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(projects:mnist:semisupervised-classification)=
# Semisupervised Classification

The QMNIST data set contains 120000 labeled images of handwritten digits. It was created to train digit recognition systems via supervised learning methods. Obtaining such a massiv amount of labeled samples is an expensive and time consuming work. The creators designed forms for writing prescribed digits, which were filled in by hundreds of people. Then the forms were scanned and digits separated. Hopefully every writer wrote the correct digit in each field.

In the project we want to train a digit recognition model based an QMNIST images without using any labels. Obtaining scanned images of handwritten digits is cheap and simple. One does not need forms with prescribed digits and nobody has to manually label scanned images. There are lots of pages with handwritten digits out there. We would have to scan them and separate digits by standard image processing routines.

Of course, having only unlabeled data at hand we cannot use supervised learning methods. Unsupervised methods do not yield labels, but only unlabeled clusters of similar images. The obvious idea is to do some unsupervised clustering and then manually label each cluster. Adding (a small amount of) manual labels to an unsupervised learning procedure is known as *semi-supervised learning*.

## Preprocessing

**Task:** Load QMNIST training images (without labels). Center and crop images to 20x20.

**Solution:**

```{code-cell} ipython3
# your solution
```

+++ {"tags": [], "user_expressions": []}

We have a 400 dimensional data space. This might be too much to obtain useful results from $k$-means (curse of dimensionality). Maybe we have to use PCA.

**Task:** Check whether our data suffers from the curse of dimensionality (don't use all samples!). Why isn't this the case?

**Solution:**

```{code-cell} ipython3
# your solution
```

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## Clustering

Although we know that there are 10 different classes there might be much more clusters. A cluster contains similar samples, but different people tend to write the same digits in several different ways. From this point of view it is not clear how many cluster we can expect.

We have to choose $k$ by elbow method or silhouette score or Davies-Bouldin index. Calculating silhouette scores is very slow for large data sets (why?), so we calculate it only for a subset. We also should use mini-batch $k$-means to save computation time.

**Task:** Apply $k$-means to the data and find the best $k$ based on elbow method, silhouette score (10000 samples) and Davies-Bouldin index. Make a first run with $k=5,10,15,\ldots,100$. Then choose a smaller intervall for $k$ and run $k$-means for each $k$ in this interval.

**Solution:**

```{code-cell} ipython3
# your solution
```

**Task:** Choose a good $k$ and visualize all cluster centers together with cluster sizes (samples per cluster). Write a function for visualizing the cluster centers. The function shall take a NumPy array of cluster centers and a list of title strings as arguments.

**Solution:**

```{code-cell} ipython3
# your solution
```

## Prediction

To use our model (set of cluster centers) for recognizing digits we have to label the cluster centers manually. For testing the prediction quality of our model we use QMNIST test images and labels.

**Task:** Load and preprocess QMNIST test images and labels.

**Solution:**

```{code-cell} ipython3
# your solution
```

**Task:** Create a mapping (1d array) from cluster labels (indices) to digit labels (manual labeling).
Then label all test images and calculate correct classifiaction rate.

**Solution:**

```{code-cell} ipython3
# your solution
```

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## Inspection

**Task:** Calculate correct classification rate per cluster and show results together with corresponding cluster centroids.

**Solution:**

```{code-cell} ipython3
# your solution
```

## More clusters?

**Task:** What do you think about using more clusters than suggested by silouette score and Davies-Bouldin-index?

**Solution:**

```{code-cell} ipython3
# your answer
```

**Task:** Try $k=100$.

**Task:** What happens for $k=60000$.

**Solution:**

```{code-cell} ipython3
# your answer
```

+++ {"user_expressions": [], "tags": []}

## Random cluster centers

$k$-means with $k$ manually labeled cluster centers is equivalent to $1$NN with the cluster centers as training set. The idea behind $k$-means is that the cluster centers are not chosen at random, but much more sensible.

**Task:** Try $1$NN with 100 randomly choosen and manually labeled training samples. Calculate correct classification rate on the test set.

**Solution:**

```{code-cell} ipython3
# your solution
```
