_________ clustering builds a tree-like diagram called a dendrogram, allowing you to visualize the relationships between clusters.
- DBSCAN
- Hierarchical
- K-Means
- Spectral
Hierarchical clustering builds a dendrogram, which allows visualization of the relationships between clusters, showing how the clusters are connected.
How does LDA maximize the separation between different classes in a dataset?
- By maximizing between-class variance and minimizing within-class variance
- By maximizing both within-class and between-class variance
- By minimizing between-class variance and maximizing within-class variance
- By minimizing both within-class and between-class variance
LDA maximizes the separation between different classes by "maximizing between-class variance and minimizing within-class variance." This process ensures that different classes are far apart, while data points within the same class are close together, resulting in better class separation.
You reduced the complexity of your model to prevent overfitting, but it led to underfitting. How would you find a balance between complexity and fit?
- Add regularization
- All of the above
- Increase dataset size
- Try cross-validation
Finding a balance might involve using cross-validation to systematically find the right level of complexity that fits well with the training data but also generalizes well to the validation data. This process helps in finding the right hyperparameters without biasing the test data.
Bootstrapping involves resampling with replacement from the dataset to create "n" _________ datasets.
- additional
- bootstrap
- copied
- resampled
Bootstrapping is a statistical method that involves resampling with replacement from the dataset to create "n" "bootstrap" datasets. It allows estimating the distribution of a statistic by creating many resampled datasets and calculating the statistic for each.
How can you evaluate the performance of an LDA model?
- By checking the size of the scatter matrices
- By comparing with PCA
- Using confusion matrix and ROC curves
- Using only accuracy
The performance of an LDA model can be evaluated using metrics like the "confusion matrix and ROC curves." These tools provide insights into the model's ability to classify instances correctly and its trade-off between sensitivity and specificity.
You applied DBSCAN and found that many points are being classified as noise. What adjustments could you make to the parameters?
- Decrease Epsilon; Increase MinPts
- Increase Epsilon; Decrease MinPts
- Increase both Epsilon and MinPts
- Use the same Epsilon and MinPts but change the clustering method
Increasing Epsilon and decreasing MinPts will make the clustering less strict, reducing the chance of points being classified as noise. Epsilon defines the neighborhood size, and MinPts defines the minimum points required to form a cluster. By adjusting them, more points can be included in clusters, reducing noise classification.
In K-Means clustering, a common approach to avoid local minima due to initial centroid selection is to run the algorithm multiple times with different _________.
- Centroid initializations
- Distance metrics
- Learning rates
- Number of clusters
Running the K-Means algorithm multiple times with different centroid initializations helps in avoiding local minima. It increases the chance of finding a more globally optimal clustering solution.
What is the role of cross-validation in detecting and preventing overfitting in Polynomial Regression?
- It assists in increasing model complexity
- It focuses on training data only
- It helps in choosing the right degree and assessing generalization
- It helps in selecting features
Cross-validation plays a key role in detecting and preventing overfitting in Polynomial Regression by helping in choosing the right degree for the polynomial and assessing how well the model generalizes to new data.
How can the 'k-distance graph' be used in selecting the optimal Epsilon for DBSCAN?
- By calculating the average distance to k-nearest neighbors
- By determining the distance between k centroids
- By displaying k clusters' distances
- By plotting the distance to the kth nearest neighbor of each point
The 'k-distance graph' can be used to select the optimal Epsilon by plotting the distance to the kth nearest neighbor for each point and looking for an "elbow" or a point of inflection. This inflection point can be a good estimate for Epsilon, helping to choose a value that balances density requirements without overly segmenting the data.
In the context of DBSCAN, if two core points are within the Epsilon distance of each other, they are said to be __________.
- directly dense reachable
- indirectly dense reachable
- separate
- unrelated
In DBSCAN, if two core points are within the Epsilon distance of each other, they are said to be directly dense reachable. This concept is used to establish connections between core points and helps in forming clusters by linking together points that are close to one another.