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Lecture 2: Image Classification pipeline

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Fei-Fei Li & Andrej Karpathy Lecture 2 - 7 Jan 2015 Fei-Fei Li & Andrej Karpathy Lecture 2 - 1 7 Jan 2015

Lecture 2:

Image Classification pipeline

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Fei-Fei Li & Andrej Karpathy Lecture 2 - 7 Jan 2015 Fei-Fei Li & Andrej Karpathy Lecture 2 - 2 7 Jan 2015

Image Classification: a core task in Computer Vision

cat

(assume given set of discrete labels)

{dog, cat, truck, plane, ...}

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Fei-Fei Li & Andrej Karpathy Lecture 2 - 7 Jan 2015 Fei-Fei Li & Andrej Karpathy Lecture 2 - 3 7 Jan 2015

The problem:

semantic gap

Images are represented as R d arrays of numbers

•  E.g. R 3 with integers

between [0, 255], where

d=3 represents 3 color

channels (RGB)

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An image classifier

Unlike e.g. sorting a list of numbers,

no obvious way to hard-code the algorithm for

recognizing a cat, or other classes.

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Data-driven approach:

1.  Collect a dataset of images and label them

2.  Use Machine Learning to train an image classifier

3.  Evaluate the classifier on a withheld set of test images

Example training set

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First classifier: Nearest Neighbor Classifier

Remember all training images and their labels

Predict the label of the

most similar training image

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Example dataset: CIFAR-10 10 labels

50,000 training images

10,000 test images.

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Example dataset: CIFAR-10 10 labels

50,000 training images

10,000 test images. For every test image (first column),

examples of nearest neighbors in rows

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How do we compare the images? What is the distance metric?

L1 distance: Where I

1

denotes image 1,

and p denotes each pixel

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Nearest Neighbor classifier

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Nearest Neighbor classifier

remember the training data

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Nearest Neighbor classifier

for every test image:

-  find nearest train image with L1 distance

-  predict the label of

nearest training image

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Nearest Neighbor classifier Q: what is the

complexity of the NN classifier w.r.t training set of N images and test set of M images?

1.  at training time?

2.  at test time?

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Nearest Neighbor classifier Q: what is the

complexity of the NN classifier w.r.t training set of N images and test set of M images?

1.  at training time?

O(1)

1.  at test time?

O(NM)

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Nearest Neighbor classifier 1.  at training time?

O(1)

2. at test time?

O(NM)

This is backwards:

- test time performance is usually much more important.

- CNNs flip this:

expensive training,

cheap test evaluation

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Aside: Approximate Nearest Neighbor

find approximate nearest neighbors quickly

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The choice of distance is a hyperparameter

L1 (Manhattan) distance L2 (Euclidean) distance

-  Two most commonly used special cases of p-norm

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k-Nearest Neighbor

find the k nearest images, have them vote on the label

the data NN classifier 5-NN classifier

http://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm

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What is the best distance to use?

What is the best value of k to use?

i.e. how do we set the hyperparameters?

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What is the best distance to use?

What is the best value of k to use?

i.e. how do we set the hyperparameters?

Very problem-dependent.

Must try them all out and see what works best.

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Trying out what hyperparameters work best on test set:

Very bad idea. The test set is a proxy for the generalization performance

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Validation data

use to tune hyperparameters

evaluate on test set ONCE at the end

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Cross-validation

cycle through the choice of which fold is

the validation fold, average results.

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Example of

5-fold cross-validation for the value of k.

Each point: single outcome.

The line goes

through the mean, bars indicated standard

deviation

(Seems that k = 7 works best

for this data)

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Summary

-  Image Classification: We are given a Training Set of labeled images, asked to predict labels on Test Set. Common to report the Accuracy of predictions (fraction of correctly predicted images)

-  We introduced the k-Nearest Neighbor Classifier, which predicts the labels based on nearest images in the training set

-  We saw that the choice of distance and the value of k are hyperparameters that are tuned using a validation set, or through cross-validation if the size of the data is small.

-  Once the best set of hyperparameters is chosen, the classifier is evaluated

once on the test set.

References

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