Supervised Vs Unsupervised Learning Fundamentals

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Questions and Answers

Match the following machine learning tasks with their descriptions:

Supervised Learning = Training examples have provided labels Unsupervised Learning = No labels provided for each training example Clustering = Grouping similar data points together Anomaly detection = Identifying abnormal or unusual data points

Match the following dimensionality reduction techniques with their descriptions:

Principle Component Analysis (PCA) = Identifies and extracts important features in a dataset PCA Process = Standardizes the data and finds new principal components Principal Components = Orthogonal variables capturing maximum variance in the data Dimensionality Reduction = Reduces dataset's dimension while preserving variance

Match the steps of Principle Component Analysis (PCA) with their descriptions:

Step 2: Compute the covariance matrix = Calculate the covariance matrix based on the standardized data to show relationships and variances between pairs of variables. Step 3: Compute the eigenvectors and eigenvalues = Obtain eigenvectors and eigenvalues by decomposing the covariance matrix, where each eigenvector represents a principal component and its corresponding eigenvalue represents the amount of variance explained. Step 4: Select the principal components = Determine the number of principal components to retain based on the amount of variance explained by each principal component, often using a threshold like retaining components that explain a certain percentage of the total variance. Step 5: Project the data onto the new feature space = Project the original data onto the selected principal components to obtain a reduced-dimensional representation by taking the dot product of the data and the selected principal components.

Match the applications of Principle Component Analysis (PCA) with their descriptions:

Dimensionality reduction = By selecting a subset of principal components, PCA reduces the dimensionality of the dataset, making it easier to visualize and analyze. Data visualization = PCA can be used to visualize high-dimensional data by projecting it onto a lower-dimensional space, typically two or three dimensions. Noise reduction = By keeping only the principal components that capture most of the variance, PCA can remove noise and retain the most informative features. Feature extraction = PCA can be used to extract the most important features from a dataset and discard less relevant or redundant features. Signup and view all the answers

Match the mathematical operations in PCA with their descriptions:

Calculate the mean = Determine the mean value for each variable in the dataset. Compute the covariance matrix = Calculate the covariance matrix based on the standardized data to show relationships and variances between pairs of variables. Compute eigenvectors and eigenvalues = Obtain eigenvectors and eigenvalues by decomposing the covariance matrix, where each eigenvector represents a principal component and its corresponding eigenvalue represents the amount of variance explained. Select principal components = Determine the number of principal components to retain based on the amount of variance explained by each principal component, often using a threshold like retaining components that explain a certain percentage of the total variance. Signup and view all the answers

Match the steps in reducing dimensionality using PCA with their descriptions:

Calculate mean for each variable = Determine the mean value for each variable in the dataset. Compute covariance matrix = Calculate the covariance matrix based on the standardized data to show relationships and variances between pairs of variables. Select principal components = Determine the number of principal components to retain based on the amount of variance explained by each principal component, often using a threshold like retaining components that explain a certain percentage of the total variance. Project data onto new feature space = Project the original data onto the selected principal components to obtain a reduced-dimensional representation by taking the dot product of the data and the selected principal components. Signup and view all the answers

Match PCA applications with their benefits:

Dimensionality reduction = Reduces complexity and makes it easier to visualize and analyze data. Data visualization = Enables representation of high-dimensional data in lower dimensions for easier understanding and interpretation. Noise reduction = Removes irrelevant or less informative features from datasets, leading to cleaner data analysis results. Feature extraction = Identifies and retains essential information while discarding redundant or less relevant features. Signup and view all the answers

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Study Notes

Machine Learning Tasks

Classification: involves predicting a categorical label or class that an instance belongs to
Regression: involves predicting a continuous or numerical value
Clustering: involves grouping similar instances together
Dimensionality Reduction: involves reducing the number of features or variables in a dataset

Dimensionality Reduction Techniques

Principal Component Analysis (PCA): linear technique that projects high-dimensional data onto a lower-dimensional space
t-SNE: non-linear technique that preserves local relationships in the data
Autoencoders: neural networks that learn to compress and reconstruct data

Steps of Principle Component Analysis (PCA)

Data Standardization: subtracting the mean and dividing by the standard deviation for each feature
Covariance Matrix Calculation: computing the covariance between each pair of features
Eigenvector and Eigenvalue Calculation: solving for the eigenvectors and eigenvalues of the covariance matrix
Component Selection: selecting the top k eigenvectors corresponding to the k largest eigenvalues
Transformation: projecting the original data onto the selected eigenvectors

Applications of Principle Component Analysis (PCA)

Data Visualization: reducing dimensionality for visualization in lower-dimensional spaces
Anomaly Detection: identifying outliers and anomalies in the data
Feature Extraction: selecting the most informative features in a dataset
Noise Reduction: removing noise and correlations in the data

Mathematical Operations in PCA

Eigen Decomposition: decomposing a matrix into eigenvectors and eigenvalues
Matrix Multiplication: projecting the original data onto the selected eigenvectors
Orthogonal Projections: projecting data onto a lower-dimensional space

Steps in Reducing Dimensionality using PCA

Selecting the Number of Components: choosing the number of dimensions to reduce to
Computing the Component Scores: projecting the original data onto the selected eigenvectors
Transforming the Data: converting the original data into the lower-dimensional space

PCA Applications and Benefits

Facial Recognition: reducing dimensionality for efficient face recognition
- Benefit: improved computational efficiency
Gene Expression Analysis: identifying relevant genes in microarray data
- Benefit: improved feature selection and identification of key genes
Image Compression: reducing dimensionality for efficient image compression
- Benefit: improved storage and transmission efficiency