I have n words and their relatedness weight that gives me a n*n matrix. I'm going to use this for a search algorithm but the problem is I need to cluster the entered keywords based on their pairwise relation. So let's say if the keywords are {tennis,federer,wimbledon,london,police} and we have the following data from our weight matrix:
tennis federer wimbledon london police
tennis 1 0.8 0.6 0.4 0.0
federer 0.8 1 0.65 0.4 0.02
wimbledon 0.6 0.65 1 0.08 0.09
london 0.4 0.4 0.08 1 0.71
police 0.0 0.02 0.09 0.71 1
I need an algorithm to to cluster them into 2 clusters : {tennis,federer,wimbledon} {london,police}. Is there any know clustering algorithm than can deal with such thing ? I did some research, it appears that K-means algorithm is the most well known algorithm being used for clustering but apparently K-means doesn't suit this case.
I would greatly appreciate any help.
You can treat it as a network clustering problem. With a recent version of mcl software (http://micans.org/mcl), you can do this (I've called your example fe.data).
mcxarray -data fe.data -skipr 1 -skipc 1 -write-tab fe.tab -write-data fe.mci -co 0 -tf 'gq(0)' -o fe.cor
# the above computes correlations (put in data file fe.cor) and a network (put in data file fe.mci).
# below proceeds with the network.
mcl fe.mci -I 3 -o - -use-tab fe.tab
# this outputs the clustering you expect. -I is the 'inflation parameter'. The latter affects
# cluster granularity. With the default parameter 2, everything ends up in a single cluster.
Disclaimer: I wrote mcl and a slew of associated network loading/conversion and analysis programs recently rebranded as 'mcl-edge'. They all come together in a single software package. Seeing your example made me curious whether it would be doable with mcl-edge, so I quickly tested it.
Consider DBSCAN. If it suits your needs, you might wish to take a closer look at an optimised version, TI-DBSCAN, which uses triangle inequality for reducing spatial query cost.
DBSCAN's advantages and disadvantages are discussed on Wikipedia. It splits input data to a set of clusters whose cardinality isn't known a priori. You'd have to transform your similarity matrix into a distance matrix, for example by taking 1 - similarity as a distance.
Check this book on Information retrieval
http://nlp.stanford.edu/IR-book/html/htmledition/hierarchical-agglomerative-clustering-1.html
it explains very well what you want to do
Your weights are higher for more similar words and lower for more different words. A clustering algorithm requires similar points/words to be closer spatially and different words to be distant. You should change the matrix M into 1-M and then use any clustering method you want, including k-means.
If you've got a distance matrix, it seems a shame not to try http://en.wikipedia.org/wiki/Single_linkage_clustering. By hand, I think you get the following clustering:
((federer, tennis), wimbledon) (london, police)
The similarity for the link that joins the two main groups (either tennis-london or federer-london) is smaller than any of the similarities that build the two groups: london-police, tennis-federer, and federer-wimbledon: this characteristic is guaranteed by single linkage clustering, since it binds together closest clusters at each stage, and the two main groups are linked by the last binding found.
DBSCAN (see other answers) and successors such as OPTICS are clearly an option.
While the examples are on vector data, all that the algorithms need is a distance function. If you have a similarity matrix, that can trivially be used as distance function.
The example data set probably is a bit too small for them to produce meaningful results. If you just have this little of data, any "hierarchical clustering" should be feasible and do the job for you. You then just need to decide on the best number of clusters.
Related
I am trying to use one-class SVM with Python scikit-learn.
But I do not understand what are the different variables X_outliers, n_error_train, n_error_test, n_error_outliers, etc. which are at this address. Why does X is randomly selected and is not a part of a dataset?
Scikit-learn "documentation" did not help me a lot. Also, I found very few examples on Internet
Can I use One-class SVM for outlier detection in a case of a hudge number of data and if I do not know if there are anomalies in my training set?
One-class SVM is an Unsupervised Outlier Detection (here)
One-class SVM is not an outlier-detection method, but a
novelty-detection method (here)
Is this possible?
