I'm having the below Azure Machine Learning question:
You need to identify which columns are more predictive by using a
statistical method. Which module should you use?
A. Filter Based Feature Selection
B. Principal Component Analysis
I choose is A but the answer is B. Can someone explain why it is B
PCA is the optimal approximation of a random vector (in N-d space) by linear combination of M (M < N) vectors. Notice that we obtain these vectors by calculating M eigenvectors with largest eigen values. Thus these vectors (features) can (and usually are) a combination of original features.
Filter Based Feature Selection is choosing the best features as they are (not combining them in any way) based on various scores and criteria.
so as you can see, PCA results in better features since it creates better set of features while FBFS merely finds the best subset.
hope that helps ;)
Related
I've got a set of F features e.g. Lab color space, entropy. By concatenating all features together, I obtain a feature vector of dimension d (between 12 and 50, depending on which features selected.
I usually get between 1000 and 5000 new samples, denoted x. A Gaussian Mixture Model is then trained with the vectors, but I don't know which class the features are from. What I know though, is that there are only 2 classes. Based on the GMM prediction I get a probability of that feature vector belonging to class 1 or 2.
My question now is: How do I obtain the best subset of features, for instance only entropy and normalized rgb, that will give me the best classification accuracy? I guess this is achieved, if the class separability is increased, due to the feature subset selection.
Maybe I can utilize Fisher's linear discriminant analysis? Since I already have the mean and covariance matrices obtained from the GMM. But wouldn't I have to calculate the score for each combination of features then?
Would be nice to get some help if this is a unrewarding approach and I'm on the wrong track and/or any other suggestions?
One way of finding "informative" features is to use the features that will maximise the log likelihood. You could do this with cross validation.
https://www.cs.cmu.edu/~kdeng/thesis/feature.pdf
Another idea might be to use another unsupervised algorithm that automatically selects features such as an clustering forest
http://research.microsoft.com/pubs/155552/decisionForests_MSR_TR_2011_114.pdf
In that case the clustering algorithm will automatically split the data based on information gain.
Fisher LDA will not select features but project your original data into a lower dimensional subspace. If you are looking into the subspace method
another interesting approach might be spectral clustering, which also happens
in a subspace or unsupervised neural networks such as auto encoder.
Suppose I have two feature vectors extracted from two samples using some methods and I want to compare these two feature vectors to predict whether they are coming from the same class or different classes. Can I use SVM for such purpose? As far as I understand, SVM is used to accept one input (now I have two) and predict whether it belongs to one specific class or not. I don't know how to use it for similarity measurement.
Simple methods like cosine distance or Euclidean distance have been tested and the performance was bad. So I just want to try some learning methods like SVM, NN or others if you have any suggestion. Thx!
Yes, they can - you are describing a new classification problem. Your input is simply now twice as large as before (the two feature vectors concatenated together) and the class labels are "same" and "not same".
ie: your feature vectors may have been [a, b] and [x, y] for two different inputs, and now you have one feature vector [a, b, x, y]. Note you may also want to train on pairs like [x, y, a, b] since either way should produce the correct classification.
You could also look at different ways of making your features, there are a number of options. There are also other ways of phrasing the problem.
When using SVMlight or LIBSVM in order to classify phrases as positive or negative (Sentiment Analysis), is there a way to determine which are the most influential words that affected the algorithms decision? For example, finding that the word "good" helped determine a phrase as positive, etc.
If you use the linear kernel then yes - simply compute the weights vector:
w = SUM_i y_i alpha_i sv_i
Where:
sv - support vector
alpha - coefficient found with SVMlight
y - corresponding class (+1 or -1)
(in some implementations alpha's are already multiplied by y_i and so they are positive/negative)
Once you have w, which is of dimensions 1 x d where d is your data dimension (number of words in the bag of words/tfidf representation) simply select the dimensions with high absolute value (no matter positive or negative) in order to find the most important features (words).
If you use some kernel (like RBF) then the answer is no, there is no direct method of taking out the most important features, as the classification process is performed in completely different way.
As #lejlot mentioned, with linear kernel in SVM, one of the feature ranking strategies is based on the absolute values of weights in the model. Another simple and effective strategy is based on F-score. It considers each feature separately and therefore cannot reveal mutual information between features. You can also determine how important a feature is by removing that feature and observe the classification performance.
You can see this article for more details on feature ranking.
With other kernels in SVM, the feature ranking is not that straighforward, yet still feasible. You can construct an orthogonal set of basis vectors in the kernel space, and calculate the weights by kernel relief. Then the implicit feature ranking can be done based on the absolute value of weights. Finally the data is projected into the learned subspace.
I'm experimenting with Chi-2 feature selection for some text classification tasks.
I understand that Chi-2 test checks the dependencies B/T two categorical variables, so if we perform Chi-2 feature selection for a binary text classification problem with binary BOW vector representation, each Chi-2 test on each (feature,class) pair would be a very straightforward Chi-2 test with 1 degree of freedom.
