Feature Selection for High-Dimensional Data: A Fast Correlation-Based Filter Solution

Lei YuHuan Liu

article2003ICML2,787 citations

Introduces the Fast Correlation-Based Filter algorithm, which efficiently removes both irrelevant and redundant features from high-dimensional data in sub-quadratic time using the concept of predominant correlation without requiring exhaustive pairwise comparisons.

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High-dimensional datasets in applications such as genomics, text categorization, and image retrieval contain many irrelevant and redundant features that degrade the speed and accuracy of machine learning algorithms. Feature selection serves as an essential preprocessing step, yet existing filter and wrapper methods struggle with scalability when the number of features reaches hundreds or thousands.

The article set out to develop and test a fast correlation-based filter algorithm that removes both irrelevant and redundant features without exhaustive pairwise comparisons.

The authors introduced the concept of predominant correlation and built the FCBF algorithm around symmetrical uncertainty, an entropy-based measure. They evaluated it on ten UCI benchmark datasets ranging from 57 to 650 features, comparing runtime, number of selected features, and classification accuracy against ReliefF, CorrSF, and ConsSF using C4.5 and naïve Bayes classifiers.

FCBF ran orders of magnitude faster than the alternatives, reduced the feature set more aggressively than competing methods in nine of ten cases, and produced average accuracy gains for both classifiers (C4.5 rose from 88.6 % to 89.1 %; naïve Bayes rose from 82.2 % to 86.9 %). Accuracy either held steady or improved on most individual datasets.

These results indicate that predominant-correlation filtering can deliver compact, high-performing feature subsets at low computational cost, making reliable feature selection practical for current high-dimensional tasks and supporting downstream gains in speed, interpretability, and generalization.

The authors recommend extending FCBF to datasets with thousands of features, examining the role of redundant features in greater depth, and integrating discretization routines for mixed data types. Further empirical validation on larger-scale problems is needed before broad deployment.

The study is limited to ten moderate-sized UCI datasets and requires a user-specified relevance threshold; performance on streaming or extremely sparse data remains untested. Confidence is moderate to high for the tested regime but should be tempered when extrapolating to substantially larger or qualitatively different data.

Arizona State University correlation coefficient genetic selection high dimensional data feature selection fast correlation-based filter high-dimensional data

jundongl/scikit-feature Yu et al (2003).pdf

Paper: Irrelevant Features and the Subset Selection Problem, George H. John et al. (1994). This paper establishes the foundational formal definitions of feature relevance and redundancy that underpin the filter selection criteria formalized by FCBF.
Paper: Supervised and Unsupervised Discretization of Continuous Features, James Dougherty et al. (1995). Understanding entropy-based discretization provides essential background for how FCBF preprocesses continuous attributes to compute symmetrical uncertainty and evaluate classification models like Naive Bayes.
Paper: Gene Selection for Cancer Classification using Support Vector Machines, ISABELLE GUYON et al. (2002). This work introduces seminal embedded feature elimination techniques for high-dimensional microarray data, representing the primary alternative paradigm that fast filter methods like FCBF aim to outperform in efficiency.
Paper: Feature Selection: Evaluation, Application, and Small Sample Performance, Anil K. Jain et al. (1997). This comprehensive evaluation of classical subset search strategies highlights the computational bottlenecks that motivate FCBF's fast heuristic filter design.
Paper: Theoretical and Empirical Analysis of ReliefF and RReliefF, M. Robnik-Sikonja et al. (2003). This study analyzes ReliefF, which serves as one of the primary benchmark algorithms evaluated against FCBF for handling high-dimensional attribute quality estimation.

