Recently I've been working on character recognition using Back Propagation Algorithm. I've taken the image and reduced to 5x7 size, therefore I got 35 pixels and trained the network using those pixels with 35 input neurons, 35 hidden nodes, and 10 output nodes. And I had completed the training successfully and I got weights that I needed. And I've got stuck here. I have my test set and I know I should feed forward the network. But I don't know what to do exactly. My test set will be 4 samples of 1x35. My output layer has 10 neurons. how do I exactly distinguish the characters with the output that I will get? I want to know how this testing works. Please guide me through this stage. Thanks in advance.
One vs All
A common approach for testing these types of neural networks is "one-vs-all" approach. We view each of the output nodes as its own classifier that is giving the probability of the sample being that class vs not being that class.
For instance if you network output [1, 0, ..., 0] then class 1 has high probability of being class 1 vs not being class 1. Class 2 has low probability of being class 2 vs not being class 2, etc.
Ties
In the case of a tie, it is common (in research) to have a random function break the tie. If you get [1, 1, 1, ..., 1] then the function would pick a number from 1-10 and that is your prediction. In practice sometimes an expert system is used to break ties. Perhaps class 1 is more expensive than class 2, so we tie in preference to class 2.
Steps
So the steps are:
Split dataset into test/train set
Train weights on train set
Pass test set forward through the neural network
For each sample, choose the argmax (the output with highest value) as your prediction
In case of tie, choose randomly between all tying classes
Aside
In your particular case, I imagine implementation of this strategy will result in a network that barely beats random performance (10%) accuracy.
I would suggest some reconsidering of the network architecture.
If you look at your 5x7 images, can you tell what number that image was originally? It seems likely that scaling the image down to this size losses too much information that the network cannot distinguish between classes.
Debugging
From what you've described I would look at the following when debugging your network.
Is your data preprocessing (down-scaling) leeching out too much information? Check this by manually investigating a few of the images and seeing if you can tell what the image should be.
Does your one-hot algorithm work? When you convert your targets for training, does it successfully convert 1 -> [1, 0, 0, ..., 0]?
Is your back-prop / gradient descent algorithm correct? You should see (roughly) a monotonic decrease in your loss function while training. Try at every step (or every few steps) printing the loss that you are optimizing. Or even for a very simple gut check, print mean squared error: (P-Y)^2
Related
I'm trying to implement the proposed model in a CVPR paper (Deep Interactive Object Selection) in which the data set contains 5 channels for each input sample:
1.Red
2.Blue
3.Green
4.Euclidean distance map associated to positive clicks
5.Euclidean distance map associated to negative clicks (as follows):
To do so, I should fine tune the FCN-32s network using "object binary masks" as labels:
As you see, in the first conv layer I have 2 extra channels, so I did net surgery to use pretrained parameters for the first 3 channels and Xavier initialization for 2 extras.
For the rest of the FCN architecture, I have these questions:
Should I freeze all the layers before "fc6" (except the first conv layer)? If yes, how the extra channels of the first conv will be learned? Are the gradients strong enough to reach the first conv layer during training process?
What should be the kernel size of the "fc6"? should I keep 7? I saw in "Caffe net_surgery" notebook that it depends on the output size of the last layer ("pool5").
The main problem is the number of outputs of the "score_fr" and "upscore" layers, since I'm not doing class segmentation (to use 21 for 20 classes and the background), how should I change it? What about 2? (one for object and the other for the non-object (background) area)?
Should I change "crop" layer "offset" to 32 to have center crops?
In case of changing each of these layers, what is the best initialization strategy for them? "bilinear" for "upscore" and "Xavier" for the rest?
Should I convert my binary label matrix values into zero-centered ( {-0.5,0.5} ) status, or it is OK to use them with the values in {0,1} ?
Any useful idea will be appreciated.
PS:
I'm using Euclidean loss, while I'm using "1" as the number of outputs for "score_fr" and "upscore" layers. If I use 2 for that, I guess it should be softmax.
I can answer some of your questions.
The gradients will reach the first layer so it should be possible to learn the weights even if you freeze the other layers.
Change the num_output to 2 and finetune. You should get a good output.
