I used the Network Analyzer core app to get the basic parameters of an undirected network on Cytoscape. All the parameters are satisfactorily measured like the degrees, centrality measures of each node, diameter of the network etc. However, the clustering co-efficient of each node is given as 0.0 and the overall clustering co-efficent of the network is calculated as 0.0. I am next going to compare my network with a random network and network co-efficient is a key measure that I would like to compare in order to prove that my network is a scale free network. What could be going wrong. There are 361 nodes and 695 edges in my network. Any ideas are appreciated
Already answered on cytoscape-helpdesk, but for completeness, I've repeated it here....
Hi Rahul,
1) So, with 361 nodes and 695 edges, the average degree of your network is 2. that could certainly lead to a cluster coefficient of 0.0 since that measure depends on the extent to which a node's neighbors are connected. Look for nodes that have well connected neighbors and take a look at the clustering coefficient of those nodes.
2) First, understand that comparing your network with a single random network will not yield a p value (or if it does, it's honestly worthless). You need to generate a distribution of random networks, then compare your network to the distribution to see if you are outside of the distribution. Take a looks at Tosadori, et al., 2016 for their discussion on the use of Network Randomizer with cytoscape.
-- scooter
Related
After reading a few papers on Neuro Evolution, more specifically NEAT, I realised that there was very little information regarding how you should weight each synapse at the start of the Neural Network. I understand that at the start, using NEAT, all the input neurons are connected to the output neuron, and then evolution takes place from there. However, should you weight each synapse randomly at the start, or simply set each one to 1?
It doesn't really matter a lot - it matters most how you mutate the weights of the connections in a genome.
However, setting the weights of each genome's connections to a random value is best: it acts like a small random search in the 'right' direction. If you'd set all the weights the same in for each genome, then weights in genomes will be extremely similar: keep in mind that a genome has a lot of connections, and with a mutation rate of 0.3 and two mutation options for example, only 15% of the population will have at least óne different weight after just 1 generation.
So make it something random, like random() * .2 - .1 (distribute between [-0.1, 0.1]). Just figure out what values work best for you.
I'm trying to navigate an agent in a n*n gridworld domain by using Q-Learning + a feedforward neural network as a q-function approximator. Basically the agent should find the best/shortest way to reach a certain terminal goal position (+10 reward). Every step the agent takes it gets -1 reward. In the gridworld there are also some positions the agent should avoid (-10 reward, terminal states,too).
So far I implemented a Q-learning algorithm, that saves all Q-values in a Q-table and the agent performs well.
In the next step, I want to replace the Q-table by a neural network, trained online after every step of the agent. I tried a feedforward NN with one hidden layer and four outputs, representing the Q-values for the possible actions in the gridworld (north,south,east, west).
As input I used a nxn zero-matrix, that has a "1" at the current positions of the agent.
To reach my goal I tried to solve the problem from the ground up:
Explore the gridworld with standard Q-Learning and use the Q-map as training data for the Network once Q-Learning is finished
--> worked fine
Use Q-Learning and provide the updates of the Q-map as trainingdata
for NN (batchSize = 1)
--> worked good
Replacy the Q-Map completely by the NN. (This is the point, when it gets interesting!)
-> FIRST MAP: 4 x 4
As described above, I have 16 "discrete" Inputs, 4 Output and it works fine with 8 neurons(relu) in the hidden layer (learning rate: 0.05). I used a greedy policy with an epsilon, that reduces from 1 to 0.1 within 60 episodes.
The test scenario is shown here. Performance is compared beetween standard qlearning with q-map and "neural" qlearning (in this case i used 8 neurons and differnt dropOut rates).
To sum it up: Neural Q-learning works good for small grids, also the performance is okay and reliable.
-> Bigger MAP: 10 x 10
Now I tried to use the neural network for bigger maps.
At first I tried this simple case.
In my case the neural net looks as following: 100 input; 4 Outputs; about 30 neurons(relu) in one hidden layer; again I used a decreasing exploring factor for greedy policy; over 200 episodes the learning rate decreases from 0.1 to 0.015 to increase stability.
At frist I had problems with convergence and interpolation between single positions caused by the discrete input vector.