Paper: Toward integrating feature selection algorithms for classification and clustering, Huan Liu et al. (2005). Co-authored by the creators of FCBF, this survey synthesizes the filter framework into an integrated taxonomy covering search strategies and data mining tasks.
Paper: An Introduction to Variable and Feature Selection, Isabelle M Guyon et al. (2003). This comprehensive tutorial expands on correlation, ranking, and subset selection methods across modern high-dimensional bioinformatics and text classification benchmarks.
Paper: Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy, Hanchuan Peng et al. (2003). This paper advances the theoretical and empirical treatment of relevance versus redundancy using mutual information criteria in the minimal-redundancy-maximal-relevance (mRMR) algorithm.
Paper: On Model Selection Consistency of Lasso, P. Zhao et al. (2006). This work formalizes the mathematical conditions required for sparse model consistency under regularized regression, extending the study of correlated predictor redundancy.

Cover for Feature Selection for High-Dimensional Data: A Fast Correlation-Based Filter Solution

Abstract

Feature selection, as a preprocessing step to machine learning, is effective in reducing dimensionality, removing irrelevant data, increasing learning accuracy, and improving result comprehensibility. However, the recent increase of dimensionality of data poses a severe challenge to many existing feature selection methods with respect to efficiency and effectiveness. In this work, we introduce a novel concept, predominant correlation, and propose a fast filter method which can identify relevant features as well as redundancy among relevant features without pairwise correlation analysis. The efficiency and effectiveness of our method is demonstrated through extensive comparisons with other methods using real-world data of high dimensionality.

Topics

correlation coefficient genetic selection high dimensional data high dimensionality

Keywords

feature selection fast correlation-based filter high-dimensional data feature relevance feature subset redundant features predominant feature correlation measures

1. Introduction
2. Related Work
3. Correlation-Based Measures
4. A Correlation-Based Filter Approach
4.1. Methodology
4.2. Algorithm and Analysis
5. Empirical Study
5.1. Experiment Setup
5.2. Results and Discussions
6. Conclusions
Acknowledgements
References

Knowls

Knowl 1 — Fast Correlation-Based Filter (FCBF) Algorithm
algorithm
The Fast Correlation-Based Filter (FCBF) algorithm selects a subset of predominant features $S_{best}$ from a dataset with $N$ features and a target class $C$ using symmetrical uncertainty ( $SU$ ) as the correlation measure.

