I want to implement some kind of improvement of DBSCAN algorithm, where user do not need to enter input parameters (minPts and Eps). My idea is to use the K-distances plot, but what is the best method to compute the 'knee' of this plot? How to count when there are 2 or more knees on the plot?
Where I can find the source code for some DBSCAN improvement, like AUTODBSCAN, VDBSCAN, PDBSCAN or DBSCAN-DLP? Im looking for some basics, but nowhere I can find a good help. Maybe you've seen somewhere sample source codes?
DBSCAN has already been improved to death.
In Google Scholar, it has 5361 citations, and probably 1000+ of these "improve" DBSCAN. And probably a dozen of these use the k-distance plot. But none of these are used in practise.
If you want to continue this line of research, best get updated on what has been done since.
In particular, have a look at OPTICS which does away with the Epsilon parameter completely (except for performance reasons when using indexes).
Also have a look at HDBSCAN* by one of the original DBSCAN authors, Joerg Sander. That will likely be the most important DBSCAN extension besides his work on OPTICS and GDBSCAN.
Related
I recently started learning neural networks, and I thought that creating a sudoku solver would be a nice application for NN. I started learning them with backward propagation neural network, but later I figured that there are tens of neural networks. At this point, I find it hard to learn all of them and then pick an appropriate one for my purpose. Hence, I am asking what would be a good choice for creating this solver. Can back propagation NN work here? If not, can you explain why and tell me which one can work.
Thanks!
Neural networks don't really seem to be the best way to solve sudoku, as others have already pointed out. I think a better (but also not really good/efficient) way would be to use an genetic algorithm. Genetic algorithms don't directly relate to NNs but its very useful to know how they work.
Better (with better i mean more likely to be sussessful and probably better for you to learn something new) ideas would include:
If you use a library:
Play around with the networks, try to train them to different datasets, maybe random numbers and see what you get and how you have to tune the parameters to get better results.
Try to write an image generator. I wrote a few of them and they are stil my favourite projects, with one of them i used backprop to teach a NN what x/y coordinate of the image has which color, and the other aproach combines random generated images with ine another (GAN/NEAT).
Try to use create a movie (series of images) of the network learning to create a picture. It will show you very well how backprop works and what parameter tuning does to the results and how it changes how the network gets to the result.
If you are not using a library:
Try to solve easy problems, one after the other. Use backprop or a genetic algorithm for training (whatever you have implemented).
Try to improove your implementation and change some things that nobody else cares about and see how it changes the results.
List of 'tasks' for your Network:
XOR (basically the hello world of NN)
Pole balancing problem
Simple games like pong
More complex games like flappy bird, agar.io etc.
Choose more problems that you find interesting, maybe you are into image recognition, maybe text, audio, who knows. Think of something you can/would like to be able to do and find a way to make you computer do it for you.
It's not advisable to only use your own NN implemetation, since it will probably not work properly the first few times and you'll get frustratet. Experiment with librarys and your own implementation.
Good way to find almost endless resources:
Use google search and add 'filetype:pdf' in the end in order to only show pdf files. Search for neural network, genetic algorithm, evolutional neural network.
Neither neural nets not GAs are close to ideal solutions for Sudoku. I would advise to look into Constraint Programming (eg. the Choco or Gecode solver). See https://gist.github.com/marioosh/9188179 for example. Should solve any 9x9 sudoku in a matter of milliseconds (the daily Sudokus of "Le monde" journal are created using this type of technology BTW).
There is also a famous "Dancing links" algorithm for this problem by Knuth that works very well https://en.wikipedia.org/wiki/Dancing_Links
Just like was mentioned in the comments, you probably want to take a look at convolutional networks. You basically input the sudoku bord as an two dimensional 'image'. I think using a receptive field of 3x3 would be quite interesting, and I don't really think you need more than one filter.
The harder thing is normalization: the numbers 1-9 don't have an underlying relation in sudoku, you could easily replace them by A-I for example. So they are categories, not numbers. However, one-hot encoding every output would mean a lot of inputs, so i'd stick to numerical normalization (1=0.1, 2 = 0.2, etc.)
The output of your network should be a softmax with of some kind: if you don't use softmax, and instead outupt just an x and y coordinate, then you can't assure that the outputedd square has not been filled in yet.
A numerical value should be passed along with the output, to show what number the network wants to fill in.
As PLEXATIC mentionned, neural-nets aren't really well suited for these kind of task. Genetic algorithm sounds good indeed.
However, if you still want to stick with neural-nets you could have a look at https://github.com/Kyubyong/sudoku. As answered Thomas W, 3x3 looks nice.
