Skip to main content
Log in

A fast and effective method to find correlations among attributes in databases

  • Published:
Data Mining and Knowledge Discovery Aims and scope Submit manuscript

Abstract

The problem of identifying meaningful patterns in a database lies at the very heart of data mining. A core objective of data mining processes is the recognition of inter-attribute correlations. Not only are correlations necessary for predictions and classifications – since rules would fail in the absence of pattern – but also the identification of groups of mutually correlated attributes expedites the selection of a representative subset of attributes, from which existing mappings allow others to be derived. In this paper, we describe a scalable, effective algorithm to identify groups of correlated attributes. This algorithm can handle non-linear correlations between attributes, and is not restricted to a specific family of mapping functions, such as the set of polynomials. We show the results of our evaluation of the algorithm applied to synthetic and real world datasets, and demonstrate that it is able to spot the correlated attributes. Moreover, the execution time of the proposed technique is linear on the number of elements and of correlations in the dataset.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aha DW, Bankert RL (1995) A comparative evaluation of sequential feature selection algorithms. In: Proceedings of the 5th international workshop on artificial intelligence and statistics, Ft. Lauderdale, FL, USA, pp 1–7

  • Babu S, Garofalakis M, Rastogi R (2001) SPARTAN: a model-based semantic compression system for massive data tables. In: Proceedings of the 2001 ACM SIGMOD international conference on management of data (SIGMOD’01), Santa Barbara, CA, USA, pp 283–294

  • Balan AGR, Traina AJM, Traina C Jr, Azevedo-Marques PM (2005) Fractal analysis of image textures for indexing and retrieval by content. In: Proceedings of the 18th IEEE symposium on computer-based medical systems (CBMS’05), Dublin, Ireland, pp 581–586

  • Barbara D, Chen P (2003) Using self-similarity to cluster large data sets. Data Min Knowl Discov 7(2):123–152

    Article  MathSciNet  Google Scholar 

  • Belussi A, Faloutsos C (1995) Estimating the selectivity of spatial queries using the ‘Correlation Fractal Dimension’. In: Proceedings of the 21st international conference on very large data bases (VLDB’95), Zurich, Switzerland, pp 299–310

  • Belussi A, Faloutsos C (1998) Self-spatial join selectivity estimation using fractal concepts. ACM Trans Inf Syst 16(2):161–201

    Article  Google Scholar 

  • Böhm C (2000) A cost model for query processing in high dimensional data spaces. ACM Trans Database Syst 25(2):129–178

    Article  Google Scholar 

  • Böhm C, Kriegel H-P (2000) Dynamically optimizing high-dimensional index structures. In: Advances in Database Technology—EDBT 2000, 7th international conference on extending database technology. Lecture notes in computer science, vol 1777, Konstanz, Germany, pp 36–50

  • Blake C, Merz C (1998) UCI repository of machine learning databases. http://www.ics.uci. edu/∼mlearn/MLRePository.html

  • Blum AL, Langley P (1997) Selection of relevant features and examples in machine learning. Artif Intell 97(1–2):245–271

    Article  MATH  MathSciNet  Google Scholar 

  • Calvo R, Partridge M, Jabri M (1998) A comparative study of principal component analysis techniques. In: Proceedings of the 9th Australian conference on neural networks, Brisbane, Australia

  • Chakrabarti D, Faloutsos C (2002) F4: large-scale automated forecasting using fractals. In: International conference on information and knowledge management (CIKM), vol 1, McLean, EUA, pp 2–9

  • Chakrabarti K, Keogh E, Mehrotra S, Pazzani M (2002) Locally adaptive dimensionality reduction for indexing large time series databases. ACM Trans Database Syst (TODS) 27(2):188–228

    Article  Google Scholar 

  • Chang K, Ghosh J (1998) Principal curves for nonlinear feature extraction and classification. Appl Artif Neural Netw Image Process III (SPIE) 3307:120–129

    Google Scholar 

  • Dash M, Liu H, Yao J (1997) Dimensionality reduction for unsupervised data. In: Proceedings of the 9th IEEE international conference on tools with artificial intelligence (ICTAI’97), Newport Beach, CA, USA, pp 532–539

  • DeMers D, Cottrell G (1993) Non-linear dimensionality reduction. In: Advances in neural information processing systems (NIPS conference), vol 5, Denver, CO, USA, pp 580–587