To solve this I added some neighbour positions to the vector with values depending on thier distance to the current position. This improved the learning a lot and the policy got better. Performance with 24 neurons is seen in the picture above.
Summary: the simple case is solved by the network, but only with a lot of parameter tuning (number of neurons, exploration factor, learning rate) and special input transformation.
Now here are my questions/problems I still haven't solved:
(1) My network is able to solve really simple cases and examples in a 10 x 10 map, but it fails as the problem gets a bit more complex. In cases where failing is very likely, the network has no change to find a correct policy.
I'm open minded for any idea that could improve performace in this cases.
(2) Is there a smarter way to transform the input vector for the network? I'm sure that adding the neighboring positons to the input vector on the one hand improve the interpolation of the q-values over the map, but on the other hand makes it harder to train special/important postions to the network. I already tried standard cartesian two-dimensional input (x/y) on an early stage, but failed.
(3) Is there another network type than feedforward network with backpropagation, that generally produces better results with q-function approximation? Have you seen projects, where a FF-nn performs well with bigger maps?
It's known that Q-Learning + a feedforward neural network as a q-function approximator can fail even in simple problems [Boyan & Moore, 1995].
Rich Sutton has a question in the FAQ of his web site related with this.
A possible explanation is the phenomenok known as interference described in [Barreto & Anderson, 2008]:
Interference happens when the update of one state–action pair changes the Q-values of other pairs, possibly in the wrong direction.
Interference is naturally associated with generalization, and also happens in conventional supervised learning. Nevertheless, in the reinforcement learning paradigm its effects tend to be much more harmful. The reason for this is twofold. First, the combination of interference and bootstrapping can easily become unstable, since the updates are no longer strictly local. The convergence proofs for the algorithms derived from (4) and (5) are based on the fact that these operators are contraction mappings, that is, their successive application results in a sequence converging to a fixed point which is the solution for the Bellman equation [14,36]. When using approximators, however, this asymptotic convergence is lost, [...]
Another source of instability is a consequence of the fact that in on-line reinforcement learning the distribution of the incoming data depends on the current policy. Depending on the dynamics of the system, the agent can remain for some time in a region of the state space which is not representative of the entire domain. In this situation, the learning algorithm may allocate excessive resources of the function approximator to represent that region, possibly “forgetting” the previous stored information.
One way to alleviate the interference problem is to use a local function approximator. The more independent each basis function is from each other, the less severe this problem is (in the limit, one has one basis function for each state, which corresponds to the lookup-table case) [86]. A class of local functions that have been widely used for approximation is the radial basis functions (RBFs) [52].
So, in your kind of problem (n*n gridworld), an RBF neural network should produce better results.
References
Boyan, J. A. & Moore, A. W. (1995) Generalization in reinforcement learning: Safely approximating the value function. NIPS-7. San Mateo, CA: Morgan Kaufmann.
André da Motta Salles Barreto & Charles W. Anderson (2008) Restricted gradient-descent algorithm for value-function approximation in reinforcement learning, Artificial Intelligence 172 (2008) 454–482
I have a simple competitive neural network algorithm which I am trying to enhance by penalizing the 'rival', ie: The output neuron with the second-largest output. My code to do so is this:
% Penalizing rival
network_output(I) = [];
[~, I] = max(network_output);
delta = (1/current_run^3)*(sample'-connections(:,I));
connections(:,I) = normc(connections(:,I) - delta);
Essentially, I removed the winner (neuron at index I) from the outputs, I then find the new winner (overall second), and I updated the connections by reducing the strength of those leading to such neuron using the standard rule. I also apply a decay in terms of current_run^3 where current_run is the iteratio numebr. I also normalize all weights before re-inserting them in the connection matrix.
However, by comparing the number of dead units to the network running without this refinement, I find that the latter performs better.
Any advice?
http://en.m.wikipedia.org/wiki/Competitive_learning
I just read that article and there it says
3. The winner updates each of its weights, moving weight from the connections that gave it weaker signals to the connections that gave it stronger signals.
Also there I didn't find that you need to remove winner.
So, I not sure that you need to remove winner. Maybe that's why network with winner works better?