FCBF operates in two stages: (1) Relevance filtering: It computes the correlation between each feature $F_i$ and the class $C$ ( $SU_{i,c}$ ), filters out features whose $SU_{i,c}$ is below a user-defined threshold $\delta$ , and sorts the remaining candidate features into an ordered list $S'_{list}$ in descending order of $SU_{i,c}$ . (2) Redundancy filtering: Starting from the highest-ranked feature $F_p$ (a predominant feature), it scans all lower-ranked features $F_q$ . If the feature-feature correlation $SU_{p,q} \ge SU_{q,c}$ , $F_q$ is identified as a redundant peer of $F_p$ and is removed from $S'_{list}$ . Once a pass is complete, the next remaining feature in the list is selected as the new reference feature $F_p$ , and the filtering process repeats until no further features can be removed.
Input: S(F_1, F_2, ..., F_N, C) // training data set
        $\delta$ // predefined threshold
Output: S_best // optimal feature subset
begin
  for i = 1 to N do begin
    calculate SU_{i,c} for F_i;
    if (SU_{i,c} >= $\delta$ )
      append F_i to S'_list;
  end;
  order S'_list in descending SU_{i,c} value;
  F_p = getFirstElement(S'_list);
  do begin
    F_q = getNextElement(S'_list, F_p);
    if (F_q <> NULL)
      do begin
        F'_q = F_q;
        if (SU_{p,q} >= SU_{q,c})
          remove F_q from S'_list;
          F_q = getNextElement(S'_list, F'_q);
        else
          F_q = getNextElement(S'_list, F_q);
      end until (F_q == NULL);
    F_p = getNextElement(S'_list, F_p);
  end until (F_p == NULL);
  S_best = S'_list;
end;
Knowl 2 — Predominant Correlation and Predominant Features
definition
Let $S = \{F_1, F_2, \dots, F_N\}$ be the full set of features, $C$ be the target class concept, and $SU(X, Y)$ denote the symmetrical uncertainty between two variables. Let $S' \subseteq S$ be the set of relevant features whose correlation with the class satisfies $SU(F_i, C) \ge \delta$ for a chosen threshold $\delta > 0$ .
- Predominant Correlation: The correlation between a feature $F_i \in S'$ and the class $C$ is defined as predominant if and only if $SU(F_i, C) \ge \delta$ , and for all $F_j \in S'$ ( $j \neq i$ ), there exists no feature $F_j$ such that $SU(F_j, F_i) \ge SU(F_i, C)$ .
- Redundant Peer: If there exists a feature $F_j \in S'$ ( $j \neq i$ ) such that $SU(F_j, F_i) \ge SU(F_i, C)$ , then $F_j$ is called a redundant peer to $F_i$ . The set of all redundant peers for $F_i$ is denoted by $S_{P_i}$ . This set is partitioned into two disjoint subsets: $S_{P_i}^+ = \{F_j \mid F_j \in S_{P_i},\; SU(F_j, C) > SU(F_i, C)\}$ $S_{P_i}^- = \{F_j \mid F_j \in S_{P_i},\; SU(F_j, C) \le SU(F_i, C)\}$
- Predominant Feature: A feature is predominant to the class if and only if its correlation to the class is predominant or becomes predominant after removing its redundant peers.
Knowl 3 — Heuristics for Redundancy Elimination in FCBF
model/method
To eliminate redundant features without computing full pairwise feature-feature correlation matrices ( $O(N^2)$ pairs), the Fast Correlation-Based Filter (FCBF) relies on the principle that if two features are redundant to each other, removing the one with lower class correlation preserves more predictive information. This is operationalized via three heuristics:
- Heuristic 1 (Empty $S_{P_i}^+$ ): If $S_{P_i}^+ = \emptyset$ , feature $F_i$ has no redundant peers with higher correlation to the class $C$ . Therefore, $F_i$ is treated as a predominant feature, all features in its lower-correlation redundant peer set $S_{P_i}^-$ are removed from the candidate pool, and identifying redundant peers for those removed features is skipped.
- Heuristic 2 (Non-empty $S_{P_i}^+$ ): If $S_{P_i}^+ \neq \emptyset$ , all features in $S_{P_i}^+$ must be processed before deciding the status of $F_i$ . If none of the features in $S_{P_i}^+$ becomes predominant, Heuristic 1 is applied to $F_i$ ; otherwise, $F_i$ is removed, and whether to remove features in $S_{P_i}^-$ is determined based on the remaining candidate features.
- Heuristic 3 (Starting Point): The candidate feature with the highest correlation to the class $SU(F_i, C)$ in the relevant feature set $S'$ is unconditionally a predominant feature ( $S_{P_i}^+ = \emptyset$ ) and serves as the deterministic starting point for filtering redundant features.
Knowl 4 — Symmetrical Uncertainty Correlation Measure
equation
For two discrete random variables $X$ and $Y$ , symmetrical uncertainty $SU(X, Y)$ normalizes information gain to the range $[0, 1]$ and compensates for information gain's inherent bias toward features with larger numbers of values:

$SU(X, Y) = 2 \left[ \frac{IG(X \mid Y)}{H(X) + H(Y)} \right]$

where the Shannon entropy of $X$ is defined as:

$H(X) = -\sum_{i} P(x_i) \log_2 P(x_i)$

the conditional entropy of $X$ given $Y$ is defined as:

$H(X \mid Y) = -\sum_{j} P(y_j) \sum_{i} P(x_i \mid y_j) \log_2 P(x_i \mid y_j)$

and the information gain $IG(X \mid Y)$ is:

$IG(X \mid Y) = H(X) - H(X \mid Y)$

A value of $SU(X, Y) = 1$ indicates that knowing either variable completely predicts the other, whereas $SU(X, Y) = 0$ indicates that $X$ and $Y$ are entirely independent. Symmetrical uncertainty is symmetric, satisfying $SU(X, Y) = SU(Y, X)$ . Continuous variables must be discretized prior to computing $SU$ .
Knowl 5 — Computational Time Complexity of the FCBF Algorithm
theoretical result
For a dataset with $M$ instances and $N$ features, the overall average computational time complexity of the Fast Correlation-Based Filter (FCBF) algorithm is $O(M N \log N)$ .
- Relevance Step: Computing the symmetrical uncertainty between every feature $F_i$ and the class label $C$ requires $O(M N)$ operations. Sorting the filtered subset of relevant features takes $O(N \log N)$ operations.
- Redundancy Step: In each filtering iteration, a predominant feature $F_p$ removes a fraction of the remaining candidate features that are redundant peers to $F_p$ . Under the average-case assumption that a constant fraction (e.g., half) of the remaining features are pruned in each round, the number of pairwise feature comparisons is $O(N \log N)$ . Because computing each pairwise symmetrical uncertainty takes $O(M)$ time, the redundancy filtering stage runs in $O(M N \log N)$ time on average.
In the worst case (where no redundant features are removed), the complexity is $O(M N^2)$ , while in the best case (where all subsequent features are redundant to the first), it is $O(M N)$ .
Knowl 6 — Symmetry of Information Gain
theoretical result
For any two discrete random variables $X$ and $Y$ , the information gain measure is symmetric:

$IG(X \mid Y) = IG(Y \mid X)$

This holds because the joint entropy decomposes as $H(X, Y) = H(X) + H(Y \mid X) = H(Y) + H(X \mid Y)$ , which implies $H(X) - H(X \mid Y) = H(Y) - H(Y \mid X)$ .
Knowl 7 — Experimental Setup for Filter Feature Selection Benchmark
experimental setup
The Fast Correlation-Based Filter (FCBF) was evaluated against three filter-based feature selection baselines using 10 benchmark datasets from the UCI Machine Learning Repository and UCI KDD Archive: Lung-cancer (57 features, 32 instances, 3 classes), Promoters (59 features, 106 instances, 2 classes), Splice (62 features, 3,190 instances, 3 classes), USCensus90 (68 features, 9,338 instances, 3 classes), CoIL2000 (86 features, 5,822 instances, 2 classes), Chemical (151 features, 936 instances, 3 classes), Musk2 (169 features, 6,598 instances, 2 classes), Arrhythmia (280 features, 452 instances, 16 classes), Isolet (618 features, 1,560 instances, 26 classes), and Multi-features (650 features, 2,000 instances, 10 classes).

The compared feature selection algorithms are:
1. ReliefF: A feature weighting algorithm configured with $k = 5$ nearest neighbors and $m = 30$ sampled instances.
2. CorrSF: A correlation-based subset search algorithm using sequential forward search guided by CFS correlation merit.
3. ConsSF: A consistency-based subset search algorithm using sequential forward search guided by inconsistency rate.
Performance was assessed on two classification algorithms: the C4.5 decision tree and the Naive Bayes Classifier (NBC). Classification accuracy was evaluated using 10-fold cross-validation on both the full feature sets and the reduced subsets obtained by each feature selection method.

Knowl 8 — Execution Time and Dimensionality Reduction Comparison Across Feature Selection Algorithms

data/table

Execution time (in milliseconds) and the number of selected features were measured for FCBF, CorrSF, ReliefF, and ConsSF across 10 benchmark datasets. FCBF demonstrated superior computational speed (averaging 995 ms compared to 32,028 ms for CorrSF, 7,911 ms for ReliefF, and 109,617 ms for ConsSF) and achieved the highest degree of dimensionality reduction (retaining an average of 7 features, compared to 30 for CorrSF, 11 for ReliefF, and 12 for ConsSF).

