Matthews Correlation Coefficient (MCC) is a powerful metric for evaluating the performance of binary classifiers in machine learning. This article explores the nuances, complexities, and current challenges of MCC, along with recent research and practical applications.

MCC takes into account all four entries of a confusion matrix (true positives, true negatives, false positives, and false negatives), providing a more representative picture of classifier performance compared to other metrics like F1 score, which ignores true negatives. However, in some cases, such as object detection problems, measuring true negatives can be intractable. Recent research has investigated the relationship between MCC and other metrics, such as the Fowlkes-Mallows (FM) score, as the number of true negatives approaches infinity.

Arxiv papers on MCC have explored its application in various domains, including protein gamma-turn prediction, software defect prediction, and medical image analysis. These studies have demonstrated the effectiveness of MCC in evaluating classifier performance and guiding the development of improved models.

Three practical applications of MCC include:

1. Protein gamma-turn prediction: A deep inception capsule network was developed for gamma-turn prediction, achieving an MCC of 0.45, significantly outperforming previous methods.

2. Software defect prediction: A systematic review found that using MCC instead of the biased F1 metric led to more reliable empirical results in software defect prediction studies.

3. Medical image analysis: A vision transformer model for chest X-ray and gastrointestinal image classification achieved high MCC scores, outperforming various CNN models.

A company case study in the field of healthcare data analysis utilized distributed stratified locality sensitive hashing for critical event prediction in the cloud. The system demonstrated a 21x speedup in the number of comparisons compared to parallel exhaustive search, at the cost of a 10% MCC loss.

In conclusion, MCC is a valuable metric for evaluating binary classifiers, offering insights into their performance and guiding the development of improved models. Its applications span various domains, and its use can lead to more accurate and efficient machine learning models.

# Matthews Correlation Coefficient (MCC)

## Matthews Correlation Coefficient (MCC) Further Reading

1.The MCC approaches the geometric mean of precision and recall as true negatives approach infinity http://arxiv.org/abs/2305.00594v1 Jon Crall2.Improving Protein Gamma-Turn Prediction Using Inception Capsule Networks http://arxiv.org/abs/1806.07341v1 Chao Fang, Yi Shang, Dong Xu3.Assessing Software Defection Prediction Performance: Why Using the Matthews Correlation Coefficient Matters http://arxiv.org/abs/2003.01182v1 Jingxiu Yao, Martin Shepperd4.A study on cost behaviors of binary classification measures in class-imbalanced problems http://arxiv.org/abs/1403.7100v1 Bao-Gang Hu, Wei-Ming Dong5.Wood-leaf classification of tree point cloud based on intensity and geometrical information http://arxiv.org/abs/2108.01002v1 Jingqian Sun, Pei Wang, Zhiyong Gao, Zichu Liu, Yaxin Li, Xiaozheng Gan6.A method to segment maps from different modalities using free space layout -- MAORIS : MAp Of RIpples Segmentation http://arxiv.org/abs/1709.09899v2 Malcolm Mielle, Martin Magnusson, Achim J. Lilienthal7.PUMiner: Mining Security Posts from Developer Question and Answer Websites with PU Learning http://arxiv.org/abs/2003.03741v1 Triet H. M. Le, David Hin, Roland Croft, M. Ali Babar8.Probabilistic prediction of Dst storms one-day-ahead using Full-Disk SoHO Images http://arxiv.org/abs/2203.11001v2 A. Hu, C. Shneider, A. Tiwari, E. Camporeale9.Vision Transformer for Efficient Chest X-ray and Gastrointestinal Image Classification http://arxiv.org/abs/2304.11529v1 Smriti Regmi, Aliza Subedi, Ulas Bagci, Debesh Jha10.Distributed Stratified Locality Sensitive Hashing for Critical Event Prediction in the Cloud http://arxiv.org/abs/1712.00206v1 Alessandro De Palma, Erik Hemberg, Una-May O'Reilly## Matthews Correlation Coefficient (MCC) Frequently Asked Questions

## What is the Matthews correlation coefficient (MCC) score?

The Matthews correlation coefficient (MCC) score is a metric used to evaluate the performance of binary classifiers in machine learning. It takes into account all four entries of a confusion matrix (true positives, true negatives, false positives, and false negatives), providing a more representative picture of classifier performance compared to other metrics like F1 score. The MCC score ranges from -1 to 1, where 1 indicates perfect classification, 0 represents random classification, and -1 signifies complete disagreement between the predicted and actual labels.

## What is the Matthews coefficient?

The Matthews coefficient, also known as the Matthews correlation coefficient (MCC), is a performance metric for binary classifiers in machine learning. It measures the correlation between the predicted and actual binary outcomes, considering all four elements of a confusion matrix. The coefficient ranges from -1 to 1, with 1 indicating perfect classification, 0 representing random classification, and -1 signifying complete disagreement between predictions and actual labels.

## What's a good MCC score?

A good MCC score depends on the specific problem and the context in which the classifier is being used. Generally, an MCC score closer to 1 indicates better classifier performance, while a score closer to -1 suggests poor performance. A score of 0 implies that the classifier is performing no better than random chance. In practice, an MCC score above 0.3 is considered moderate, and a score above 0.5 is considered strong.

## How does MCC compare to other performance metrics like F1 score?

MCC is a more comprehensive metric than the F1 score, as it takes into account all four entries of a confusion matrix (true positives, true negatives, false positives, and false negatives). The F1 score, on the other hand, only considers true positives, false positives, and false negatives, ignoring true negatives. This makes MCC a more representative measure of classifier performance, especially in cases where true negatives are important or when the class distribution is imbalanced.

## What are some practical applications of MCC in machine learning?

MCC has been applied in various domains, including protein gamma-turn prediction, software defect prediction, and medical image analysis. In these applications, MCC has been used to evaluate classifier performance and guide the development of improved models. For example, a deep inception capsule network for gamma-turn prediction achieved an MCC of 0.45, significantly outperforming previous methods. Similarly, a vision transformer model for chest X-ray and gastrointestinal image classification achieved high MCC scores, outperforming various CNN models.

## How can I calculate the Matthews correlation coefficient for my binary classifier?

To calculate the Matthews correlation coefficient (MCC) for your binary classifier, you need to first obtain the confusion matrix, which consists of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). The formula for MCC is: MCC = (TP * TN - FP * FN) / sqrt((TP + FP) * (TP + FN) * (TN + FP) * (TN + FN)) By plugging in the values from your confusion matrix into this formula, you can compute the MCC score for your classifier. This will give you a better understanding of its performance, especially in cases where true negatives are important or when the class distribution is imbalanced.

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