I2dl classifiers

= Classifiers =

Implementation overview
To implement k-NN, you'll need to perform the following steps:


 * Prepare your data: You need to have a labeled training dataset, which is used to train the k-NN model. This dataset is used to calculate distances between the new data point and the nearest neighbors.


 * Choose a distance metric: Common distance metrics used in k-NN include Euclidean distance, Manhattan distance, and Minkowski distance. The choice of distance metric will affect the results of your k-NN algorithm.


 * Select the value of k: The value of k represents the number of nearest neighbors used to make predictions. A common approach is to start with a small value for k (e.g. k=3), and increase it until the performance of the algorithm reaches an acceptable level.


 * Calculate the distances between the new data point and the training dataset: This step involves calculating the distances between the new data point and all the data points in the training dataset.


 * Find the k nearest neighbors: From the calculated distances, select the k nearest neighbors based on the chosen distance metric.


 * Assign a class label: The class label is assigned based on the majority vote of the k nearest neighbors. If k=3 and two out of three nearest neighbors belong to class A, then the new data point will be assigned to class A.


 * Repeat the process for each new data point.

k-NN Classifier
In k-NN, there are two main parameters:


 * k: This is the number of nearest neighbors to consider when making a prediction. Choosing a good value for k can affect the performance of the k-NN algorithm. A small value of k (e.g., k=1) can lead to overfitting, where the model is too closely tied to the training data, while a large value of k (e.g., k=n, where n is the number of training samples) can lead to underfitting, where the model is too generalized. A common choice for k is 5 or 10.


 * Distance metric: This is the method used to measure the distance between the test data and the training data. Common choices for the distance metric include Euclidean distance, Manhattan distance, and Minkowski distance. It's important to choose a distance metric that is appropriate for the data being used, as it can affect the performance of the k-NN algorithm.

Additionally, there are several other factors to consider when using k-NN:


 * Scaling of the data: It's important to scale the data before using the k-NN algorithm, as the distance metric is sensitive to the scale of the data.


 * Imbalanced classes: If the class labels in the training data are imbalanced (i.e., one class has significantly more samples than the other), it can affect the performance of the k-NN algorithm.


 * Curse of dimensionality: The k-NN algorithm can be sensitive to the curse of dimensionality, which refers to the difficulty of finding nearest neighbors in high-dimensional data.


 * Outliers: Outliers can have a significant impact on the k-NN algorithm, as they can be chosen as nearest neighbors and affect the prediction.

Note about overfitting
Overfitting in k-NN can occur when the model is too closely tied to the training data, and is unable to generalize to unseen data. Here are a few signs of overfitting in k-NN:


 * High Training Accuracy, Low Testing Accuracy: If the k-NN model has a high accuracy on the training data but a low accuracy on the testing data, it's a sign of overfitting. This indicates that the model has learned the training data too well and is unable to generalize to unseen data.


 * Complex Decision Boundaries: Overfitting can cause the decision boundaries in k-NN to become too complex and overly fit to the training data. This can result in the model being highly sensitive to small fluctuations in the data, making it less robust to unseen data.


 * Overly Small k: If the value of k is set too small, it can lead to overfitting in k-NN. This is because the model is considering only a few nearest neighbors when making predictions, which can result in the model being overly influenced by the training data.


 * Noisy Data: If the training data contains a lot of noise or irrelevant features, it can lead to overfitting in k-NN. This is because the model may learn the noise in the data instead of the underlying pattern.

To avoid overfitting in k-NN, it's important to choose a good value for k, and to use techniques like cross-validation to evaluate the performance of the model on unseen data. Additionally, it's important to pre-process the data to remove any noise or irrelevant features before using k-NN.

Python example
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