Dataset	Running Time (ms)				# Selected Features
	FCBF	CorrSF	ReliefF	ConsSF	FCBF	CorrSF	ReliefF	ConsSF
Lung-cancer	20	50	50	110	5	8	5	4
Promoters	20	50	100	190	4	4	4	4
Splice	200	961	2343	34920	6	6	11	10
USCensus90	541	932	7601	161121	2	1	2	13
CoIL2000	470	3756	7751	341231	3	10	12	29
Chemical	121	450	2234	14000	4	7	7	11
Musk2	971	8903	18066	175453	2	10	2	11
Arrhythmia	151	2002	2233	31235	6	25	25	24
Isolet	3174	177986	17025	203973	23	137	23	11
Multi-Features	4286	125190	21711	133932	14	87	14	7
Average	995	32028	7911	109617	7	30	11	12

Knowl 9 — Classification Accuracy of C4.5 and Naive Bayes Classifiers After Feature Selection

data/table

Classification accuracy (percentage $\pm$ standard deviation from 10-fold cross-validation) was evaluated for C4.5 and Naive Bayes Classifier (NBC) on the full feature set and on subsets selected by FCBF, CorrSF, ReliefF, and ConsSF. Feature selection with FCBF improved the average accuracy of both C4.5 (from 88.62% on the full feature set to 89.13%) and NBC (from 82.20% on the full feature set to 86.92%), matching or exceeding the baseline feature selectors while using fewer features.

Dataset	Full Set	FCBF	CorrSF	ReliefF	ConsSF
C4.5 Accuracy (%)
Lung-cancer	80.83 $\pm 22.92$	87.50 $\pm 16.32$	84.17 $\pm 16.87$	80.83 $\pm 22.92$	84.17 $\pm 16.87$
Promoters	86.91 $\pm 6.45$	87.73 $\pm 6.55$	87.73 $\pm 6.55$	89.64 $\pm 5.47$	84.00 $\pm 6.15$
Splice	94.14 $\pm 1.57$	93.48 $\pm 2.20$	93.48 $\pm 2.20$	89.25 $\pm 1.94$	93.92 $\pm 1.53$
USCensus90	98.27 $\pm 0.19$	98.08 $\pm 0.22$	97.95 $\pm 0.15$	98.08 $\pm 0.22$	98.22 $\pm 0.30$
CoIL2000	93.97 $\pm 0.21$	94.02 $\pm 0.07$	94.02 $\pm 0.07$	94.02 $\pm 0.07$	93.99 $\pm 0.20$
Chemical	94.65 $\pm 2.03$	95.51 $\pm 2.31$	96.47 $\pm 2.15$	93.48 $\pm 1.79$	95.72 $\pm 2.09$
Musk2	96.79 $\pm 0.81$	91.33 $\pm 0.51$	95.56 $\pm 0.73$	94.62 $\pm 0.92$	95.38 $\pm 0.75$
Arrhythmia	67.25 $\pm 3.68$	72.79 $\pm 6.30$	68.58 $\pm 7.41$	65.90 $\pm 8.23$	67.48 $\pm 4.49$
Isolet	79.10 $\pm 2.79$	75.77 $\pm 4.07$	80.70 $\pm 4.94$	52.44 $\pm 3.61$	69.23 $\pm 4.53$
Multi-Features	94.30 $\pm 1.49$	95.06 $\pm 0.86$	94.95 $\pm 0.96$	80.45 $\pm 2.41$	90.80 $\pm 1.75$
Average	88.62 $\pm 9.99$	89.13 $\pm 8.52$	89.36 $\pm 9.24$	83.87 $\pm 14.56$	87.29 $\pm 11.04$
NBC Accuracy (%)
Lung-cancer	80.00 $\pm 23.31$	90.00 $\pm 16.10$	90.00 $\pm 16.10$	80.83 $\pm 22.92$	86.67 $\pm 17.21$
Promoters	90.45 $\pm 7.94$	94.45 $\pm 8.83$	94.45 $\pm 8.83$	87.82 $\pm 10.99$	92.64 $\pm 7.20$
Splice	95.33 $\pm 0.88$	93.60 $\pm 1.74$	93.60 $\pm 1.74$	88.40 $\pm 1.97$	94.48 $\pm 1.39$
USCensus90	93.38 $\pm 0.90$	97.93 $\pm 0.16$	97.95 $\pm 0.15$	97.93 $\pm 0.16$	97.87 $\pm 0.26$
CoIL2000	79.03 $\pm 2.08$	93.94 $\pm 0.21$	92.94 $\pm 0.80$	93.58 $\pm 0.43$	83.18 $\pm 1.94$
Chemical	60.79 $\pm 5.98$	72.11 $\pm 2.51$	70.72 $\pm 4.20$	78.20 $\pm 3.58$	67.20 $\pm 2.51$
Musk2	84.69 $\pm 2.01$	84.59 $\pm 0.07$	64.85 $\pm 2.09$	84.59 $\pm 0.07$	83.56 $\pm 1.05$
Arrhythmia	60.61 $\pm 3.32$	66.61 $\pm 5.89$	68.80 $\pm 4.22$	66.81 $\pm 3.62$	68.60 $\pm 7.64$
Isolet	83.72 $\pm 2.38$	80.06 $\pm 2.52$	86.28 $\pm 2.14$	52.37 $\pm 3.17$	71.67 $\pm 3.08$
Multi-Features	93.95 $\pm 1.50$	95.95 $\pm 1.06$	96.15 $\pm 0.94$	76.05 $\pm 3.26$	93.75 $\pm 1.95$
Average	82.20 $\pm 12.70$	86.92 $\pm 10.79$	85.57 $\pm 12.53$	80.66 $\pm 13.38$	83.96 $\pm 11.31$

Coverage note — None was omitted; all key theoretical definitions, the FCBF algorithm, time complexity derivations, and experimental results have been captured as self-contained knowls.

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Citation

MLA

Yu, L., and H. Liu. “Feature Selection for High-dimensional Data: A Fast Correlation-based Filter Solution”. International Conference on Machine Learning, 2003, pp. 856–63, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.566.3227.

APA

Yu, L., & Liu, H. (2003). Feature selection for high-dimensional data: a fast correlation-based filter solution. International Conference on Machine Learning, 856–863. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.566.3227

Chicago

Yu, L., and H. Liu. 2003. “Feature Selection for High-dimensional Data: A Fast Correlation-based Filter Solution”. International Conference on Machine Learning, 856–63. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.566.3227.

Harvard

Yu, L. and Liu, H. (2003) “Feature selection for high-dimensional data: a fast correlation-based filter solution”, International Conference on Machine Learning, pp. 856–863. Available at: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.566.3227.

Vancouver

1. Yu L, Liu H (2003) Feature selection for high-dimensional data: a fast correlation-based filter solution. International Conference on Machine Learning 856–863

BibTeX

@article{yu2003feature,
  title = {Feature selection for high-dimensional data: a fast correlation-based filter solution},
  author = {Yu, Lei and Liu, Huan},
  year = {2003},
  journal = {International Conference on Machine Learning},
  pages = {856-863},
  url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.566.3227}
}

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Feature Selection for High-Dimensional Data: A Fast Correlation-Based Filter Solution

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Fast Correlation-Based Filter (FCBF) Algorithm

Knowl 2 — Predominant Correlation and Predominant Features

Knowl 3 — Heuristics for Redundancy Elimination in FCBF

Knowl 4 — Symmetrical Uncertainty Correlation Measure

Knowl 5 — Computational Time Complexity of the FCBF Algorithm

Knowl 6 — Symmetry of Information Gain

Knowl 7 — Experimental Setup for Filter Feature Selection Benchmark