# python - implementing a perceptron classifier

Hi I'm pretty new to Python and to NLP. I need to implement a perceptron classifier. I searched through some websites but didn't find enough information. For now I have a number of documents which I grouped according to category(sports, entertainment etc). I also have a list of the most used words in these documents along with their frequencies. On a particular website there was stated that I must have some sort of a decision function accepting arguments x and w. x apparently is some sort of vector ( i dont know what w is). But I dont know how to use the information I have to build the perceptron algorithm and how to use it to classify my documents. Have you got any ideas? Thanks :)

### How a perceptron looks like

From the outside, a perceptron is a function that takes `n` arguments (i.e an `n`-dimensional vector) and produces `m` outputs (i.e. an `m`-dimensional vector).

On the inside, a perceptron consists of layers of neurons, such that each neuron in a layer receives input from all neurons of the previous layer and uses that input to calculate a single output. The first layer consists of `n` neurons and it receives the input. The last layer consist of `m` neurons and holds the output after the perceptron has finished processing the input.

### How the output is calculated from the input

Each connection from a neuron `i` to a neuron `j` has a weight `w(i,j)` (I'll explain later where they come from). The `total input` of a neuron `p` of the second layer is the sum of the weighted output of the neurons from the first layer. So

``````total_input(p) = Σ(output(k) * w(k,p))
``````

where `k` runs over all neurons of the first layer. The activation of a neuron is calculated from the total input of the neuron by applying an activation function. An often used activation function is the Fermi function, so

``````activation(p) = 1/(1-exp(-total_input(p))).
``````

The output of a neuron is calculated from the activation of the neuron by applying an `output function`. An often used output function is the identity `f(x) = x` (and indeed some authors see the output function as part of the activation function). I will just assume that

``````output(p) = activation(p)
``````

When the output off all neurons of the second layer is calculated, use that output to calculate the output of the third layer. Iterate until you reach the output layer.

### Where the weights come from

At first the weights are chosen randomly. Then you select some examples (from which you know the desired output). Feed each example to the perceptron and calculate the error, i.e. how far off from the desired output is the actual output. Use that error to update the weights. One of the fastest algorithms for calculating the new weights is Resilient Propagation.

### How to construct a Perceptron

Some questions you need to address are

1. What are the relevant characteristics of the documents and how can they be encoded into an `n`-dimansional vector?
2. Which examples should be chosen to adjust the weights?
3. How shall the output be interpreted to classify a document? Example: A single output that yields the most likely class versus a vector that assigns probabilities to each class.
4. How many hidden layers are needed and how large should they be? I recommend starting with one hidden layer with `n` neurons.

The first and second points are very critical to the quality of the classifier. The perceptron might classify the examples correctly but fail on new documents. You will probably have to experiment. To determine the quality of the classifier, choose two sets of examples; one for training, one for validation. Unfortunately I cannot give you more detailed hints to answering these questions due to lack of practical experience.

I think that trying to solve an NLP problem with a Neural Network when you're not familiar with either might be a step too far. That you're doing it in a new language is the least of your worries.

I'll link you to my Neural Computation module slides that gets taught at my university. You'll want the slides from session 1 and session 2 in week 2. Right at the bottom of the page is a link to how to implement a neural network in C. With a few modifications should be able to port it to python. You should note that it details how to implement a multilayer perceptron. You only need to implement a single layer perceptron, so ignore anything that talks about hidden layers.

A quick explanation of `x` and `w`. Both x and w are vectors. x is the input vector. `x` contains normalised frequencies for each word you are concerned about. `w` contains weights for each word you are concerned with. The perceptron works by multiplying the input frequency for each word by its respective weight and summing them up. It passes the result to a function (typically a sigmoid function) that turns the result into a value between 0 and 1. 1 means the perceptron is positive that the inputs are an instance of the class it represents and 0 means it is sure that the inputs really aren't an example of its class.

With NLP you typically learn about the bag of words model first, before moving on to other, more complex, models. With a neural network, hopefully, it will learn its own model. The problem with this is that the neural network will not give you much of an understanding of NLP, other than documents can be classified by the words they contain, and that usually the number and type of words in a document contains most of the information you need to classify a document -- context and grammar do not add much extra detail.

Anyway, I hope that gives a better place from which to start your project. If you're still stuck on a particular part then ask again and I'll do my best to help.

You should take a look at this survey paper on text classification by Frabizio Sebastiani. It tells you all of the best ways to do text classification.

Now, I'm not going to bother you to read the whole thing, but there's one table near the end, where he compares how lots of different people's techniques stack up on lots of different test corpora. Find it, pick the best one (the best perceptron one, if you assignment is specifically to learn how to do this with perceptron), and read the paper he cites that describes that method in detail.

You now know how to construct a good topical text classifier.

Turning the algorithm that Oswald gave you (and that you posted in your other question) into code is a Small Matter of Programming (TM). And if you encounter unfamiliar terms like TF-IDF while you're working, ask your teacher to help you by explaining those terms.

MultiLayer perceptrons (A specific NeuralNet architecture for general classification problem.) Now available for Python from the GraphLab folks:

https://dato.com/products/create/docs/generated/graphlab.deeplearning.MultiLayerPerceptrons.html#graphlab.deeplearning.MultiLayerPerceptrons

I had a try at implementing something similar the other day. I made some code to recognize english looking text vs non-english. I hadn't done AI or statistics in many years, so it was a bit of a shotgun attempt.

My code is here (don't want to bloat the post): http://cnippit.com/content/perceptron-statistically-recognizing-english

Inputs:

• I take a text file, split it up into tri-grams (eg "abcdef" => ["abc", "bcd", "cde", "def"])
• I calculate the relative frequencies of each, and feed that as the inputs to the perceptron (so there are 26^3 inputs)

Despite me not really knowing what I was doing, it seems to work fairly well. The success depends quite heavily on the training data though. I was getting poor results until I trained it on more french/spanish/german text etc.

It's a very small example though, with lots of "lucky guesses" at values (eg. initial weights, bias, threshold, etc.).

Multiple classes: If you have multiple classes you want to distinquish between (ie. not as simple as "is A or NOT-A"), then one approach is to use a perceptron for each class. Eg. one for sport, one for news, etc.

Train the sport-perceptron on data grouped as either sport or NOT-sport. Similar for news or Not-news, etc.

When classifying new data, you pass your input to all perceptrons, and whichever one returns true (or "fires"), then that's the class the data belongs to.

I used this approach way back in university, where we used a set of perceptrons for recognizing handwritten characters. It's simple and worked pretty effectively (>98% accuracy if I recall correctly).