If you don't want to deal with CNN, you could find some answers here as well. https://www.kaggle.com/dithyrambe/neural-nets-as-sudoku-solvers
I've been looking around scipy and sklearn for clustering algorithms for a particular problem I have. I need some way of characterizing a population of N particles into k groups, where k is not necessarily know, and in addition to this, no a priori linking lengths are known (similar to this question).
I've tried kmeans, which works well if you know how many clusters you want. I've tried dbscan, which does poorly unless you tell it a characteristic length scale on which to stop looking (or start looking) for clusters. The problem is, I have potentially thousands of these clusters of particles, and I cannot spend the time to tell kmeans/dbscan algorithms what they should go off of.
Here is an example of what dbscan find:
You can see that there really are two separate populations here, though adjusting the epsilon factor (the max. distance between neighboring clusters parameter), I simply cannot get it to see those two populations of particles.
Is there any other algorithms which would work here? I'm looking for minimal information upfront - in other words, I'd like the algorithm to be able to make "smart" decisions about what could constitute a separate cluster.
I've found one that requires NO a priori information/guesses and does very well for what I'm asking it to do. It's called Mean Shift and is located in SciKit-Learn. It's also relatively quick (compared to other algorithms like Affinity Propagation).
Here's an example of what it gives:
I also want to point out that in the documentation is states that it may not scale well.
When using DBSCAN it can be helpful to scale/normalize data or
distances beforehand, so that estimation of epsilon will be relative.
There is a implementation of DBSCAN - I think its the one
Anony-Mousse somewhere denoted as 'floating around' - , which comes
with a epsilon estimator function. It works, as long as its not fed
with large datasets.
There are several incomplete versions of OPTICS at github. Maybe
you can find one to adapt it for your purpose. Still
trying to figure out myself, which effect minPts has, using one and
the same extraction method.
You can try a minimum spanning tree (zahn algorithm) and then remove the longest edge similar to alpha shapes. I used it with a delaunay triangulation and a concave hull:http://www.phpdevpad.de/geofence. You can also try a hierarchical cluster for example clusterfck.
Your plot indicates that you chose the minPts parameter way too small.
Have a look at OPTICS, which does no longer need the epsilon parameter of DBSCAN.
I'm having issue with using OPTICS implementation in ELKI environment. I have used the same data for DBSCAN implementation and it worked like a charm. Probably I'm missing something with parameters but I can't figure it out, everything seems to be right.
Data is a simple 300х2 matrix, consists of 3 clusters with 100 points in each.
DBSCAN result:
Clustering result of DBSCAN
MinPts = 10, Eps = 1
OPTICS result:
Clustering result of OPTICS
MinPts = 10
You apparently already found the solution yourself, but here is the long story:
The OPTICS class in ELKI only computes the cluster order / reachability diagram.
In order to extract clusters, you have different choices, one of which (the one from the original OPTICS publication) is available in ELKI.
So in order to extract clusters in ELKI, you need to use the OPTICSXi algorithm, which will in turn use either OPTICS or the index based DeLiClu to compute the cluster order.
The reason why this is split into two parts in ELKI probably is so that you can on one hand implement another logic for extracting the clusters, and on the other hand implement different methods like DeLiClu for computing the cluster order. That would align well with the modular architecture of ELKI.
IIRC there is at least one more method (apparently not yet in ELKI) that extracts clusters by looking for local maxima, then extending them horizontally until they hit the end of the valley. And there was a different one that used "inflexion points" of the plot.
#AnonyMousse pretty much put it right. I just can't upvote or comment yet.
We hope to have some students contribute the other cluster extraction methods as small student projects over time. They are not essential for our research, but they are good tasks for students that want to learn about ELKI to get started.
ELKI is a fast moving project, and it lives from community contributions. We would be happy to see you contribute some code to it. We know that the codebase is not easy to get started with - it is fairly large, and the generality of the implementation and the support for index structures make it a bit hard to get started. We try to add Tutorials to help you to get started. And once you are used to it, you will actually benefit from the architecture: your algorithms get the benfits of indexing and arbitrary distance functions, while if you would implement from scratch, you would likely only support Euclidean distance, and no index acceleration.
Seeing that you struggled with OPTICS, I will try to write an OPTICS tutorial in the new year. In particular, OPTICS can benefit a lot from using an appropriate index structure.
I find genetic algorithm simulations like this to be incredibly entrancing and I think it'd be fun to make my own. But the problem with most simulations like this is that they're usually just hill climbing to a predictable ideal result that could have been crafted with human guidance pretty easily. An interesting simulation would have countless different solutions that would be significantly different from each other and surprising to the human observing them.
