𝑖𝑠Jaccard 𝐴, 𝐵 = 1 − 𝑖=1 𝑛 𝐴 𝑖 𝐵 𝑖 𝑖=1 𝑛 𝐴 𝑖 2 + 𝑖=1 𝑛 𝐵 𝑖 2− 𝑖=1 𝑛 𝐴 𝑖 𝐵 𝑖 (Eq. 22) • 𝑑𝑖𝑠dice 𝐴, 𝐵 = 1 − 𝟐 𝒊=𝟏 𝒏 𝐴 𝑖 𝐵 𝑖 𝒊=𝟏 𝒏 𝐴 𝑖 2 + 𝒊=𝟏 𝒏 𝐵 𝑖 2 (Eq. 23) • 𝑑𝑖𝑠Harmonic_mean 𝐴, 𝐵 = 2 i=1 n AiBi Ai+Bi (Eq. 24)
- 14. Shannon’s entropy family Proximity Measures This family is based on probabilistic uncertainty or entropy. Here all data point Ai must be non-negative and their sum is always equal to 1 and logarithm base is fixed as 2 for distance measure. • 𝑑𝑖𝑠kullback_leibler 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴𝑖 ln 𝐴 𝑖 𝐵 𝑖 (Eq. 25) • 𝑑𝑖𝑠jeffreys 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴𝑖 −𝐵𝑖 ln 𝐴 𝑖 𝐵 𝑖 (Eq. 26) • 𝑑𝑖𝑠k_divergence 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴𝑖 ln 2𝐴 𝑖 𝐴 𝑖−𝐵 𝑖 (Eq. 27) • 𝑑𝑖𝑠topsoe 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴𝑖 ln 2𝐴 𝑖 𝐴 𝑖−𝐵 𝑖 + 𝐵𝑖 ln 2𝐴 𝑖 𝐴 𝑖−𝐵 𝑖 (Eq. 28) • 𝑑𝑖𝑠jensen_shannon 𝐴, 𝐵 = 𝟏 𝟐 𝑖=1 𝑛 𝐴𝑖 ln 2𝐴 𝑖 𝐴 𝑖−𝐵 𝑖 + 𝑖=1 𝑛 𝐵𝑖 ln 2𝐴 𝑖 𝐴 𝑖−𝐵 𝑖 (Eq. 29) • 𝑑𝑖𝑠jensen_difference 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴 𝑖 ln 𝐴 𝑖+𝐵 𝑖 ln 𝐵 𝑖 2 − 𝐴 𝑖−𝐵 𝑖 2 ln 𝐴 𝑖−𝐵 𝑖 2 (Eq. 30)
- 15. Combination family Proximity Measures This family member defines a distance measure on the bases of a combination of two or more distance measures. • 𝑑𝑖𝑠taneja 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴 𝑖+𝐵 𝑖 2 ln 𝐴 𝑖+𝐵 𝑖 2 𝐴 𝑖 𝐵 𝑖 (Eq. 31) • 𝑑𝑖𝑠kumar_johnson 𝐴, 𝐵 = 𝑖=1 𝑛 𝐴 𝑖 2 −𝐵 𝑖 2 2 2 𝐴 𝑖 𝐵 𝑖 3 2 (Eq. 32)
- 16. Intersection family Proximity Measures This family member defines a distance measure on the basis of intersection between data points. The formulation of intersection distance measure is shown as (Eq. 33) and their variance shown as Eq. 34 to Eq. 36 . • 𝑑𝑖𝑠intersection 𝐴, 𝐵 = 𝑖=1 𝑛 min 𝐴𝑖 𝐵𝑖 (Eq. 33) • 𝑑𝑖𝑠wavehedges 𝐴, 𝐵 = 𝑖=1 𝑛 |𝐴 𝑖−𝐵 𝑖| max 𝐴 𝑖 𝐵 𝑖 (Eq. 34) • 𝑑𝑖𝑠ruzicka 𝐴, 𝐵 = 𝒊=𝟏 𝒏 mix 𝐴 𝑖 𝐵 𝑖 𝒊=𝟏 𝒏 max 𝐴 𝑖 𝐵 𝑖 (Eq. 35) • 𝑑𝑖𝑠tanimoto 𝐴, 𝐵 = 𝒊=𝟏 𝒏 max 𝐴 𝑖 𝐵 𝑖 − 𝒊=𝟏 𝒏 mix 𝐴 𝑖 𝐵 𝑖 𝒊=𝟏 𝒏 max 𝐴 𝑖 𝐵 𝑖 (Eq. 36)
- 17. Analysis of Proximity Measure for Big Data Mining Fahad et al. 2014 and Pandove et al., 2015 describe clustering algorithm criteria on the bases of the Volume, Velocity, and Variety dimensions of big data. • Volume related criteria such as cluster is must be dealt huge scale size, high dimensional and noisy of the dataset. • Variety related criteria such as cluster is must be recognized as dataset categorization and clusters Shape. • Velocity related criteria define the complexity, scalability, and performance of the clustering algorithm during the execution of real dataset. This paper takes Volume as clustering algorithm must be deal high scale dataset, Variety deal data type of clustering as continuous (numerical) and categorical (nominal and binary) data , and Velocity defines time complexity for identification of big data enable distance measures.
