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This chapter has explored a number of the central concepts and algorithms of machine learning.
But moving from these concepts to real-world application can be a challenge.
Real-world datasets are noisy and heterogeneous, may have missing features, and data may be in a form that is difficult to map to a clean `[n_samples, n_features]`

matrix.
Before applying any of the methods discussed here, you must first extract these features from your data: there is no formula for how to do this that applies across all domains, and thus this is where you as a data scientist must exercise your own intuition and expertise.

One interesting and compelling application of machine learning is to images, and we have already seen a few examples of this where pixel-level features are used for classification.
In the real world, data is rarely so uniform and simple pixels will not be suitable: this has led to a large literature on *feature extraction* methods for image data (see Feature Engineering).

In this section, we will take a look at one such feature extraction technique, the Histogram of Oriented Gradients (HOG), which transforms image pixels into a vector representation that is sensitive to broadly informative image features regardless of confounding factors like illumination. We will use these features to develop a simple face detection pipeline, using machine learning algorithms and concepts we've seen throughout this chapter.

We begin with the standard imports:

The Histogram of Gradients is a straightforward feature extraction procedure that was developed in the context of identifying pedestrians within images. HOG involves the following steps:

- Optionally pre-normalize images. This leads to features that resist dependence on variations in illumination.
- Convolve the image with two filters that are sensitive to horizontal and vertical brightness gradients. These capture edge, contour, and texture information.
- Subdivide the image into cells of a predetermined size, and compute a histogram of the gradient orientations within each cell.
- Normalize the histograms in each cell by comparing to the block of neighboring cells. This further suppresses the effect of illumination across the image.
- Construct a one-dimensional feature vector from the information in each cell.

A fast HOG extractor is built into the Scikit-Image project, and we can try it out relatively quickly and visualize the oriented gradients within each cell:

Using these HOG features, we can build up a simple facial detection algorithm with any Scikit-Learn estimator; here we will use a linear support vector machine (refer back to In-Depth: Support Vector Machines if you need a refresher on this). The steps are as follows:

- Obtain a set of image thumbnails of faces to constitute "positive" training samples.
- Obtain a set of image thumbnails of non-faces to constitute "negative" training samples.
- Extract HOG features from these training samples.
- Train a linear SVM classifier on these samples.
- For an "unknown" image, pass a sliding window across the image, using the model to evaluate whether that window contains a face or not.
- If detections overlap, combine them into a single window.

Let's go through these steps and try it out:

Let's start by finding some positive training samples that show a variety of faces. We have one easy set of data to work with—the Labeled Faces in the Wild dataset, which can be downloaded by Scikit-Learn:

(13233, 62, 47)

This gives us a sample of 13,000 face images to use for training.

Next we need a set of similarly sized thumbnails which *do not* have a face in them.
One way to do this is to take any corpus of input images, and extract thumbnails from them at a variety of scales.
Here we can use some of the images shipped with Scikit-Image, along with Scikit-Learn's `PatchExtractor`

:

(30000, 62, 47)

We now have 30,000 suitable image patches which do not contain faces. Let's take a look at a few of them to get an idea of what they look like:

Our hope is that these would sufficiently cover the space of "non-faces" that our algorithm is likely to see.

Now that we have these positive samples and negative samples, we can combine them and compute HOG features. This step takes a little while, because the HOG features involve a nontrivial computation for each image:

(43233, 1215)

We are left with 43,000 training samples in 1,215 dimensions, and we now have our data in a form that we can feed into Scikit-Learn!

Next we use the tools we have been exploring in this chapter to create a classifier of thumbnail patches.
For such a high-dimensional binary classification task, a Linear support vector machine is a good choice.
We will use Scikit-Learn's `LinearSVC`

, because in comparison to `SVC`

it often has better scaling for large number of samples.

First, though, let's use a simple Gaussian naive Bayes to get a quick baseline:

array([ 0.9408785 , 0.8752342 , 0.93976823])

We see that on our training data, even a simple naive Bayes algorithm gets us upwards of 90% accuracy. Let's try the support vector machine, with a grid search over a few choices of the C parameter:

0.98667684407744083

{'C': 4.0}

Let's take the best estimator and re-train it on the full dataset:

LinearSVC(C=4.0, class_weight=None, dual=True, fit_intercept=True, intercept_scaling=1, loss='squared_hinge', max_iter=1000, multi_class='ovr', penalty='l2', random_state=None, tol=0.0001, verbose=0)

Now that we have this model in place, let's grab a new image and see how the model does. We will use one portion of the astronaut image for simplicity (see discussion of this in Caveats and Improvements), and run a sliding window over it and evaluate each patch:

Next, let's create a window that iterates over patches of this image, and compute HOG features for each patch:

(1911, 1215)

Finally, we can take these HOG-featured patches and use our model to evaluate whether each patch contains a face:

33.0

We see that out of nearly 2,000 patches, we have found 30 detections. Let's use the information we have about these patches to show where they lie on our test image, drawing them as rectangles: