代写机器学习算法，对图像进行分类处理。
Introduction
The objective of this assignment is to develop and evaluate several algorithms
for classifying images of handwritten digits. You will work with a simplified
version of the famous MNIST data set: a collection of 2707 digits represented
by vectors of 256 numbers that represent 16x16 images. The data is split into
a training set (1707 images) and a test set (1000 images). These data sets are
stored in 4 files: train in.csv, train out.csv, test in.csv, test out.csv,
where in and out refer to the input records (images) and the corresponding
digits (class labels), respectively. These files are stored in data.zip.
You may find more information about the original problem of handwritten digit
recognition, more data sets and an overview of accuracies of best classifiers
(it is about 99.6%!) at http://yann.lecun.com/exdb/mnist/
.
Task 1: Analyze distances between images
The purpose of this task is to develop some intuitions about clouds of points
in highly dimensional spaces. In particular, you are supposed to develop a
very simple algorithm for classifying hand-written digits.
Let us start with developing a simple distance-based classifier. For each
digit d, d = 0, 1, ... , 9, let us consider a cloud of points in 256
dimensional space, which consists of all training images (vectors) that
represent d. Then, for each cloud we can calculate its center, which is just a
256-dimensional vector of means over all coordinates of vectors that belong
to. Once we have these centers, we can easily classify new images: to classify
an image, calculate the distance from the vector that represents this image to
each of the 10 centers; select as a label the closest one. But first let us
take a closer look at out data.
For each cloud, d = 0, 1, ... , 9, calculate its center, and the radius.
The radius is defined as the biggest distance between the center and points.
Additionally, find the number of points that belong to. Clearly, at this stage
you are supposed to work with the training set only.
Next, calculate the distances between the centers of the 10 clouds. Given all
these distances, try to say something about the expected accuracy of your
classifier. What pairs of digits seem to be most difficult to separate?
Task 2: Implement and evaluate the simplest classifier
Now, given the centers of 10 clouds, you should implement the simplest
distance-based classifier that was described above. Apply your classifier to
all points from the training set and calculate the percentage of correctly
classified digits. Do the same with the test set, using the centers that were
calculated from the training set. In both cases, generate a confusion matrix
which should provide a deeper insight into classes that are difficult to
separate. A confusion matrix is here a 10-by-10 matrix. Which digits were most
difficult to classify correctly? For calculating and visualising confusion
matrices you may use the sklearn package. Describe your findings. Compare
performance of your classifier on the train and test sets. How do the results
compare to the observations you’ve made in Step 1? How would you explain it?
So far, we have implicitly assumed that you have measured the distance between
two vectors with help of the Euclidean distance measure. However, this is not
the only choice. Rerun your code using alternative distance measures that are
implemented in sklearn.metrics.pairwise.pairwise distances. Which distance
measure provided best results (on the test set)?
Task 3: Implement a Bayes Rule classifier
Now approach the problem in the same way as in the “a” or “b”? example that
was discussed during the course. To keep things simple, limit yourself to
images of two digits only, for example, 5 and 7. Which feature do you want to
use to discriminate between the two classes? Create corresponding histograms
and calculate the terms P (X|C) and P (C) so you could apply the Bayes rule to
both the train and the test set. What accuracy have you achieved?
Task 4: Implement a multi-class perceptron algorithm
Implement (from scratch) a multi-class perceptron training algorithm (to be
discussed on
15 Feb.) and use it for training a single layer perceptron with 10 nodes (one
per digit), each node having 256+1 inputs and 1 output. Train your network on
the train set and evaluate on both the train and the test set, in the same way
as you did in the previous steps.
Task 5: Find the best possible model with existing software
This is probably the most rewarding, but also time consuming activity. Study
the first two chapters of the book
http://neuralnetworksanddeeplearning.com/index.html
and play with the
software that is discussed in these two chapters. When you mastered this
software, modify and apply it to our original problem: find the best
classifier, trained on our small train set (with 1707 records) and test it on
the test set (with 1000 records).
Summarize your results in a table: the algorithms that you tried, key
parameters you used, the obtained accuracies on the train and test sets.
Organization
Your solution should consist of a report in the pdf format (at most 10 pages)
and neatly organized code that you’ve used in your experiments (but no data)
so we could reproduce your results.
More details about the submission procedure and evaluation criteria will
follow soon-we are working on a new method that will require your substantial
involvement in the evaluation process!
