Explained Variance

Definition

Explained variance is a statistical measure that indicates how much of the total variance in a dataset can be attributed to a particular model or feature. In the context of data analysis and dimensionality reduction techniques, such as PCA, it helps in understanding the effectiveness of the components in capturing the underlying structure of the data.

5 Must Know Facts For Your Next Test

1. Explained variance is calculated as the ratio of the variance captured by a principal component to the total variance of the dataset.
2. In PCA, explained variance helps determine how many components to keep by showing how much information each component retains.
3. A higher explained variance indicates that the principal components effectively summarize the data, while lower values suggest that important information may be lost.
4. Cumulatively, explained variance can be used to create scree plots, which visually represent the proportion of total variance attributed to each principal component.
5. Selecting components based on explained variance aids in improving model performance while reducing complexity and avoiding overfitting.

Review Questions

• How does explained variance inform decisions about the number of principal components to retain in PCA?
  • Explained variance quantifies how much of the total data variability is captured by each principal component. By examining the explained variance associated with each component, one can identify an optimal number of components that effectively represent the data while minimizing loss of information. This assessment helps balance model complexity and performance, guiding users to choose components that provide significant insights without overwhelming detail.
• Discuss the relationship between explained variance and eigenvalues in the context of PCA.
  • In PCA, eigenvalues represent the amount of variance captured by each principal component. The explained variance for a given component is directly proportional to its corresponding eigenvalue. By analyzing these eigenvalues, one can determine which components contribute most significantly to explaining data variability. This relationship helps in selecting principal components that maximize information retention while simplifying data representation.
• Evaluate how understanding explained variance can impact modeling decisions and outcomes in machine learning.
  • Understanding explained variance is crucial in machine learning as it directly affects model selection and performance. It allows practitioners to choose a set of features or components that capture most of the relevant information, leading to more efficient models. By retaining only those components with high explained variance, one can reduce noise and avoid overfitting, ultimately enhancing prediction accuracy and interpretability while maintaining computational efficiency.

Related terms

Variance: Variance is a statistical measurement that describes the spread of data points in a dataset, indicating how far each data point is from the mean.

Principal Component Analysis (PCA): PCA is a dimensionality reduction technique that transforms high-dimensional data into a lower-dimensional space while preserving as much variance as possible.

Eigenvalues: Eigenvalues are coefficients that provide information about the amount of variance captured by each principal component in PCA.