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Questions and Answers
What is the main objective of an optimal separating hyperplane?
What is the main objective of an optimal separating hyperplane?
- To equally distribute points from both classes.
- To maximize the distance to the closest point from either class. (correct)
- To minimize the distance between the classes.
- To ensure that all points are classified correctly.
Which of the following describes support vectors?
Which of the following describes support vectors?
- Data points that are incorrectly classified.
- Data points that determine the position of the decision boundary. (correct)
- All data points used for training the model.
- Data points that are far from the decision boundary.
What is the relationship between maximizing margin and minimizing $||w||^2$?
What is the relationship between maximizing margin and minimizing $||w||^2$?
- Maximizing margin leads to maximizing $||w||$.
- Maximizing margin can be seen as minimizing $||w||^2$. (correct)
- Minimizing $||w||^2$ is unrelated to maximizing margin.
- Maximizing margin requires increasing $||w||^2$.
In scenarios where data points are not linearly separable, which principle is typically applied?
In scenarios where data points are not linearly separable, which principle is typically applied?
What characterizes a Support Vector Machine (SVM)?
What characterizes a Support Vector Machine (SVM)?
What is the role of k in k-NN algorithms?
What is the role of k in k-NN algorithms?
What is a main disadvantage of the k-NN algorithm?
What is a main disadvantage of the k-NN algorithm?
What does choosing a hyperparameter such as k involve?
What does choosing a hyperparameter such as k involve?
What effect does the curse of dimensionality have on k-NN performance?
What effect does the curse of dimensionality have on k-NN performance?
What is lazy learning in the context of the k-NN algorithm?
What is lazy learning in the context of the k-NN algorithm?
Why might k-NN be biased toward the majority class?
Why might k-NN be biased toward the majority class?
In the context of separating hyperplanes, what characterizes the decision boundary?
In the context of separating hyperplanes, what characterizes the decision boundary?
What is the primary characteristic of hyperparameters like k in machine learning algorithms?
What is the primary characteristic of hyperparameters like k in machine learning algorithms?
What does k-NN classify new data points based on?
What does k-NN classify new data points based on?
What is the outcome of using k=1 in k-NN classification?
What is the outcome of using k=1 in k-NN classification?
What is a potential downside of using a small value of k in k-NN?
What is a potential downside of using a small value of k in k-NN?
Which distance measure is commonly used in k-NN classification?
Which distance measure is commonly used in k-NN classification?
What happens when k is set to a large value in k-NN classification?
What happens when k is set to a large value in k-NN classification?
How does k-NN decide which label to assign to a new data point?
How does k-NN decide which label to assign to a new data point?
Which option describes a scenario where k-NN may underfit the training data?
Which option describes a scenario where k-NN may underfit the training data?
In k-NN, what is the significance of class noise?
In k-NN, what is the significance of class noise?
What is the purpose of slack variables 𝜉𝑖 in the context of non-separable data points?
What is the purpose of slack variables 𝜉𝑖 in the context of non-separable data points?
What does the hyperparameter 𝛾 control in the soft-margin SVM?
What does the hyperparameter 𝛾 control in the soft-margin SVM?
What is a consequence of using a hard margin SVM with a very high penalty (C = 1000)?
What is a consequence of using a hard margin SVM with a very high penalty (C = 1000)?
Which kernel trick is specifically mentioned as a way to transform data into a higher dimension for better separability?
Which kernel trick is specifically mentioned as a way to transform data into a higher dimension for better separability?
What can occur when using the kernel trick in soft-margin SVM problems?
What can occur when using the kernel trick in soft-margin SVM problems?
In the soft-margin SVM objective function, what does the term $ rac{1}{2}
orm{w}^2$ represent?
In the soft-margin SVM objective function, what does the term $ rac{1}{2} orm{w}^2$ represent?
What is true regarding the parameters of a soft-margin SVM?
What is true regarding the parameters of a soft-margin SVM?
What aspect of the soft-margin SVM is primarily adjusted using the penalty parameter (C)?
What aspect of the soft-margin SVM is primarily adjusted using the penalty parameter (C)?
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Study Notes
Nearest Neighbors
- K-Nearest Neighbor (k-NN) is an instance-based learning algorithm.
- It classifies new data points by finding the k closest instances in the training set and assigning the most common label among them.
- 1-NN predicts the label based on the closest instance in the training dataset.
- k-NN finds the k closest instances and predicts the label by majority voting.
- The distance between the test data and all the training data is calculated to select the k closest training data points (k-nearest neighbors).
- The label (class) is predicted through majority voting.
- Common distance measures include Euclidean distance, Mahalanobis distance, correlation, and cosine similarity.
- Choosing an appropriate value for k is crucial.
- Small k is good at capturing fine-grained patterns but may overfit.
- Large k makes stable predictions but may underfit.
- The optimal value of k is a hyperparameter that can be tuned using a validation set.
k-NN Advantages
- No explicit model is built during training.
- The algorithm simply stores the dataset and performs computations during prediction (lazy learning).
- Simple and easy to program.
- As more data becomes available, k-NN can better approximate decision boundaries.
k-NN Disadvantages
- Calculating the distance between the query point and all training samples at prediction time is computationally expensive for large datasets.
- Can be biased toward the majority class if the data is imbalanced.
- Curse of dimensionality: In high-dimensional data, the distance between points becomes less meaningful.
- Performance depends heavily on the choice of k.
Support Vector Machine
- SVM is a type of supervised learning algorithm for classification.
- It finds an optimal separating hyperplane that maximizes the distance to the closest points from each class, known as the margin.
- The data points that lie on the edge of the margin are called support vectors.
- The position of the decision boundary is determined entirely by the support vectors.
- The margin can be maximized using a max-margin objective, which minimizes the squared norm of the weight vector.
- The max-margin principle can be applied to non-separable data by allowing some points to be within the margin or be misclassified.
- Slack variables are used to represent the misclassification of points.
- The soft-margin SVM objective minimizes a weighted combination of the squared norm of the weight vector and the total amount of slack.
- The hyperparameter 𝛾 balances the margin with the amount of slack.
- Different values of C (a hyperparameter) can lead to overfitting or underfitting.
Kernel Trick
- The kernel trick transforms data into a higher dimension using kernels, enabling the construction of a decision boundary that can be linearly separable.
- Examples of kernels include polynomial kernels and RBF (Radial Basis Function) kernels.
- When using the kernel trick with soft-margin SVM, overfitting may occur.
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