Clustering and Regression Techniques

Python for Rapid Engineering Solutions: Regression Analysis

• Regression analysis is used to map features of a house to a continuous variable, like price
• Zillow has held a contest with a $1,000,000 prize to predict housing prices.
• Methods include linear regression, polynomial regression, decision trees, and random forests.
• Outliers need to be addressed with a policy

Measuring Model Quality: MSE (Mean Square Error)

• MSE = (1/n) * Σ(y(i) – ŷ(i))²

• It's the average squared distance from the actual value.

• A smaller MSE indicates a higher quality model.

Measuring Model Quality: R²

• R² = 1 - (MSE / Var(y))
• R² is the coefficient of determination; it describes the amount of variance in the dependent variable explained by the independent variables in the model.
• A higher R² indicates a better fit.

Housing Data

• CRIM: Per capita crime rate
• ZN: % of residential land zoned for lots over 25,000 sq ft
• INDUS: % of non-retail acres
• CHAS: 1 if on a river; 0 otherwise
• NOX: Nitric Oxide concentration
• RM: Average number of rooms
• AGE: % of owner-occupied built before 1940
• DIS: Weighted distance to 5 business centers
• RAD: Index of accessibility to radial highways
• TAX: Full-value property tax rate
• PTRATIO: Pupil-teacher ratio
• B: Measure of population of African descent
• LSTAT: % of lower status of population
• MEDV: Median value of owner-occupied homes in $1000s

Data Analysis Set Up

• The code imports necessary libraries for plotting and data analysis.
• DataFrame created.
• Data printed.

Data Analysis: Create Charts

• Pair plots are created using mlxtend to visualize relationships between pairs of features.
• A correlation heatmap is generated to visualize correlations.

Regression Analysis: Set Up

• The code imports Python libraries
• Input data loaded and column names are assigned.
• Features (X) are extracted from data excluding the last column.
• Target variable (MEDV) is extracted
• Data split into training and testing sets using 'train_test_split'.

Regression Analysis: Train and Test

• A linear regression model is instantiated and trained.
• Training and testing data sets' predicted values are generated.
• Residuals (difference between predicted and actual values) are plotted against predicted values to indicate the quality of model fit.

Regression Analysis: Quality Check

• Calculate mean squared error (MSE) for train and test sets
• MSE train should be significantly lower than MSE test for good prediction.
• Calculate and compare the coefficient of determination (R²) of the train and test sets.
• A high R² value indicates the model fits the training data well.

Clustering Analysis

• Unsupervised learning finds patterns in data without pre-existing labels.
• K-means clustering assumes data points form spherical clusters.
• The algorithm randomly picks cluster centers and iteratively assigns data points to the nearest cluster center and moves cluster centers to the centroid of the associated data points.
• Use SSE (sum of squares error) to determine the optimal number of clusters (k). A plot of SSE vs. k shows an "elbow" point where further addition of clusters doesn't significantly reduce SSE.

DBSCAN

• Density-based spatial clustering of applications with noise (DBSCAN) clusters data points based on density. It does not assume data must form spherical clusters.
• Core points: Points within the specified epsilon radius (eps) with the minimum number of data points (min_samples) in a neighborhood.
• Border points: Points within eps of a core point.
• Outliers/noise points: Do not belong to any cluster.

Deep Learning

• Scientists investigating vision found neurons fired for specific features (edges, angles).
• Deep Neural Networks use layers of perceptrons to learn successively more complex features.
• A single hidden layer is a neural network. Having multiple hidden layers is a deep neural network.
• Key issues with early deep learning: computational expense and vanishing gradients.

Addressing Deep Learning Issues

• Batch normalization: Normalizes input to each layer to prevent vanishing gradient issues.
• Non-saturating activation functions, like ReLU, help gradients flow smoothly.
• Reuse of pretrained models: Efficient since models are already trained on similar tasks.

Learning Rate Scheduling

• Large changes to learning rate are allowed initially. Learning rate is reduced over time.
• Various strategies exist (piecewise linear, exponential, power scheduling).

Regularization

• Helps avoid overfitting by adding a term to penalize large weights
• Techniques include early stopping and introducing penalties during training.
• L1 and L2 regularization are two particular regularization approaches.

Dropout

• Randomly drops out neurons during training.
• Helps to prevent overfitting.

Max-Norm Regularization

• Restricts the magnitude of weight vectors.
• Prevents gradient from exploding or vanishing.
• Useful technique for avoiding overfitting.

Data Augmentation

• Creates additional training data by modifying existing images (shift, rotate, reflect).
• Addresses issues like limited data.

Model Zoos

• Publicly available collections of deep learning models can be utilized to enhance learning and understanding.

Prizes

• Companies and organizations, including government agencies, offer prizes for innovative machine learning solutions.

Image Processing: Convolution

• Convolution maps multiple pixel values to a single pixel.
• It emphasizes features of an image.
• Using a 3x3 kernel with stride one extracts information from the image.

Full Padding

• Full padding adds zeros around the edge of an image during convolution.
• Output image has a larger dimension compared to input.

Same Padding

• Same padding adds zeros around the edge that maintain the original dimensions of the input and output image.
• It helps in extracting information from a given feature that is important for a CNN.

Image Processing: Pooling

• Pooling subsamples an image.
• Max pooling selects the maximum value from a window.
• Mean pooling takes the average of values in a window.

Convolution Code: Set Up

Convolution Code: The Function

Convolution Code: Copy and Blur

Convolution Code: Sobel and Laplacian

Convolution Code: Generate Images

This quiz covers essential concepts related to clustering algorithms like KMeans and DBSCAN, as well as key aspects of regression analysis. Test your understanding of their definitions, parameters, applications, and objectives. A great resource for students learning about machine learning techniques.