  • Faloutsos C, Seeger B, Traina AJM, Traina C (2000) Spatial join selectivity using power laws. In: Proceedings of the 2000 ACM SIGMOD international conference on management of data (SIGMOD’00), Dallas, TX, USA, pp 177–188

  • Fayyad UM (1998) Mining databases: towards algorithms for knowledge discovery. IEEE Data Eng Bull 21(1):39–48

    Google Scholar 

  • Hyvärinen A (1999) Survey on independent component analysis. Neural Comput Surv 2:94–128

    Google Scholar 

  • Jebara TS, Jaakkola TS (2000) Feature selection and dualities in maximum entropy discrimination. In: Proceedings of the 16th conference on uncertainty in artificial intelligence (UAI’2000), San Francisco, CA, USA, pp 291–300

  • Jiang D, Tang C, Zhang A (2004) Cluster analysis for gene expression data: a survey. IEEE Trans Knowl Data Eng 16(11):1370–1386

    Article  Google Scholar 

  • John GH, Kohavi R, Pfleger K (1994) Irrelevant features and the subset selection problem. In: Proceedings of the 11th international conference on machine learning (ICML’94), New Brunswick, NJ, USA, pp 121–129

  • Kamel I, Faloutsos C (1994) Hilbert R-tree: an improved R-tree using fractals. In: Proceedings of 20th international conference on very large data bases (VLDB’94), Santiago de Chile, Chile, pp 500–509

  • Kantardzic M, Sadeghian P, Shen C (2004) The time diversification monitoring of a stock portfolio: an approach based on the fractal dimension. In: Proceedings of the 2004 ACM symposium on applied computing (SAC’04), pp 637–641

  • Kanth KVR, Agrawal D, Singh AK (1998) Dimensionality reduction for similarity searching in dynamic databases. In: Proceedings of the 1998 ACM SIGMOD international conference on management of data (SIGMOD’98), Seattle, WA, USA, pp 166–176

  • Keogh EJ, Chakrabarti K, Mehrotra S, Pazzani MJ (2001) Locally adaptive dimensionality reduction for indexing large time series databases. In: Proceedings of the 2001 ACM SIGMOD international conference on management of data (SIGMOD’01), Santa Barbara, CA, USA, pp 151–162

  • Kira K, Rendell LA (1992) A practical approach to feature selection. In: Proceedings of the 9th international workshop on machine learning (ML’92), Aberdeen, Scotland, pp 249–256

  • Kononenko I (1994) Estimating attributes: analysis and extensions of RELIEF. In: Proceeding of European conference on machine learning (ECML-94). Lecture notes in computer science, vol 784, Catania, Italy, pp 171–182

  • Korn F, Jagadish HV, Faloutsos C (1997) Efficiently supporting ad hoc queries in large datasets of time sequences. In: Proceedings of the 1997 ACM SIGMOD international conference on management of data (SIGMOD’97), Tucson, AZ, USA, pp 289–300

  • Korn F, Pagel B-U, Faloutsos C (2001) On the ‘dimensionality curse’ and the self-similarity blessing. IEEE Trans Knowl Data Eng 13(1):96–111

    Article  Google Scholar 

  • Kramer MA (1991) Nonlinear principal component analysis using autoassociative neural networks. Am Inst Chem Eng J (AIChE) 37(2):233–243

    Google Scholar 

  • Langley P, Sage S (1997) Scaling to domains with many irrelavant features. In: Computational learning theory and natural learning system, vol IV, Cambrige, MA, USA

  • Liu H, Yu L (2005) Toward integrating feature selection algorithms for classification and clustering. IEEE Trans Knowl Data Eng 17(4):491–502

    Article  Google Scholar 

  • Liu Y, Lazar NA, Rothfus WE, Buzoianu M, Kanade T (2001) Classification-driven feature space reduction for semantic-based neuroimage retrieval. In: VISIM workshop: information retrieval and exploration in large medical image collections, Utrecht, The Netherlands

  • Mitra P, Murthy C, Pal S (2002) Unsupervised feature selection using feature similarity. IEEE Trans Pattern Anal Mach Intel 24(4):301–312

    Article  Google Scholar 

  • Moon B, Jagadish HV, Faloutsos C, Saltz JH (2001) Analysis of the clustering properties of the Hilbert space-filling curve. IEEE Trans Knowl Data Eng 13(1):124–141

