I would like to perform classification on a small data set 65x9 using some of the Machine Learning Classification Methods (SVM, Decision Trees or any other).
So, before starting with the classification I would like to do attribute analyses with PCA in Matlab or Weka (preferred MatLab). I would like to obtain which Attribute contribute most to the performance of the classifier. So I can maybe reduce the number of some Attribute or/and include more in the future. Any example of PCA can find regarding this in MatLab or Weka?
Thanks
PCA is a unsupervised feature extraction method.
If your question is on selecting attributes to use with PCA, i don't know what your purpose is but it is unnecessary to do something like that to improve classification performance. Just use the whole attributes. PCA will give you best attributes in decreasing order for each instance.
If your question is on selecting attributes after PCA, you can chose a treshold (for example 0.95) and calculate #attributes enough for treshold beginning from the first attribute to last one. You can use the eigenvalues of covariance matrix to calculate and achive treshold in PCA.
After running PCA, we know that the first attribute is the best one, the second attribute is the best one after first etc...
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I am trying to cluster a dataset using an encoder and since I am new in this field I cant tell how to do it.My main issue is how to define the loss function since the dataset is unlabeled and up to know, what I have seen from bibliography they define as loss function the distance between the desired output and the predicted output.My question is since that I dont have a desired output how should I implement this?
You can use an auto encoder to pre-train your convolutional layers, like it described in my question here with usage of convolutional autoencoder for images
As you can see form code, loss function is Adam with metrics accuracy and dice coefficient, I think you can use accuracy only, since dice coefficient is image-specific
I’m not sure how it will work for you, because you hadn’t provided your idea how you will transform your bibliography lists to vector, perhaps you will create a list for bibliography id’s sorted by the cosine distance between them
For example, you can use a set of vector with cosine distances to each item in a bibliography list above for each reference in your dataset and use it as input for autoencoder
After encoder will be trained, you can remove the decoder part from your model output and use as an input for one of unsupervised clustering algorithms, for example, k-mean. You can find details about them here
I have run LDA with MATLAB using the fitcdiscr function and predict.
I have a feeling there may be some bugs in my code however and as a sanity check would like to identify which features are being most heavily weighted in the classification.
Can this be done?
There is a Coeffs field in your fitted object containing all the relevant information http://uk.mathworks.com/help/stats/classificationdiscriminant-class.html
In particular, if you fit a linear LDA there will be Linear field which is the linear operator used for projection. However, one should bear in mind that value of coefficients of linear models are not feature importances. There is much more in that to consider. Weight can be big because your feature have small values or because there is a highly biased distribution of the values. If you need feature selection technique - use feature selection methods (like L1 regularized models) otherwise you might easily get wrong conclusions from your data.
I have a dataset which I use for classifcation with libSVM in Matlab. The dataset consists of 4 classes.
For parameter selection of SVM I can do nested cross-validation. The problem is that I also need the value of the best parameters in the end.
After having done the nested cross-validation and having the final accuracy I want the values of the best parameters. Then I will train a SVM for each class (one-vs-all) with the best parameters for selecting the most important features (according to heighest weight), i.e. feature importance map.
How can I do this? Should I just not do nested cross-validation and only looping over all parameters and doing cross-validation?
Second, if I use a linear SVM then using this weight vector w for assigning importance to features works, but does it also work for non-linear SVM (e.g. rbf kernel)?
To find the "best" parameters for your kernel of choice, you have to loop through all parameters to perform a so called "grid search". LIBSVM does not support a build-in grid-search mechanismn.
Regarding your second question, I would suggest to perform a feature selection (e.g. Information Gain, Mutual Information, ...) as a pre-processing step before the actual work with the SVM and in a second step take the weight vector
s into consideration (but I am not sure, if this will work with RBF or Gaußian Kernels...).
Is it possible to train classifiers in sklearn with a cost matrix with different costs for different mistakes? For example in a 2 class problem, the cost matrix would be a 2 by 2 square matrix. For example A_ij = cost of classifying i as j.
The main classifier I am using is a Random Forest.
Thanks.
The cost-sensitive framework you describe is not supported in scikit-learn, in any of the classifiers we have.
