Part1 Image Classification
graph LR
Image --> Classifier["classifier with training data"] --> Score
classDef borderless stroke-width:0px,fill:#fff;
class Image,Score borderless;
classDef smallBox stroke:#333,stroke-width:1px,fill:#f9f9f9,font-size:10px,padding:4px;L1 and L2 Distance
How to measure the similarity between images?
L1 Distance: Two images are subtracted elementwise and then all differences are added up to a single number.
$$d_1(I_1,I_2)=\sum\limits_p|I_1^p-I_2^p|$$
L2 Distance: Two images are subtracted elementwise, squared, and then all differences are added up to a single number, which is then square-rooted.
$$d_2(I_1,I_2)=\sqrt{\sum\limits_p|I_1^p-I_2^p|^2}$$
Nearest Neighbor Classifier
The nearest neighbor classifier will take a test image, compare it to every single one of the training images, and predict the label of the closest training image.
K-Nearest Neighbors Classifier
Instead of finding the single closest image in the training set, we will find the top k closest images, and have them vote on the label of the test image.
Classifier Structure
How to determine the best $k$ and distance metric?
- Training Set: train the model
- Validation Set: tune hyperparameters (e.g. $k$, distance metric)
- Test Set: evaluate performance
Cross Validation
In cases where the size of your training data (and therefore also the validation data) might be small, you can get a better and less noisy estimate of how well a certain value of $k$ works by iterating over different validation sets and averaging the performance across these.
The training set is split into folds. The folds 1-4 become the training set. One fold (e.g. fold 5 here in yellow) is denoted as the validation fold and is used to tune the hyperparameters. Cross-validation goes a step further and iterates over the choice of which fold is the validation fold, separately from 1-5.