# An Efficient AdaBoost Algorithm for Enhancing Skin Cancer Detection and Classification
## 3 Materials and Methods
### Principal Component Analysis (PCA)  
The curse of dimensionality refers to the difficulties that come when working with datasets that have a large number of dimensions. It makes it difficult to generate statistically significant findings, increases overfitting, takes longer to compute, and reduces accuracy in machine learning models. This issue is addressed using feature engineering approaches such as feature selection and extraction. PCA is a widely used dimensionality-reduction approach that uses an orthogonal transformation to convert correlated variables into uncorrelated ones. It detects primary components, captures the highest variation in the data, and decreases dimensionality while keeping key patterns, as shown in Algorithm 1. Using PCA in skin cancer-classification procedures improves efficiency and efficacy by lowering computing complexity and the risk of overfitting. PCA works by preprocessing the data, calculating the covariance matrix, conducting eigen decomposition, selecting principal components based on eigenvalues, and projection the data onto the chosen components. It enhances data visualization, computational efficiency, and the effectiveness of machine learning algorithms by collecting useful aspects. PCA is a strong feature extraction approach that minimizes dimensionality while maintaining crucial properties. Here is how PCA works to extract features:  
1. Data preprocessing: Initially, the input data are preprocessed by shifting them to a mean of zero. This step ensures that the data are centered on the mean. The preprocessed data are then grouped into matrix X, which has n samples and m variables. This matrix is typically referred to as X and has dimensions (n \(\times\) m). 2. Mean calculation: We determine the mean for each variable across all samples. The mean vector has dimensions of 1 \(\times\) m
3. Calculate the covariance matrix: It quantifies the associations between various characteristics in the dataset, revealing how they co-vary with one another. The covariance matrix is generated from preprocessed data and represents the connections between variables. The following formula is used to determine each element in the matrix. \[\text{cov (x,y)}=(1/(n-1))\times\Sigma\left((\text{x\_i}-\text{mean(x)})\times( \text{y\_i}-\text{mean(y)})\right) \tag{1}\]
4. Eigen decomposition: The covariance matrix is decomposed to obtain its eigenvectors and eigenvalues. The resulting eigenvectors reflect the primary components, which encapsulate the data's key patterns. The associated eigenvalues indicate the amount of variation explained by each major component. During the eigen decomposition procedure, the covariance matrix is divided into eigenvectors and eigenvalues. Eigen-value decomposition and Singular Value Decomposition (SVD) are typical techniques for obtaining these eigenvectors and eigenvalues. 5. Selecting principal components: The corresponding eigenvalues are used to calculate the principal components. The eigenvalues are arranged in descending sequence, with the top k eigenvalues chosen as principal components. PCA reduces the dimensionality of the data by identifying the top k main components. These main components are orthogonal to one another, implying they are uncorrelated. This quality enables PCA to reduce duplicate and less useful elements while focusing on the most important ones. 6. Feature projection: The original data are projected onto the chosen primary components to produce a lower-dimensional representation. This projection effectively converts the data to a new feature space, with each dimension representing a primary component. This is accomplished by multiplying the transposed eigenvector matrix by the preprocessed data matrix (X). Overall, PCA is an effective feature extraction approach that reduces the dimensionality of data while retaining its key properties. By identifying the most important features, PCA improves data visualization and computational efficiency, in addition to the effectiveness of subsequent machine learning techniques.