I think you'll need to experiment with each of the options and see how the accuracy is.
You can use the values 0,1.
I've read a few ideas on the correct sample size for Feed Forward Neural networks. x5, x10, and x30 the # of weights. This part I'm not overly concerned about, what I am concerned about is can I reuse my training data (randomly).
My data is broken up like so
5 independent vars and 1 dependent var per sample.
I was planning on feeding 6 samples in (6x5 = 30 input neurons), confirm the 7th samples dependent variable (1 output neuron.
I would train on neural network by running say 6 or 7 iterations. before trying to predict the next iteration outside of my training data.
Say I have
each sample = 5 independent variables & 1 dependent variables (6 vars total per sample)
output = just the 1 dependent variable
sample:sample:sample:sample:sample:sample->output(dependent var)
Training sliding window 1:
Set 1: 1:2:3:4:5:6->7
Set 2: 2:3:4:5:6:7->8
Set 3: 3:4:5:6:7:8->9
Set 4: 4:5:6:7:8:9->10
Set 5: 5:6:7:6:9:10->11
Set 6: 6:7:8:9:10:11->12
Non training test:
7:8:9:10:11:12 -> 13
Training Sliding Window 2:
Set 1: 2:3:4:5:6:7->8
Set 2: 3:4:5:6:7:8->9
...
Set 6: 7:8:9:10:11:12->13
Non Training test: 8:9:10:11:12:13->14
I figured I would randomly run through my set's per training iteration say 30 times the number of my weights. I believe in my network I have about 6 hidden neurons (i.e. sqrt(inputs*outputs)). So 36 + 6 + 1 + 2 bias = 45 weights. So 44 x 30 = 1200 runs?
So I would do a randomization of the 6 sets 1200 times per training sliding window.
I figured due to the small # of data, I was going to do simulation runs (i.e. rerun over the same problem with new weights). So say 1000 times, of which I do 1140 runs over the sliding window using randomization.
I have 113 variables, this results in 101 training "sliding window".
Another question I have is if I'm trying to predict up or down movement (i.e. dependent variable). Should I match to an actual # or just if I guessed up/down movement correctly? I'm thinking I should shoot for an actual number, but as part of my analysis do a % check on if this # is guessed correctly as up/down.
If you have a small amount of data, and a comparatively large number of training iterations, you run the risk of "overtraining" - creating a function which works very well on your test data but does not generalize.
The best way to avoid this is to acquire more training data! But if you cannot, then there are two things you can do. One is to split the training data into test and verification data - using say 85% to train and 15% to verify. Verification means compute the fitness of the learner on the training set, without adjusting the weights/training. When the verification data fitness (which you are not training on) stops improving (in general it will be noisy), and your training data fitness continues improving - stop training. If on the other hand you use a "sliding window", you may not have a good criterion to know when to stop training - the fitness function will bounce around in unpredictable ways (you might slowly make the effect of each training iteration have less effect on the parameters, however, to give you convergence... maybe not the best approach but some training regimes do this) The other thing you can do normalize out your node's weights via some metric to ensure some notion of 'smoothness' - if you visualize overfitting for a second you'll find that in the extreme case your fitness function sharply curves around your dataset positives...
As for the latter question - for the training to converge, you fitness function needs to be smooth. If you were to just use binary all-or-nothing fitness terms, most likely what would happen is that whatever algorithm you are using to train (backprop, BGFS, etc...) would not converge. In practice, the classification criterion should be an activation that is above for a positive result, less than or equal to for a negative result, and varies smoothly in your weight/parameter space. You can think of 0 as "I am certain that the answer is up" and 1 as "I am certain that the answer is down", and thus realize a fitness function that has a higher "cost" for incorrect guesses that were more certain... There are subtleties possible in how the function is shaped (for example you might have different ideas about how acceptable a false negative and false positive are) - and you may also introduce regions of "uncertain" where the result is closer to "zero weight" - but it should certainly be continuous/smooth.
You can re-use sliding window's.
It basically the same concept as bootstrapping (your training set); which in itself reduces training time, but don't know if it's really helpful in making the net more adaptive to anything other than the training data.