    Article  Google Scholar 

  • Pagel B-U, Korn F, Faloutsos C (2000) Deflating the dimensionality curse using multiple fractal dimensions. In: Proceedings of the 16th international conference on data engineering (ICDE’00), San Diego, CA, USA, pp 589–598

  • Quinlan JR (1993) C4.5: programs for machine learning. Morgan Kaufmann, San Francisco, CA, USA

    Google Scholar 

  • Reynolds HT (1977) The analysis of cross-classifications. The Free Press, New York, NY, USA

    Google Scholar 

  • Robnik-Sikonja M (1997) CORE—a system that predicts continuous variables. In: Proceedings of ERK’97, Portoroz, Slovenia

  • Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326

    Article  Google Scholar 

  • Scherf M, Brauer W (1997) Feature selection by means of a feature weighting approach. Technical report FKI-221-97, Munich University of Technology, Munich, Germany

  • Schölkopf AS, Müller K-R (1998) Nonlinear component analysis as a Kernel Eigenvalue problem. Neural Comput 10:1299–1319

    Article  Google Scholar 

  • Schroeder M, (1991) Fractals, chaos, power laws: minutes from an infinite paradise. W. H. Freeman and Company, New York, NY, USA

    MATH  Google Scholar 

  • Singh M, Provan GM (1995) A comparison of induction algorithms for selective and non-selective bayesian classifiers. In: Proceedings of the 12th international conference on machine learning (ICML’95), Tahoe City, CA, USA, pp 497–505

  • Takahashi T, Tokunaga R (1999) Nonlinear dimensionality reduction by multi layer perceptron using superposed energy. In: Proceedings of 1999 international symposium on nonlinear theory and its applications, vol 2, Hawaii, USA, pp 863–866

  • Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323

    Article  Google Scholar 

  • Traina A, Traina C, Papadimitriou S, Faloutsos C (2001) Tri-Plots: scalable tools for multidimensional data mining. In: Proceedings of the 7th ACM SIGKDD international conference on knowledge discovery and data mining (KDD’01), San Francisco, CA, USA, pp 184–193

  • Traina AJM, Castan̆ón CAB, Traina C (2003) MultiWaveMed: a system for medical image retrieval by wavelets transformations. In: Proceedings of the 16th IEEE symposium on computer-based medical systems, New York, NY, USA, pp 150–155

  • Traina C, Traina A, Wu L, Faloutsos C (2000) Fast feature selection using fractal dimension. In: Anais do XV Simpósio Brasileiro de Banco de Dados (SBBD’00), Joäo Pessoa, Brasil, pp 158–171

  • Traina C, Traina AJM, Faloutsos C (1999) Distance exponent: a new concept for selectivity estimation in metric trees. Technical report CMU-CS-99-110, Carnegie Mellon University, School of Computer Science, Pittsburgh, PA, USA

  • Traina C, Traina AJM, Faloutsos C, Seeger B (2002) Fast indexing and visualization of metric data sets using Slim-Trees. IEEE Trans Knowl Data Eng 14(2):244–260

    Article  Google Scholar 

  • Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86

    Article  Google Scholar 

  • Vafaie H, DeJong K (1993) Robust feature selection algorithms. In: Proceedings of the 5th international conference on tools with artificial intelligence (ICTAI ’93), Boston, MA, USA, pp 356–363

  • Vailaya A, Figueiredo MAT, Jain AK, Zhang H-J (2001) Image classification for content-based indexing. IEEE Trans Image Process 10(1):117–130

    Article  MATH  Google Scholar 

  • Wactlar HD, Kanade T, Smith MA, Stevens SM (1996) Intelligent access to digital video: informedia project. IEEE Comput 29(5):46–52

    Google Scholar 

  • Witten IH, Frank E (2000) Data mining: practical machine learning tools with Java implementations. Morgan Kaufmann, San Francisco, CA, USA

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elaine P. M. de Sousa.

Additional information

Responsible editor: E. Keogh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Sousa, E.P.M., Traina, C., Traina, A.J.M. et al. A fast and effective method to find correlations among attributes in databases. Data Min Knowl Disc 14, 367–407 (2007). https://doi.org/10.1007/s10618-006-0056-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10618-006-0056-4

Keywords

Navigation