Ok, so this is not really a Python question, more of a SVM comprehension question, but eh. A typical SVM is two-classed, and is an algorithm which is going to have two phases :
First, it will learn relationships between variables and attributes. For example, you show your algorithm tomato pictures and banana pictures, telling him each time if it's a banana or a tomato, and you tell him to count the number of red pixels in each picture. If you do it correctly, the SVM will be trained, meaning he will know that pictures with lots of red pixels are more likely to be tomatoes than bananas.
Then comes the predicting phase. You show him a picture of a tomato or a banana without telling him which it is. And since he has been trained before, he will count the red pixels, and know which it is.
In your case of a one-class SVM, it's a bit simpler, basically the training phase is showing him a bunch of variables which are all supposed to be similar. You show him a bunch of tomato pictures telling him "these are tomatoes, everything else too different from these are not tomatoes".
The code you link to is a code to test the SVM's capability of learning. You start by creating variables X_train. Then you generate two other sets, X_test which is similar to X_train (tomato pictures) and X_outliers which is very different. (banana pictures)
Then you show him the X_train variables and tell your SVM "this is the kind of variables we're looking for" with the line clf.fit(X_train). This is equivalent in my example to showing him lots of tomato images, and the SVN learning what a "tomato" is.
And then you test your SVM's capability to sort new variables, by showing him your two other sets (X_test and X_outliers), and asking him whether he thinks they are similar to X_train or not. You ask him that with the predict fuction, and predict will yield for every element in the sets either "1" i.e. "yes this is a similar element to X_train", or "-1", i.e. "this element is very different".
In an ideal case, the SVM should yield only "1" for X_test and only "-1" for X_outliers. But this code is to show you that this is not always the case. The variables n_error_ are here to count the mistakes that the SVM makes, misclassifying X_test elements as "not similar to X_train and X_outliers elements as "similar to X_train". You can see that there are even errors when the SVM is asked to predict on the very set that is has been trained on ! (n_error_train)
Why are there such errors ? Welcome to machine learning. The main difficulty of SVMs is setting the training set such that it enables the SVM to learn efficiently to distinguish between classes. So you need to set carefully the number of images you show him, (and what he has to look out for in the images (in my example, it was the number of red pixels, in the code, it is the value of the variable), but that is a different question).
In the code, the bounded but random initialization of the X sets means that for example you could during on run train the SVM on an X_train set with lots of values between -0.3 and 0 even though they are randomly initialized between -0.3 and 0.3 (espcecially if you have few elements per set, say for example 5, and you get [-0.2 -0.1 0 -0.1 0.1]). And so, when you show the SVM an element with a value of 0.2, then he will have trouble associating it to X_train, because it will have learned that X_train elements are more likely to have negative values.
This is equivalent to show your SVM a few yellow-ish tomatoes when you train him, so when you show him a really red tomato afterwards, it will have trouble clasifying it as a tomato.
This one-class SVM is a classifier to determine whether entries are similar or dissimilar to entries that the classifier has been trained with.
The script generates three sets:
A training set.
A test-set of entries that are similar to the training a set.
A test-set of entries that are dissimilar to the training set.
The error is the number of entries from each of the sets, that have been classified wrongly. That is; That have been classified as dissimilar to the training set when they were similar (for set 1 and 2), or that have been classifier as similar to the training set when they were dissimilar (set 3).
X_outliers: This is set 3.
n_error_train: The number of classification errors for the elements in the train-set (1).
n_error_test: The number of classification errors for the elements in the test-set (2).
n_error_outliers: The number of classification errors for the elements in the outlier-set (3).
This answer should be complementary to scikit-description but I agree that is a bit technical. I will elaborate some aspects of the One Class SVM algorithm (OCSVM) here. OCSVM is designed to solve the unsupervised anomaly detection problem.
Given unstructured (unlabelled) data it will find a n-dimensional space a matrix W^T with d columns (T stands for transpose).
The objective function of all SVM based methods (and OCSVM) is:
$$f(x) = sign(wT x + b)$$, where sign means sign (-1 anomalous 1 nominal) shifted by a bias term b.
In the classification problem the matrix W is associated with the distance(margin) between 2 classes but this differs in OCSVM since there is only 1 class and it maximizes from the origin (original paper of OCSVM demonstrates this ) .