Below is an example of a sliding window in pictorial format (using spreadsheet magic)
http://i.imgur.com/nxhtgaQ.png
https://github.com/thistleknot/FredAPI/blob/05f74faf85d15f6898aa05b9b08d5363fe27c473/FredAPI/Program.cs
Line 294 shows how the code is ran using randomization, it resets the randomization at position 353 so the rest flows as normal.
I was also able to use a 1 (up) or 0 (down) as my target values and the network did converge.
I'm having problems in understanding how K-NN classification works in MATLAB.ยด
Here's the problem, I have a large dataset (65 features for over 1500 subjects) and its respective classes' label (0 or 1).
According to what's been explained to me, I have to divide the data into training, test and validation subsets to perform supervised training on the data, and classify it via K-NN.
First of all, what's the best ratio to divide the 3 subgroups (1/3 of the size of the dataset each?).
I've looked into ClassificationKNN/fitcknn functions, as well as the crossval function (idealy to divide data), but I'm really not sure how to use them.
To sum up, I wanted to
- divide data into 3 groups
- "train" the KNN (I know it's not a method that requires training, but the equivalent to training) with the training subset
- classify the test subset and get it's classification error/performance
- what's the point of having a validation test?
I hope you can help me, thank you in advance
EDIT: I think I was able to do it, but, if that's not asking too much, could you see if I missed something? This is my code, for a random case:
nfeats=60;ninds=1000;
trainRatio=0.8;valRatio=.1;testRatio=.1;
kmax=100; %for instance...
data=randi(100,nfeats,ninds);
class=randi(2,1,ninds);
[trainInd,valInd,testInd] = dividerand(1000,trainRatio,valRatio,testRatio);
train=data(:,trainInd);
test=data(:,testInd);
val=data(:,valInd);
train_class=class(:,trainInd);
test_class=class(:,testInd);
val_class=class(:,valInd);
precisionmax=0;
koptimal=0;
for know=1:kmax
%is it the same thing use knnclassify or fitcknn+predict??
predicted_class = knnclassify(val', train', train_class',know);
mdl = fitcknn(train',train_class','NumNeighbors',know) ;
label = predict(mdl,val');
consistency=sum(label==val_class')/length(val_class);
if consistency>precisionmax
precisionmax=consistency;
koptimal=know;
end
end
mdl_final = fitcknn(train',train_class','NumNeighbors',know) ;
label_final = predict(mdl,test');
consistency_final=sum(label==test_class')/length(test_class);
Thank you very much for all your help
For your 1st question "what's the best ratio to divide the 3 subgroups" there are only rules of thumb:
The amount of training data is most important. The more the better.
Thus, make it as big as possible and definitely bigger than the test or validation data.
Test and validation data have a similar function, so it is convenient to assign them the same amount
of data. But it is important to have enough data to be able to recognize over-adaptation. So, they
should be picked from the data basis fully randomly.
Consequently, a 50/25/25 or 60/20/20 partitioning is quite common. But if your total amount of data is small in relation to the total number of weights of your chosen topology (e.g. 10 weights in your net and only 200 cases in the data), then 70/15/15 or even 80/10/10 might be better choices.
Concerning your 2nd question "what's the point of having a validation test?":
Typically, you train the chosen model on your training data and then estimate the "success" by applying the trained model to unseen data - the validation set.
If you now would completely stop your efforts to improve accuracy, you indeed don't need three partitions of your data. But typically, you feel that you can improve the success of your model by e.g. changing the number of weights or hidden layers or ... and now a big loops starts to run with many iterations:
1) change weights and topology, 2) train, 3) validate, not satisfied, goto 1)
The long-term effect of this loop is, that you increasingly adapt your model to the validation data, so the results get better not because you so intelligently improve your topology but because you unconsciously learn the properties of the validation set and how to cope with them.
Now, the final and only valid accuracy of your neural net is estimated on really unseen data: the test set. This is done only once and is also useful to reveal over-adaption. You are not allowed to start a second even bigger loop now to prohibit any adaption to the test set!
I'm working on a feed forward artificial neural network (ffann) that will take input in form of a simple calculation and return the result (acting as a pocket calculator). The outcome wont be exact.
