#ml/algorithms The k-nearest neighbors (KNN) algorithm is a simple, intuitive, and widely used machine learning algorithm for #ml/classification and #ml/regression tasks. It is a type of Instance-Based learning (or lazy learning), meaning it does not explicitly learn a model during training but instead stores the entire dataset and makes predictions based on similarity measures at inference time.
#How it works
- Input Data:
- A dataset with labeled examples (for classification) or continuous target values (for regression).
- Each example is represented as a feature vector in a multidimensional space.
- Distance Metric:
- KNN relies on a distance metric to measure the similarity between data points.
- Common distance metrics include Minkowski Distances and Cosine Similarity
- Choosing $k$:
- $k$ is a user-defined parameter representing the number of nearest neighbors to consider.
- A small $k$ (e.g., 1) makes the algorithm sensitive to noise, while a large $k$ smooths out predictions but may include irrelevant neighbors.
- Prediction:
- For a new, unlabeled data point:
- Calculate the distance between the new point and all points in the training dataset.
- Identify the $k$ nearest neighbors (the $k$ points with the smallest distances).
- For #ml/classification : Use majority voting among the $k$ neighbors to assign the class label.
- For #ml/regression: Use the average (or weighted average) of the target values of the $k$ neighbors.
- For a new, unlabeled data point:
- Output:
- The predicted class (for classification) or value (for regression) for the new data point.
#Key Considerations
#Choice of $k$:
- A small $k$ leads to high variance and low bias (overfitting).
- A large $k$ leads to low variance and high bias (underfitting).
- $k$ is often chosen using cross-validation.
#Feature Scaling:
- KNN is sensitive to the scale of features, so normalization or standardization is often required.
#Computational Complexity:
- KNN can be computationally expensive for large datasets because it requires calculating distances for all training points during inference.
- Optimizations like KD-trees or Ball trees can speed up neighbor searches.
#Curse of Dimensionality:
- In high-dimensional spaces, distances between points become less meaningful, reducing the effectiveness of KNN.
#Advantages
- Simple to understand and implement
- Adabtable
- No training phase (lazy learning)
- Naturally handles multi-class classification
#Disadvantages
- Computationally and memory expensive for large datasets
- Sensitive to irrelevant or redundant Features (noise).
- Requires careful tuning of k and distance metrics.
#Applications
- Image Recognition
- Recommendation systems
- Medical diagnosis
- Anomaly detection
K-Means Clustering