As you see it is a generic algorithm because SVM is a family of models that can approximate any non linear boundary such as neural networks. To achieve something complicated you have to construct your own kernel matrix.
To do this you need to find some convenient mathematical property (suggestions to improve the answer are welcome at this point).
But in the most cases Gaussian kernel is a kernel that has some quite nice mathematical properties and associated ML theorems such as the Large
of large numbers.
The scikit implementation provides a wrapper to LIBSVM implementation for SVM and has 4 such kernels.
-nu parameter is a problem formulation parameter it allows to say to the model here is how dirty my sample is.
More formally it makes the problem a outlier detection problem where you know your data is mixed (nominal and anomalous) instead of pure where the problem is different and it is called novelty detection.
kernel parameter: One of the most important decisions. Mathematically kernel is a big matrix of numbers where by multiplying you achieve to project data in a higher dimensions. A nice read demonstrating the issue is here while the paper of Scholkopf who created OCSVMK goes into more detail.
gamma
In the case of robust kernel you essentially use a gaussian projection.
Disclaimer my interpretation: Essentially with gamma parameter you describe how big the variance of the Normal distribution $N(\mu, \sigma)$ is.
-tolerance
One class svm search the margin tha separates better among training data and the origin. The tolerance refers to the stopping criterion or how small should the tolerance for satisfaction of the quadratic optimization of the
objective function. The objective function the thing that tells SVM what the parameters should like to describe a specific margin - the space between nominal and anomalous) seen in Figure~().
Many Sklearn examples are usually based on randomly generated data. If you want to see an example of how OneClassSVM works on a real dataset for outlier detection, you can go through my post: https://justanoderbit.com/outlier-detection/one-class-svm/
I have implemented AdaBoost sequence algorithm and currently I am trying to implement so called Cascaded AdaBoost, basing on P. Viola and M. Jones original paper. Unfortunately I have some doubts, connected with adjusting the threshold for one stage. As we can read in original paper, the procedure is described in literally one sentence:
Decrease threshold for the ith classifier until the current
cascaded classifier has a detection rate of at least
d × Di − 1 (this also affects Fi)
I am not sure mainly two things:
What is the threshold? Is it 0.5 * sum (alpha) expression value or only 0.5 factor?
What should be the initial value of the threshold? (0.5?)
What does "decrease threshold" mean in details? Do I need to iterative select new threshold e.g. 0.5, 0.4, 0.3? What is the step of decreasing?
I have tried to search this info in Google, but unfortunately I could not find any useful information.
Thank you for your help.
I had the exact same doubt and have not found any authoritative source so far. However, this is what is my best guess to this issue:
1. (0.5*sum(aplha)) is the threshold.
2. Initial value of the threshold is what is above. Next, try to classify the samples using the intermediate strong classifier (what you currently have). You'll get the scores each of the samples attain, and depending on the current value of threshold, some of the positive samples will be classified as negative etc. So, depending on the desired detection rate desired for this stage (strong classifier), reduce the threshold so that that many positive samples get correctly classified ,
eg:
say thresh. was 10, and these are the current classifier outputs for positive training samples:
9.5, 10.5, 10.2, 5.4, 6.7
and I want a detection rate of 80% => 80% of above 5 samples classified correctly => 4 of above => set threshold to 6.7
Clearly, by changing the threshold, the FP rate also changes, so update that, and if the desired FP rate for the stage not reached, go for another classifier at that stage.
I have not done a formal course on ada-boost etc, but this is my observation based on some research papers I tried to implement. Please correct me if something is wrong. Thanks!
I have found a Master thesis on real-time face detection by Karim Ayachi (pdf) in which he describes the Viola Jones face detection method.
As it is written in Section 5.2 (Creating the Cascade using AdaBoost), we can set the maximal threshold of the strong classifier to sum(alpha) and the minimal threshold to 0 and then find the optimal threshold using binary search (see Table 5.1 for pseudocode).
Hope this helps!
my topic is similarity and clustering of (a bunch of) text(s). In a nutshell: I want to cluster collected texts together and they should appear in meaningful clusters at the end. To do this, my approach up to now is as follows, my problem is in the clustering. The current software is written in php.
