I used the function for gower distance from this link: https://sourceforge.net/projects/gower-distance-4python/files/. My data (df) is such that each row is a trade, and each of the columns are features. Since it contains a lot of categorical data, I then converted the data using gower distance to measure "similarity"... I hope this is correct (as below..):
D = gower_distances(df)
distArray = ssd.squareform(D)
hierarchal_cluster=scipy.cluster.hierarchy.linkage(distArray, method='ward', metric='euclidean', optimal_ordering=False)
I then plot the hierarchical_cluster from above into a dendogram:
plt.title('Hierarchical Clustering Dendrogram (truncated)')
plt.xlabel('sample index or (cluster size)')
plt.ylabel('distance')
dendrogram(
hierarchal_cluster,
truncate_mode='lastp', # show only the last p merged clusters
p=15, # show only the last p merged clusters
leaf_rotation=90.,
leaf_font_size=12.,
show_contracted=True # to get a distribution impression in truncated branches
)
I cannot show it, since I do not have enough privilege points, but on the dendogram I can see separate colors.
What is the main discriminator separating them?
How can I find this out?
How can I use PCA to extract useful features?
Do I pass my 'hierarchal_cluster' into a PCA function?
Something like the below..?
pca = PCA().fit(hierarchal_cluster.T)
plt.plot(np.arange(1,len(pca.explained_variance_ratio_)+1,1),pca.explained_variance_ratio_.cumsum())
I hope you do know that PCA works only for continuous data? Since you mentioned, there are many categorical features. From what you have written, it occurs that you got mixed data.
A common practice when dealing with mixed data is to separate the continuous and categorical features/variables. Then find the Euclidean distance between data points for continuous (or numerical) features and Hamming distance for the categorical features [1].
This will enable you to find similarity between continuous and categorical feature separately. Now, while you are at this, apply PCA on the continuous variables to extract important features. And apply Multiple Correspondence Analysis MCA on the categorical features. Thereafter, you can combine the obtained relevant features together, and apply any clustering algorithm.
So essentially, I'm suggesting feature selection/feature extraction before clustering.
[1] Huang, Z., 1998. Extensions to the k-means algorithm for clustering large data sets with categorical values. Data mining and knowledge discovery, 2(3), pp.283-304.
Quoting the documentation of scipy on the matter of Ward linkage:
Methods ‘centroid’, ‘median’ and ‘ward’ are correctly defined only if Euclidean pairwise metric is used. If y is passed as precomputed pairwise distances, then it is a user responsibility to assure that these distances are in fact Euclidean, otherwise the produced result will be incorrect.
So you can't use Ward linkage with Gower!
Related
I have a small set of aerial images where different terrains visible in the image have been have been labelled by human experts. For example, an image may contain vegetation, river, rocky mountains, farmland etc. Each image may have one or more of these labelled regions. Using this small labeled dataset, I would like to fit a gaussian mixture model for each of the known terrain types. After this is complete, I would have N number of GMMs for each N types of terrains that I might encounter in an image.
Now, given a new image, I would like to determine for each pixel, which terrain it belongs to by assigning the pixel to the most probable GMM.
Is this the correct line of thought ? And if yes, how can I go about clustering an image using GMMs
Its not clustering if you use labeled training data!
You can, however, use the labeling function of GMM clustering easily.
For this, compute the prior probabilities, mean and covariance matrixes, invert them. Then classify each pixel of the new image by the maximum probability density (weighted by prior probabilities) using the multivariate Gaussians from the training data.
Intuitively, your thought process is correct. If you already have the labels that makes this a lot easier.
For example, let's pick on a very well known and non-parametric algorithm like Known Nearest Neighbors https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm
In this algorithm, you would take your new "pixels" which would then find the closest k-pixels like the one you are currently evaluating; where closest is determined by some distance function (usually Euclidean). From there, you would then assign this new pixel to the most frequently occurring classification label.
I am not sure if you are looking for a specific algorithm recommendation, but KNN would be a very good algorithm to begin testing this type of exercise out on. I saw you tagged sklearn, scikit learn has a very good KNN implementation I suggest you read up on.
I'm looking to implement a hierarchical clustering model for my set of training variables with respect to their correlation matrix (it's a 100x100 matrix, and I want the largest cluster whose elements are the most uncorrelated). I've been able to use the scipy family of functions to do this, however, for visualization and presentations sake, I'd like an alternative correlation distance defined for my data.
The inbuilt distance 'correlation' metric is defined to be 1-r, where r is the pearson score between two variables. I'd like to change it to 1-absvalue(r)-as my most interesting variables are the most uncorrelated ones (so say the variables who find themselves 1-.8 distance apart). Thanks!
For big datasets with 2bil+ samples and approximately 100+ features per sample. Among these, 10% features you have are numerical/continuous variables and the rest of it are categorical variables (position, languages, url etc...).
Let's use some examples:
e.g: dummy categorical feature
feature: Position
real values: SUD | CENTRE | NORTH
encoded values: 1 | 2 | 3
...would have sense use reduction like SVD because distance beetween sud:north > sud:centre and, moreover, it's possible to encode (e.g OneHotEncoder, StringIndexer) this variable because of the small cardinality of it values-set.
e.g: real categorical feature
feature: url
real values: very high cardinality
encoded values: ?????
1) In MLlibthe 90% of the model works just with numerical values (a part of Frequent Itemset and DecisionTree techniques)
2) Features transformers/reductor/extractor as PCA or SVD are not good for these kind of data, and there is no implementation of (e.g) MCA
a) Which could be your approach to engage with this kind of data in spark, or using Mllib?
b) Do you have any suggestions to cope with this much categorical values?
c) After reading a lot in literature, and counting the implemented model in spark, my idea, about make inference on one of that features using the others (categorical), the models at point 1 could be the best coiche. What do you think about it?