- 18. Analysis of Proximity Measure for Big Data Mining Distance measure Type of function Volume (High Data Set) Variety (Type of Data) Velocity (Time Complexity) Minkowski family Eq. 2 Distance Large Continuous 0(n) Eq. 3 Distance Large Continuous 0(n) Eq. 4 Distance Large Continuous 0(n) Eq. 5 Distance Large Continuous 0(n) L(1) family Eq. 6 Semi-metric Large Categorical 0(2n) Eq. 7 Distance Large Continuous 0(n) Eq. 8 Semi-metric Medium Categorical 0(n) Eq. 9 similarity Medium Categorical 0(n) Eq. 10 Distance Large Continuous 0(n) Eq. 11 Distance Large Continuous 0(n) Eq. 12 Distance Large Continuous 0(n)
- 19. Analysis of Proximity Measure for Big Data Mining Distance measure Type of function Volume (High Data Set) Variety (Type of Data) Velocity (Time Complexity) L(2) or χ 2 family Eq. 13 Distance Large Continuous 0(n) Eq. 14 Distance Large Continuous 0(n) Eq. 15 Semi-metric Large Categorical 0(n) Eq. 16 Semi-metric Large Categorical 0(n) Eq. 17 Semi-metric Large Categorical 0(2n) Eq. 18 Semi-metric Large Categorical 0(2n) Eq. 19 Semi-metric Large Categorical 0(2n) Inner product family Eq. 20 Similarity Medium Categorical 0(3n) Eq. 21 Similarity Medium Categorical 0(3n) Eq. 22 Semi-metric Large Categorical 0(2n) Eq. 23 Semi-metric Large Categorical 0(2n)
- 20. Analysis of Proximity Measure for Big Data Mining Distance measure Type of function Volume (High Data Set) Variety (Type of Data) Velocity (Time Complexity) Shannon’s entropy family Eq. 25 Similarity Medium Categorical 0(n) Eq. 26 Semi-metric Large Categorical 0(n) Eq. 27 Similarity Medium Categorical 0(n) Eq. 28 Semi-metric Large Categorical 0(n) Eq. 29 Semi-metric Large Categorical 0(n) Eq. 30 Semi-metric Large Categorical 0(n) Combination family Eq. 31 Semi-metric Large Categorical 0(2n) Eq. 32 Semi-metric Large Categorical 0(2n) Intersection family Eq. 33 Similarity Medium Categorical 0(2n) Eq. 34 Distance Large Continuous 0(2n)
- 21. Conclusions This paper analyzed all studied 34 proximity measures for big data mining characteristics as volume (dataset size) Variety (dataset type, and Velocity (time complexity) and find Eq. 2 Manhattan distance, Eq. 3 Euclidean distance, Eq. 4 Minkowski distance, Eq. 5 Chebyshev distance, Eq. 7 soergel, Eq. 10 canberra, Eq. 11 lorentzian, Eq. 12 wavehedge, Eq. 13 matusita, Eq. 14 clark, Eq. 34 wavehedges are more scalable for big data based on theoretical, practical and the existing research perspective.
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