Suppose we have a standard autoencoder with three layers (i.e. L1 is the input layer, L3 the output layer with #input = #output = 100 and L2 is the hidden layer (50 units)). I know the interesting part of an autoencoder is the hidden part L2. Instead of passing 100 inputs to my supervised model, it will feed it with 50 inputs. What is the optimal hidden units size? 50 is well, but why not using 51, 52 or 63 hidden units? Does 51 will perform better the supervised model than 50 hidden units?
Suppose now that the number of inputs is 1,000,000. If N is the number of units, then I don't want to test out each possible value for N to find out the optimal N. I thought there exists at least an algorithm to do not be obligated to test each possible value or eliminate some of them.
Could that question help?
There is no rule for it. number of Hidden layer selection is purely based on hit and trial.
Related
The problem I'm trying to solve is about the best allocation for electric vehicles (EVs) in the electrical power grid. My grid has 20 possible positions (busbar) allowed to receive one EV each. Each chromosome has length 20 and its genes can be 0 or 1, where 0 means no EV and 1 means there´s an EV at that position (busbar).
I start my population (100 individuals) with a fixed number of EVs (5, for instance) allocated randomly. And let them evolve through my GA. The GA utilizes tournament selection, 2-points crossover and flip-bit mutation. Each chromosome/individual is evaluated through a fitness function that calculate the power losses between bars (sum of RI^2). The best chromosome is the one with the lowest power losses.
The problem is that utilizing 2-points crossover and flip-bit mutation changes the fixed number of EVs that must be in the grid. I would like to know what are the best techniques for my GA operations. Besides this, I get this weird looking graphic of the most fitness chromosome throughout generations 1
I would appreciate any help/suggestions. Thanks.
You want to define your state space in such a way where the mutations you've chosen can't create an illegal configuration.
This is probably not a great fit for a genetic algorithm. If you want to pick 5 from 20, there are ~15k possibilities. Testing a population of 100 over 50 generations already gives you enough computations to have done 1/3 of the brute force work.
If you have N EV to assign on your grid, you can use chromosomes of size N, each gene being an integer representing the position of an EV. For the crossover, you first need to separate the values that are the same in both parents from the rest and apply a classic (1 or 2 points) crossover on the parts that differ, and mutate a gene randomly picking a valid available position.
so by google translating i figured out
Вход means input
Слой means layer.
Свертка means convolution (this
must be the number of filters?)
Шаг means step (this must be stride?)
субдискр means subdiskr (i guess this is pooling?)
Now my question is how would a
size 22x256 image result in 6x256 with a 5 filters?
The filter size (kernel) that i found out results in 6x256 is [17,1] with 1 filter. From layer 1 to layer a kernel size of [1,8] and stride [1,8] is what i found to work. This just does not look like anything on this graph though.
In the paper they wrote this about the layer between 1 and 2
"The second layer allows to reduce the dimensionality of the signal in time, producing a weighted average of the signal over 16 values"
Heres a clear explanation how the sizes of the inputs vary with proceeding among the layers.
In the input the dimensions that you are giving are 28 wide and 28 height and depth as 1. For filters in layer1 the depth dimension of filter must be equal to the depth of the input. so the dimension of the filter will be 5x5x1, applying one filter the dimension is reduced (due to strides)to produce 14x14x1 dimension activation map, so applying 32 such filters will give you 32 activations maps. Combining all of these 14x14x32 is output of the layer 1 and input to your second layer. Again in second layer you need to apply a filter of dimension 5(width)x5(height)x32(depth) on the layer to produce one activation map of 14x14x1 , stacking all the 64 activation maps give you output dimension of the second layer as 14x14x64 and so on.
In the figure that you posted looks very different in representation. Check the standard ones in your language.
I asked the authors:
They told me that they used 1 dimensional CNN.
This Means that the first number is the depth and the second number is the Width:
depth # width.
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 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