The artificial network is trained using genetic algorithm on the weights.
Currently my program gets stuck at a local maximum at:
5-6% correct answers, with 1% error margin
30 % correct answers, with 10% error margin
40 % correct answers, with 20% error margin
45 % correct answers, with 30% error margin
60 % correct answers, with 40% error margin
I currently use two different genetic algorithms:
The first is a basic selection, picking two random from my population, naming the one with best fitness the winner, and the other the loser. The loser receives one of the weights from the winner.
The second is mutation, where the loser from the selection receives a slight modification based on the amount of resulting errors. (the fitness is decided by correct answers and incorrect answers).
So if the network outputs a lot of errors, it will receive a big modification, where as if it has many correct answers, we are close to a acceptable goal and the modification will be smaller.
So to the question: What are ways I can prevent my ffann from getting stuck at local maxima?
Should I modify my current genetic algorithm to something more advanced with more variables?
Should I create additional mutation or crossover?
Or Should I maybe try and modify my mutation variables to something bigger/smaller?
This is a big topic so if I missed any information that could be needed, please leave a comment
Edit:
Tweaking the numbers of the mutation to a more suited value has gotten be a better answer rate but far from approved:
10% correct answers, with 1% error margin
33 % correct answers, with 10% error margin
43 % correct answers, with 20% error margin
65 % correct answers, with 30% error margin
73 % correct answers, with 40% error margin
The network is currently a very simple 3 layered structure with 3 inputs, 2 neurons in the only hidden layer, and a single neuron in the output layer.
The activation function used is Tanh, placing values in between -1 and 1.
The selection type crossover is very simple working like the following:
[a1, b1, c1, d1] // Selected as winner due to most correct answers
[a2, b2, c2, d2] // Loser
The loser will end up receiving one of the values from the winner, moving the value straight down since I believe the position in the array (of weights) matters to how it performs.
The mutation is very simple, adding a very small value (currently somewhere between about 0.01 and 0.001) to a random weight in the losers array of weights, with a 50/50 chance of being a negative value.
Here are a few examples of training data:
1, 8, -7 // the -7 represents + (1+8)
3, 7, -3 // -3 represents - (3-7)
7, 7, 3 // 3 represents * (7*7)
3, 8, 7 // 7 represents / (3/8)
Use a niching techniche in the GA. A useful alternative is niching. The score of every solution (some form of quadratic error, I think) is changed in taking account similarity of the entire population. This maintains diversity inside the population and avoid premature convergence an traps into local optimum.
Take a look here:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.7342
A common problem when using GAs to train ANNs is that the population becomes highly correlated
as training progresses.
You could try increasing mutation chance and/or effect as the error-change decreases.
In English. The population becomes genetically similar due to crossover and fitness selection as a local minim is approached. You can introduce variation by increasing the chance of mutation.
You can do a simple modification to the selection scheme: the population can be viewed as having a 1-dimensional spatial structure - a circle (consider the first and last locations to be adjacent).
The production of an individual for location i is permitted to involve only parents from i's local neighborhood, where the neighborhood is defined as all individuals within distance R of i. Aside from this restriction no changes are made to the genetic system.
It's only one or a few lines of code and it can help to avoid premature convergence.
References:
TRIVIAL GEOGRAPHY IN GENETIC PROGRAMMING (2005) - Lee Spector, Jon Klein
Basically i know the concept of a neural network and what it is, but i can't figure out how it looks when you code it or how do you store the data, i went through many tutorials that i found on google but couldn't find any piece of code, just concepts and algorithms.
Can anyone give me a piece of code of a simple neural network something like "Hello World!"?
What you mainly need is an object representing a single neuron with the corrispective associations with other neurons (that represent synapses) and their weights.
A single neuron in a typical OOP language will be something like
class Synapse
{
Neuron sending;
Neuron receiving;
float weight;
}
class Neuron
{
ArrayList<Synapse> toSynapses;
ArrayList<Synapse> fromSynapses;
Function threshold;
}
where threshold represents the function that is applied on weighted sum of inputs to see if the neuron activates itself and propagates the signal.