1) Similarity:
I treat every document as a "bag-of-words" and convert words into vectors. I use
filtering (only "real" words)
tokenization (split sentences into words)
stemming (reduce words to their base form; Porter's stemmer)
pruning (cut of words with too high & low frequency)
as methods for dimensionality reduction. After that, I'm using cosine similarity (as suggested / described on various sites on the web and here.
The result then is a similarity matrix like this:
A B C D E
A 0 30 51 75 80
B X 0 21 55 70
C X X 0 25 10
D X X X 0 15
E X X X X 0
A…E are my texts and the number is the similarity in percent; the higher, the more similar the texts are. Because sim(A,B) == sim(B,A) only half of the matrix is filled in. So the similarity of Text A to Text D is 71%.
I want to generate a a priori unknown(!) number of clusters out of this matrix now. The clusters should represent the similar items (up to a certain stopp criterion) together.
I tried a basic implementation myself, which was basically like this (60% as a fixed similarity threshold)
foreach article
get similar entries where sim > 60
foreach similar entry
check if one of the entries already has a cluster number
if no: assign new cluster number to all similar entries
if yes: use that number
It worked (somehow), but wasn't good at all and the results were often monster-clusters.
So, I want to redo this and already had a look into all kinds of clustering algorithms, but I'm still not sure which one will work best. I think it should be an agglomerative algoritm, because every pair of texts can be seen as a cluster in the beginning. But still the questions are what the stopp criterion is and if the algorithm should divide and / or merge existing clusters together.
Sorry if some of the stuff seems basic, but I am relatively new in this field. Thanks for the help.
Since you're both new to the field, have an unknown number of clusters and are already using cosine distance I would recommend the FLAME clustering algorithm.
It's intuitive, easy to implement, and has implementations in a large number of languages (not PHP though, largely because very few people use PHP for data science).
Not to mention, it's actually good enough to be used in research by a large number of people. If nothing else you can get an idea of what exactly the shortcomings are in this clustering algorithm that you want to address in moving onto another one.
Just try some. There are so many clustering algorithms out there, nobody will know all of them. Plus, it also depends a lot on your data set and the clustering structure that is there.
In the end, there also may be just this one monster cluster with respect to cosine distance and BofW features.
Maybe you can transform your similarity matrix to a dissimilarity matrix such as transforming x to 1/x, then your problem is to cluster a dissimilarity matrix. I think the hierarchical cluster may work. These may help you:hierarchical clustering and Clustering a dissimilarity matrix
I'm searching for a usable metric for SURF. Like how good one image matches another on a scale let's say 0 to 1, where 0 means no similarities and 1 means the same image.
SURF provides the following data:
interest points (and their descriptors) in query image (set Q)
interest points (and their descriptors) in target image (set T)
using nearest neighbor algorithm pairs can be created from the two sets from above
I was trying something so far but nothing seemed to work too well:
metric using the size of the different sets: d = N / min(size(Q), size(T)) where N is the number of matched interest points. This gives for pretty similar images pretty low rating, e.g. 0.32 even when 70 interest points were matched from about 600 in Q and 200 in T. I think 70 is a really good result. I was thinking about using some logarithmic scaling so only really low numbers would get low results, but can't seem to find the right equation. With d = log(9*d0+1) I get a result of 0.59 which is pretty good but still, it kind of destroys the power of SURF.
metric using the distances within pairs: I did something like find the K best match and add their distances. The smallest the distance the similar the two images are. The problem with this is that I don't know what are the maximum and minimum values for an interest point descriptor element, from which the distant is calculated, thus I can only relatively find the result (from many inputs which is the best). As I said I would like to put the metric to exactly between 0 and 1. I need this to compare SURF to other image metrics.
The biggest problem with these two are that exclude the other. One does not take in account the number of matches the other the distance between matches. I'm lost.
EDIT: For the first one, an equation of log(x*10^k)/k where k is 3 or 4 gives a nice result most of the time, the min is not good, it can make the d bigger then 1 in some rare cases, without it small result are back.
You can easily create a metric that is the weighted sum of both metrics. Use machine learning techniques to learn the appropriate weights.