So how would I go about trying to create something like that? Is it even reasonable to expect to achieve what I'm describing? Are there any "standard" simulations (in the sense that the game of life is sort of standardized) that I could draw inspiration from?
Depends on what you mean by interesting. That's a pretty subjective term. I once programmed a graph analyzer for fun. The program would first let you plot any f(x) of your choice and set the bounds. The second step was creating a tree holding the most common binary operators (+-*/) in a random generated function of x. The program would create a pool of such random functions, test how well they fit to the original curve in question, then crossbreed and mutate some of the functions in the pool.
The results were quite cool. A totally weird function would often be a pretty good approximation to the query function. Perhaps not the most useful program, but fun nonetheless.
Well, for starters that genetic algorithm is not doing hill-climbing, otherwise it would get stuck at the first local maxima/minima.
Also, how can you say it doesn't produce surprising results? Look at this vehicle here for example produced around generation 7 for one of the runs I tried. It's a very old model of a bicycle. How can you say that's not a surprising result when it took humans millennia to come up with the same model?
To get interesting emergent behavior (that is unpredictable yet useful) it is probably necessary to give the genetic algorithm an interesting task to learn and not just a simple optimisation problem.
For instance, the Car Builder that you referred to (although quite nice in itself) is just using a fixed road as the fitness function. This makes it easy for the genetic algorithm to find an optimal solution, however if the road would change slightly, that optimal solution may not work anymore because the fitness of a solution may have grown dependent on trivially small details in the landscape and not be robust to changes to it. In real, cars did not evolve on one fixed test road either but on many different roads and terrains. Using an ever changing road as the (dynamic) fitness function, generated by random factors but within certain realistic boundaries for slopes etc. would be a more realistic and useful fitness function.
I think EvoLisa is a GA that produces interesting results. In one sense, the output is predictable, as you are trying to match a known image. On the other hand, the details of the output are pretty cool.
I'm quite new with this topic so any help would be great. What I need is to optimize a neural network in MATLAB by using GA. My network has [2x98] input and [1x98] target, I've tried consulting MATLAB help but I'm still kind of clueless about what to do :( so, any help would be appreciated. Thanks in advance.
Edit: I guess I didn't say what is there to be optimized as Dan said in the 1st answer. I guess most important thing is number of hidden neurons. And maybe number of hidden layers and training parameters like number of epochs or so. Sorry for not providing enough info, I'm still learning about this.
If this is a homework assignment, do whatever you were taught in class.
Otherwise, ditch the MLP entirely. Support vector regression ( http://www.csie.ntu.edu.tw/~cjlin/libsvm/ ) is much more reliably trainable across a broad swath of problems, and pretty much never runs into the stuck-in-a-local-minima problem often hit with back-propagation trained MLP which forces you to solve a network topography optimization problem just to find a network which will actually train.
well, you need to be more specific about what you are trying to optimize. Is it the size of the hidden layer? Do you have a hidden layer? Is it parameter optimization (learning rate, kernel parameters)?
I assume you have a set of parameters (# of hidden layers, # of neurons per layer...) that needs to be tuned, instead of brute-force searching all combinations to pick a good one, GA can help you "jump" from this combination to another one. So, you can "explore" the search space for potential candidates.
GA can help in selecting "helpful" features. Some features might appear redundant and you want to prune them. However, say, data has too many features to search for the best set of features by some approaches such as forward selection. Again, GA can "jump" from this set candidate to another one.
You will need to find away to encode the data (input parameters, features...) fed to GA. For finding a set of input paras or a good set of features, I think binary encoding should work. In addition, choosing operators for GA to reproduce offsprings is also important. Yet GA needs to be tuned, too (early stopping which can also be applied to ANN).
Here are just some ideas. You might want to search for more info about GA, feature selection, ANN pruning...
Since you're using MATLAB already I suggest you look into the Genetic Algorithms solver (known as GATool, part of the Global Optimization Toolbox) and the Neural Network Toolbox. Between those two you should be able to save quite a bit of figuring out.
You'll basically have to do 2 main tasks:
Come up with a representation (or encoding) for your candidate solutions
Code your fitness function (which basically tests candidate solutions) and pass it as a parameter to the GA solver.
If you need help in terms of coming up with a fitness function, or encoding of candidate solutions then you'll have to be more specific.
Hope it helps.
Matlab has a simple but great explanation for this problem here. It explains both the ANN and GA part.
For more info on using ANN in command line see this.
There is also plenty of litterature on the subject if you google it. It is however not related to MATLAB, but simply the results and the method.
Look up Matthew Settles on Google Scholar. He did some work in this area at the University of Idaho in the last 5-6 years. He should have citations relevant to your work.