You could use a custom scoring function that accepts a matrix of per-class or per-instance costs. Here's an example of a scorer that calculates per-instance misclassification cost:
def financial_loss_scorer(y, y_pred, **kwargs):
import pandas as pd
totals = kwargs['totals']
# Create an indicator - 0 if correct, 1 otherwise
errors = pd.DataFrame((~(y == y_pred)).astype(int).rename('Result'))
# Use the product totals dataset to create results
results = errors.merge(totals, left_index=True, right_index=True, how='inner')
# Calculate per-prediction loss
loss = results.Result * results.SumNetAmount
return loss.sum()
The scorer becomes:
make_scorer(financial_loss_scorer, totals=totals_data, greater_is_better=False)
Where totals_data is a pandas.DataFrame with indexes that match the training set indexes.
You could always just look at your ROC curve. Each point on the ROC curve corresponds to a separate confusion matrix. So by specifying the confusion matrix you want, via choosing your classifier threshold implies some sort of cost weighting scheme. Then you just have to choose the confusion matrix that would imply the cost matrix you are looking for.
On the other hand if you really had your heart set on it, and really want to "train" an algorithm using a cost matrix, you could "sort of" do it in sklearn.
Although it is impossible to directly train an algorithm to be cost sensitive in sklearn you could use a cost matrix sort of setup to tune your hyper-parameters. I've done something similar to this using a genetic algorithm. It really doesn't do a great job, but it should give a modest boost to performance.
One way to circumvent this limitation is to use under or oversampling. E.g., if you are doing binary classification with an imbalanced dataset, and want to make errors on the minority class more costly, you could oversample it. You may want to have a look at imbalanced-learn which is a package from scikit-learn-contrib.
May not be direct to your question (since you are asking about Random Forest).
But for SVM (in Sklearn), you can utilize the class_weight parameter to specify the weights of different classes. Essentially, you will pass in a dictionary.
You might want to refer to this page to see an example of using class_weight.
I have a 40X3249 noisy dataset and 40X1 resultset. I want to perform simple sequential feature selection on it, in Matlab. Matlab example is complicated and I can't follow it. Even a few examples on SoF didn't help. I want to use decision tree as classifier to perform feature selection. Can someone please explain in simple terms.
Also is it a problem that my dataset has very low number of observations compared to the number of features?
I am following this example: Sequential feature selection Matlab and I am getting error like this:
The pooled covariance matrix of TRAINING must be positive definite.
I've explained the error message you're getting in answers to your previous questions.
In general, it is a problem that you have many more variables than samples. This will prevent you using some techniques, such as the discriminant analysis you were attempting, but it's a problem anyway. The fact is that if you have that high a ratio of variables to samples, it is very likely that some combination of variables would perfectly classify your dataset even if they were all random numbers. That's true if you build a single decision tree model, and even more true if you are using a feature selection method to explicitly search through combinations of variables.
I would suggest you try some sort of dimensionality reduction method. If all of your variables are continuous, you could try PCA as suggested by #user1207217. Alternatively you could use a latent variable method for model-building, such as PLS (plsregress in MATLAB).
If you're still intent on using sequential feature selection with a decision tree on this dataset, then you should be able to modify the example in the question you linked to, replacing the call to classify with one to classregtree.
This error comes from the use of the classify function in that question, which is performing LDA. This error occurs when the data is rank deficient (or in other words, some features are almost exactly correlated). In order to overcome this, you should project the data down to a lower dimensional subspace. Principal component analysis can do this for you. See here for more details on how to use pca function within statistics toolbox of Matlab.
[basis, scores, ~] = pca(X); % Find the basis functions and their weighting, X is row vectors
indices = find(scores > eps(2*max(scores))); % This is to find irrelevant components up to machine precision of the biggest component .. with a litte extra tolerance (2x)
new_basis = basis(:, indices); % This gets us the relevant components, which are stored in variable "basis" as column vectors
X_new = X*new_basis; % inner products between the new basis functions spanning some subspace of the original, and the original feature vectors
This should get you automatic projections down into a relevant subspace. Note that your features won't have the same meaning as before, because they will be weighted combinations of the old features.
Extra note: If you don't want to change your feature representation, then instead of classify, you need to use something which works with rank deficient data. You could roll your own version of penalised discriminant analysis (which is quite simple), use support vector machines, or other classification functions which don't break with correlated features as LDA does (by virtue of requiring matrix inversion of the covariance estimate).
EDIT: P.S I haven't tested this, because I have rolled my own version of PCA in Matlab.