Update PCA

contrib/machine-learning/Principal Component Analysis .md

@@ -1,13 +1,13 @@
 ### Principal Component Analysis (PCA)
 
 #### Introduction
-Principal Component Analysis (PCA) is a statistical technique used in machine learning and data analysis for dimensionality reduction. It transforms a dataset with possibly correlated variables into a set of linearly uncorrelated variables called principal components. This method helps in simplifying the complexity of high-dimensional data while retaining as much variability as possible.
+Principal Component Analysis (PCA) is a powerful statistical technique used in machine learning and data analysis for dimensionality reduction. By transforming a dataset with potentially correlated variables into a set of linearly uncorrelated variables called principal components, PCA simplifies the complexity of high-dimensional data while retaining as much variability as possible.
 
 #### How PCA Works
-PCA involves several steps, each transforming the dataset in a specific way to achieve dimensionality reduction:
+PCA involves several steps, each contributing to the goal of dimensionality reduction:
 
 1. **Standardize the Data**: 
-   - Ensure the dataset is standardized so that each feature has a mean of zero and a variance of one. This step is crucial because PCA is affected by the scale of the variables.
+   - Ensure the dataset is standardized so that each feature has a mean of zero and a variance of one. Standardization is crucial because PCA is sensitive to the scale of the variables.
 
    ```python
    from sklearn.preprocessing import StandardScaler
@@ -17,7 +17,7 @@ PCA involves several steps, each transforming the dataset in a specific way to a
    ```
 
 2. **Covariance Matrix Computation**:
-   - Compute the covariance matrix to understand how the variables in the dataset are varying from the mean with respect to each other.
+   - Compute the covariance matrix to understand how the variables in the dataset vary from the mean with respect to each other.
 
    ```python
    covariance_matrix = np.cov(X_scaled.T)
@@ -55,10 +55,10 @@ PCA involves several steps, each transforming the dataset in a specific way to a
    ```
 
 #### Applications of PCA
-PCA is widely used in various fields to simplify data analysis and visualization:
+PCA is extensively used in various fields to simplify data analysis and visualization:
 
 - **Image Compression**: Reducing the dimensionality of image data to store images with less memory.
-- **Noise Reduction**: Filtering out the noise from data by selecting only the most important components.
+- **Noise Reduction**: Filtering out noise from data by selecting only the most important components.
 - **Data Visualization**: Projecting high-dimensional data to 2D or 3D for easier visualization.
 - **Feature Extraction**: Identifying the most significant features in a dataset for use in other machine learning models.
 
@@ -86,10 +86,5 @@ print("Transformed Data:\n", X_pca)
 ```
 
 #### Conclusion
-Principal Component Analysis (PCA) is a powerful tool for reducing the dimensionality of datasets while preserving as much variance as possible. It is especially useful in exploratory data analysis and preprocessing for other machine learning algorithms.
-
-#### References
-- Jolliffe, I. T. (2002). *Principal Component Analysis*. Springer Series in Statistics.
-- [PCA Explained](https://towardsdatascience.com/a-step-by-step-explanation-of-principal-component-analysis-118e7d7c15e8)
-- [Scikit-Learn PCA Documentation](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html)
+Principal Component Analysis (PCA) is an indispensable tool for reducing the dimensionality of datasets while preserving as much variance as possible. It is particularly useful in exploratory data analysis and preprocessing for other machine learning algorithms.