Quoting from the documentation: http://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.chi2.html#sklearn.feature_selection.chi2,
This score can be used to select the n_features features with the highest values for the χ² (chi-square) statistic from X, which must contain booleans or frequencies (e.g., term counts in document classification), relative to the classes.
It seems to me that we we can also perform Chi-2 feature selection on DF (word counts) vector presentation. My 1st question is: how does sklearn discretize the integer-valued feature into categorical?
My second question is similar to the first. From the demo codes here: http://scikit-learn.sourceforge.net/dev/auto_examples/document_classification_20newsgroups.html
It seems to me that we can also perform Chi-2 feature selection on a TF*IDF vector representation. How sklearn perform Chi-2 feature selection on real-valued features?
Thank you in advance for your kind advise!
The χ² features selection code builds a contingency table from its inputs X (feature values) and y (class labels). Each entry i, j corresponds to some feature i and some class j, and holds the sum of the i'th feature's values across all samples belonging to the class j. It then computes the χ² test statistic against expected frequencies arising from the empirical distribution over classes (just their relative frequencies in y) and a uniform distribution over feature values.
This works when the feature values are frequencies (of terms, for example) because the sum will be the total frequency of a feature (term) in that class. There's no discretization going on.
It also works quite well in practice when the values are tf-idf values, since those are just weighted/scaled frequencies.
All this time (specially in Netflix contest), I always come across this blog (or leaderboard forum) where they mention how by applying a simple SVD step on data helped them in reducing sparsity in data or in general improved the performance of their algorithm in hand.
I am trying to think (since long time) but I am not able to guess why is it so.
In general, the data in hand I get is very noisy (which is also the fun part of bigdata) and then I do know some basic feature scaling stuff like log-transformation stuff , mean normalization.
But how does something like SVD helps.
So lets say i have a huge matrix of user rating movies..and then in this matrix, I implement some version of recommendation system (say collaborative filtering):
1) Without SVD
2) With SVD
how does it helps
SVD is not used to normalize the data, but to get rid of redundant data, that is, for dimensionality reduction. For example, if you have two variables, one is humidity index and another one is probability of rain, then their correlation is so high, that the second one does not contribute with any additional information useful for a classification or regression task. The eigenvalues in SVD help you determine what variables are most informative, and which ones you can do without.
The way it works is simple. You perform SVD over your training data (call it matrix A), to obtain U, S and V*. Then set to zero all values of S less than a certain arbitrary threshold (e.g. 0.1), call this new matrix S'. Then obtain A' = US'V* and use A' as your new training data. Some of your features are now set to zero and can be removed, sometimes without any performance penalty (depending on your data and the threshold chosen). This is called k-truncated SVD.
SVD doesn't help you with sparsity though, only helps you when features are redundant. Two features can be both sparse and informative (relevant) for a prediction task, so you can't remove either one.
Using SVD, you go from n features to k features, where each one will be a linear combination of the original n. It's a dimensionality reduction step, just like feature selection is. When redundant features are present, though, a feature selection algorithm may lead to better classification performance than SVD depending on your data set (for example, maximum entropy feature selection). Weka comes with a bunch of them.
See: http://en.wikibooks.org/wiki/Data_Mining_Algorithms_In_R/Dimensionality_Reduction/Singular_Value_Decomposition
https://stats.stackexchange.com/questions/33142/what-happens-when-you-apply-svd-to-a-collaborative-filtering-problem-what-is-th
The Singular Value Decomposition is often used to approximate a matrix X by a low rank matrix X_lr:
Compute the SVD X = U D V^T.
Form the matrix D' by keeping the k largest singular values and setting the others to zero.
Form the matrix X_lr by X_lr = U D' V^T.
The matrix X_lr is then the best approximation of rank k of the matrix X, for the Frobenius norm (the equivalent of the l2-norm for matrices). It is computationally efficient to use this representation, because if your matrix X is n by n and k << n, you can store its low rank approximation with only (2n + 1)k coefficients (by storing U, D' and V).
This was often used in matrix completion problems (such as collaborative filtering) because the true matrix of user ratings is assumed to be low rank (or well approximated by a low rank matrix). So, you wish to recover the true matrix by computing the best low rank approximation of your data matrix. However, there are now better ways to recover low rank matrices from noisy and missing observations, namely nuclear norm minimization. See for example the paper The power of convex relaxation: Near-optimal matrix completion by E. Candes and T. Tao.
(Note: the algorithms derived from this technique also store the SVD of the estimated matrix, but it is computed differently).
PCA or SVD, when used for dimensionality reduction, reduce the number of inputs. This, besides saving computational cost of learning and/or predicting, can sometimes produce more robust models that are not optimal in statistical sense, but have better performance in noisy conditions.
Mathematically, simpler models have less variance, i.e. they are less prone to overfitting. Underfitting, of-course, can be a problem too. This is known as bias-variance dilemma. Or, as said in plain words by Einstein: Things should be made as simple as possible, but not simpler.