(to standardize a classical use case you can imagine the problem of infer the gender of a person using visited url and other categorical features).
Given that I am a newbie in regards to MLlib, may I ask you to provide a concrete example?
Thanks in advance
Well, first I would say stackoverflow works in a different way, you should be the one providing a working example with the problem you are facing and we help you out using this example.
Anyways I got intrigued with the use of the categorical values like the one you show as position. If this is a categorical value as you mention with 3 levels SUD,CENTRE, NORTH, there is no distance between them if they are truly categorical. In this sense I would create dummy variables like:
SUD_Cat CENTRE_Cat NORTH_Cat
SUD 1 0 0
CENTRE 0 1 0
NORTH 0 0 1
This is a truly dummy representation of a categorical variable.
On the other hand if you want to take that distance into account then you have to create another feature which takes this distance into account explicitly, but that is not a dummy representation.
If the problem you are facing is that after you wrote your categorical features as dummy variables (note that now all of them are numerical) you have very many features and you want to reduce your feature's space, then is a different problem.
As a rule of thumbs I try to utilize the entire feature space first, now a plus since in spark computing power allows you to run modelling tasks with big datasets, if it is too big then I would go for dimensionality reduction techniques, PCA etc...
I have been trying to cluster a set of text documents. I have a sparse TFIDF matrix with around 10k documents (subset of a large dataset), and I try to run the scikit-learn k-means algorithm with different sizes of clusters (10,50,100). Rest all the parameters are default values.
I get a very strange behavior that no matter how many clusters I specify or even if I change the number of iterations, there would be 1 cluster in the lot which would contain most of the documents in itself and there will be many clusters which would have just 1 document in them. This is highly non-uniform behavior
Does anyone know what kind of problem am I running into?
Here are the possible things that might be going "wrong":
Your k-means cluster initialization points are chosen as the same set of points in each run. I recommend using the 'random' for the init parameter of k-means http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html. If that doesn't work then supply to k-means your own set of random initial cluster centers. Remember to initialize your random generator using its seed() method as the current date and time. https://docs.python.org/2/library/random.html uses current date-time as the default value.
Your distance function, i.e. euclidean distance might be the culprit. This is less likely but it is always good to run k-means using cosine similarity especially when you are using it for document similarity. scikits doesn't have this functionality at present but you should look here: Is it possible to specify your own distance function using scikit-learn K-Means Clustering?
These two combined should give you good clusters.
I noticed with the help of above answers and comments that there was a problem with outliers and noise in original space. For this, we should use a dimensionality reduction method which eliminates the unwanted noise in the data. I tried random projections first but it failed to work with text data, simply because the problem was still not solved.
Then using Truncated Singular Value Decomposition, I was able to get perfect uniform clusters. Hence, the Truncated SVD is the way to go with textual data in my opinion.
I am working on a simple AI program that classifies shapes using unsupervised learning method. Essentially I use the number of sides and angles between the sides and generate aggregates percentages to an ideal value of a shape. This helps me create some fuzzingness in the result.
The problem is how do I represent the degree of error or confidence in the classification? For example: a small rectangle that looks very much like a square would yield night membership values from the two categories but can I represent the degree of error?
Thanks
Your confidence is based on used model. For example, if you are simply applying some rules based on the number of angles (or sides), you have some multi dimensional representation of objects:
feature 0, feature 1, ..., feature m
Nice, statistical approach
You can define some kind of confidence intervals, baesd on your empirical results, eg. you can fit multi-dimensional gaussian distribution to your empirical observations of "rectangle objects", and once you get a new object you simply check the probability of such value in your gaussian distribution, and have your confidence (which would be quite well justified with assumption, that your "observation" errors have normal distribution).
Distance based, simple approach
Less statistical approach would be to directly take your model's decision factor and compress it to the [0,1] interaval. For example, if you simply measure distance from some perfect shape to your new object in some metric (which yields results in [0,inf)) you could map it using some sigmoid-like function, eg.
conf( object, perfect_shape ) = 1 - tanh( distance( object, perfect_shape ) )
Hyperbolic tangent will "squash" values to the [0,1] interval, and the only remaining thing to do would be to select some scaling factor (as it grows quite quickly)
Such approach would be less valid in the mathematical terms, but would be similar to the approach taken in neural networks.
Relative approach
And more probabilistic approach could be also defined using your distance metric. If you have distances to each of your "perfect shapes" you can calculate the probability of an object being classified as some class with assumption, that classification is being performed at random, with probiability proportional to the inverse of the distance to the perfect shape.
dist(object, perfect_shape1) = d_1
dist(object, perfect_shape2) = d_2
dist(object, perfect_shape3) = d_3
...
inv( d_i )
conf(object, class_i) = -------------------
sum_j inv( d_j )
where
inv( d_i ) = max( d_j ) - d_i
Conclusions
First two ideas can be also incorporated into the third one to make use of knowledge of all the classes. In your particular example, the third approach should result in confidence of around 0.5 for both rectangle and circle, while in the first example it would be something closer to 0.01 (depending on how many so small objects would you have in the "training" set), which shows the difference - first two approaches show your confidence in classifing as a particular shape itself, while the third one shows relative confidence (so it can be low iff it is high for some other class, while the first two can simply answer "no classification is confident")
Building slightly on what lejlot has put forward; my preference would be to use the Mahalanobis distance with some squashing function. The Mahalanobis distance M(V, p) allows you to measure the distance between a distribution V and a point p.
In your case, I would use "perfect" examples of each class to generate the distribution V and p is the classification you want the confidence of. You can then use something along the lines of the following to be your confidence interval.
1-tanh( M(V, p) )