What you're describing is related closely to the field of Content-Based Image Retrieval which is a very rich and diverse field. Googling that will get you lots of hits. While SURF is an excellent general purpose low-mid level feature detector, it is far from sufficient. SURF and SIFT (what SURF was derived from), is great at duplicate or near-duplicate detection but is not that great at capturing perceptual similarity.
The best performing CBIR systems usually utilize an ensemble of features optimally combined via some training set. Some interesting detectors to try include GIST (fast and cheap detector best used for detecting man-made vs. natural environments) and Object Bank (a histogram-based detector itself made of 100's of object detector outputs).
I have a couple of numerical datasets that I need to create a concept hierarchy for. For now, I have been doing this manually by observing the data (and a corresponding linechart). Based on my intuition, I created some acceptable hierarchies.
This seems like a task that can be automated. Does anyone know if there is an algorithm to generate a concept hierarchy for numerical data?
To give an example, I have the following dataset:
Bangladesh 521
Brazil 8295
Burma 446
China 3259
Congo 2952
Egypt 2162
Ethiopia 333
France 46037
Germany 44729
India 1017
Indonesia 2239
Iran 4600
Italy 38996
Japan 38457
Mexico 10200
Nigeria 1401
Pakistan 1022
Philippines 1845
Russia 11807
South Africa 5685
Thailand 4116
Turkey 10479
UK 43734
US 47440
Vietnam 1042
for which I created the following hierarchy:
LOWEST ( < 1000)
LOW (1000 - 2500)
MEDIUM (2501 - 7500)
HIGH (7501 - 30000)
HIGHEST ( > 30000)
Maybe you need a clustering algorithm?
Quoting from the link:
Cluster analysis or clustering is the
assignment of a set of observations
into subsets (called clusters) so that
observations in the same cluster are
similar in some sense. Clustering is a
method of unsupervised learning, and a
common technique for statistical data
analysis used in many fields
Jenks Natural Breaks is a very efficient single dimension clustering scheme: http://www.spatialanalysisonline.com/OUTPUT/html/Univariateclassificationschemes.html#_Ref116892931
As comments have noted, this is very similar to k-means. However, I've found it even easier to implement, particularly the variation found in Borden Dent's Cartography: http://www.amazon.com/Cartography-Thematic-Borden-D-Dent/dp/0697384950
I think you're looking for something akin to data discretization that's fairly common in AI to convert continuous data (or discrete data with such a large number of classes as to be unwieldy) into discrete classes.
I know Weka uses Fayyad & Irani's MDL Method as well as Kononeko's MDL method, I'll see if I can dig up some references.
This is only a 1-dimensional problem, so there may be a dynamic programming solution. Assume that it makes sense to take the points in sorted order and then make n-1 cuts to generate n clusters. Assume that you can write down a penalty function f() for each cluster, such as the variance within the cluster, or the distance between min and max in the cluster. You can then minimise the sum of f() evaluated at each cluster. Work from one point at a time, from left to right. At each point, for 1..# clusters - 1, work out the best way to split the points so far into that many clusters, and store the cost of that answer and the location of its rightmost split. You can work this out for point P and cluster size c as follows: consider all possible cuts to the left of P. For each cut add f() evaluated on the group of points to the right of the cut to the (stored) cost of the best solution for cluster size c-1 at the point just to the left of the cut. Once you have worked your way to the far right, do the same trick once more to work out the best answer for cluster size c, and use the stored locations of rightmost splits to recover all the splits that give that best answer.
This might actually be more expensive than a k-means variant, but has the advantage of guaranting to find a global best answer (for your chosen f() under these assumptions).
Genetic hierarchical clustering algorithm
I was wondering.
Apparently what you are looking for are clean breaks. So before launching yourself into complicated algorithms, you may perhaps envision a differential approach.
[1, 1.2, 4, 5, 10]
[20%, 333%, 25%, 100%]
Now depending on the number of breaks we are looking for, it's a matter of selecting them:
2 categories: [1, 1.2] + [4, 5, 10]
3 categories: [1, 1.2] + [4, 5] + [10]
I don't know about you but it does feel natural in my opinion, and you can even use a treshold approach saying that a variation less than x% is not worth considering a cut.
For example, here 4 categories does not seem to make much sense.