Sometime it is good idea to remove nodes from neural network during optimization, but after each removal network need too be retrained.
I have created a neural network with 2 inputs nodes, 4 hidden nodes and 3 output nodes. The initial weights are random between -1 to 1. I used backpropagation method to update the network with TD error. However, the performance is not good.
I want to know, where the problem might be?
1. Is a bias node necessary?
2. Are eligibility traces necessary?
If anyone can provide me any sample code, I'm very grateful.
Yes, you should include the bias nodes, and yes you should use eligibility traces. The bias nodes just give one additional tunable parameter. Think of the neural network as a "function approximator" as described in Sutton and Barto's book (free online). If the neural network has parameters theta (a vector containing all of the weights in the network), then the Sarsa update is just (using LaTeX notation):
\delta_t = r_t + \gamma*Q(s_{t+1},a_{t+1},\theta_t) - Q(s_t,a_t, \theta_t)
\theta_{t+1} = \theta_t + \alpha*\delta_t*\frac{\partial Q(s,a,\theta)}{\partial \theta}
This is for any function approximator Q(s,a,\theta), which estimates Q(s,a) by tuning its parameters, \theta.
However, I must ask why you're doing this. If you're just trying to get Q learning working really well, then you should use the Fourier Basis instead of a neural network:
http://all.cs.umass.edu/pubs/2011/konidaris_o_t_11.pdf
If you really want to use a neural network for RL, then you should use a natural actor-critic (NAC). NACs follow something called the "natural gradient," which was developed by Amari specifically to speed up learning using neural networks, and it makes a huge difference.
We need more information. What is the problem domain. What are the inputs? What are the outputs?
RL can take a very long time to train and, depending on how you're training, can go from good to great to good to not-so-good during training. Therefore, you should plot the performance of your agent during learning, not just the end result.
You always should use bias nodes. Eligibility traces? Probably not.
I'm trying to cluster some images depending on the angles between body parts.
The features extracted from each image are:
angle1 : torso - torso
angle2 : torso - upper left arm
..
angle10: torso - lower right foot
Therefore the input data is a matrix of size 1057x10, where 1057 stands for the number of images, and 10 stands for angles of body parts with torso.
Similarly a testSet is 821x10 matrix.
I want all the rows in input data to be clustered with 88 clusters.
Then I will use these clusters to find which clusters does TestData fall into?
In a previous work, I used K-Means clustering which is very straightforward. We just ask K-Means to cluster the data into 88 clusters. And implement another method that calculates the distance between each row in test data and the centers of each cluster, then pick the smallest values. This is the cluster of the corresponding input data row.
I have two questions:
Is it possible to do this using SOM in MATLAB?
AFAIK SOM's are for visual clustering. But I need to know the actual class of each cluster so that I can later label my test data by calculating which cluster it belongs to.
Do you have a better solution?
Self-Organizing Map (SOM) is a clustering method considered as an unsupervised variation of the Artificial Neural Network (ANN). It uses competitive learning techniques to train the network (nodes compete among themselves to display the strongest activation to a given data)
You can think of SOM as if it consists of a grid of interconnected nodes (square shape, hexagonal, ..), where each node is an N-dim vector of weights (same dimension size as the data points we want to cluster).
The idea is simple; given a vector as input to SOM, we find the node closet to it, then update its weights and the weights of the neighboring nodes so that they approach that of the input vector (hence the name self-organizing). This process is repeated for all input data.
The clusters formed are implicitly defined by how the nodes organize themselves and form a group of nodes with similar weights. They can be easily seen visually.
SOM are in a way similar to the K-Means algorithm but different in that we don't impose a fixed number of clusters, instead we specify the number and shape of nodes in the grid that we want it to adapt to our data.
Basically when you have a trained SOM, and you want to classify a new test input vector, you simply assign it to the nearest (distance as a similarity measure) node on the grid (Best Matching Unit BMU), and give as prediction the [majority] class of the vectors belonging to that BMU node.
For MATLAB, you can find a number of toolboxes that implement SOM:
The Neural Network Toolbox from MathWorks can be used for clustering using SOM (see the nctool clustering tool).
Also worth checking out is the SOM Toolbox