Of course then you will need the specific algorithm to feed-forward the net or back-propagate the learning that will operate on this data structure.
The simplest thing you could start implement would be a simple perceptron, you can find some infos here.
You said you're already familiar with neural networks, but since there are many different types of neural networks of differing complexity (convolutional, hebbian, kohonen maps, etc.), I'll go over a simple Feed-forward neural network again, just to make sure we're on the same page.
A basic neural network consists of the following things
Neurons
Input Neuron(s)
Hidden Neurons (optional)
Output Neuron(s)
Links between Neurons (sometimes called synapses in analogy to biology)
An activation function
The Neurons have an activation value. When you evaluate a network, the input nodes' activation is set to the actual input. The links from the input nodes lead to nodes closer to the output, usually to one or more layers of hidden nodes. At each neuron, the input activation is processed using an activation function. Different activation functions can be used, and sometimes they even vary within the neurons of a single network.
The activation function processes the activation of the neuron into it's output. The early experiments usually used a simple threshold function (i.e. activation > 0.5 ? 1 : 0), nowadays a Sigmoid function is often used.
The output of the activation function is then propagated over the links to the next nodes. Each link has an associated weight it applies to its input.
Finally, the output of the network is extracted from the activation of the output neuron(s).
I've put together a very simple (and very verbose...) example here. It's written in Ruby and computes AND, which is about as simple as it gets.
A much trickier question is how to actually create a network that does something useful. The trivial network of the example was created manually, but that is infeasible with more complex problems. There are two approaches I am aware of, with the most common being backpropagation. Less used is neuroevolution, where the weights of the links are determined using a genetic algorithm.
AI-Junkie has a great tutorial on (A)NNs and they have the code posted there.
Here is a neuron (from ai-junkie):
struct SNeuron
{
//the number of inputs into the neuron
int m_NumInputs;
//the weights for each input
vector<double> m_vecWeight;
//ctor
SNeuron(int NumInputs);
};
Here is a neuron layer (ai-junkie):
struct SNeuronLayer
{
//the number of neurons in this layer
int m_NumNeurons;
//the layer of neurons
vector<SNeuron> m_vecNeurons;
SNeuronLayer(int NumNeurons, int NumInputsPerNeuron);
};
Like I mentioned before... you can find all of the code with the ai-junkie (A)NN tutorial.
This is the NUPIC programmer's guide. NuPIC is the framework to implement their theory (HTM) based on the structure and operation of the neocortex
This is how they define HTM
HTM technology has the potential to solve many difficult problems in machine learning, inference, and prediction. Some of the application areas we are exploring with our customers include recognizing objects in images, recognizing behaviors in videos, identifying the gender of a speaker, predicting traffic patterns, doing optical character recognition on messy text, evaluating medical images, and predicting click through patterns on the web.
this is a simple net with nument 1.5
from nupic.network import *
from nupic.network.simpledatainterface import WideDataInterface
def TheNet():
net=SimpleHTM(
levelParams=[
{ # Level 0
},
{ # Level 1
'levelSize': 8, 'bottomUpOut': 8,
'spatialPoolerAlgorithm': 'gaussian',
'sigma': 0.4, 'maxDistance': 0.05,
'symmetricTime': True, 'transitionMemory': 1,
'topNeighbors': 2, 'maxGroupSize': 1024,
'temporalPoolerAlgorithm': 'sumProp'
},
{ # Level 2
'levelSize': 4, 'bottomUpOut': 4,
'spatialPoolerAlgorithm': 'product',
'symmetricTime': True, 'transitionMemory': 1,
'topNeighbors': 2, 'maxGroupSize': 1024,
'temporalPoolerAlgorithm': 'sumProp'
},
{ # Level 3
'levelSize': 1,
'spatialPoolerAlgorithm': 'product',
'mapperAlgorithm': 'sumProp'
},],)
Data=WideDataInterface('Datos/__Categorias__.txt', 'Datos/Datos_Entrenamiento%d.txt', numDataFiles = 8)#
net.createNetwork(Data)
net.train(Datos)
if __name__ == '__main__':
print "Creating HTM Net..."
TheNet()