I'm interested in understanding what "features" are most impactful in a multi-class classification.
I've done this with PCA and that appears to allow me to inspect the directional variance in each feature per component via the components_ vector.
I'm struggling to interrogate the results of LDA as to understanding which features are part of each component and what their impact is...
Any suggestions on what elements of the LDA object after fit_transform can be used to gain feature specific insights per component?
Here is an answer from the documentation of sklearn itself.
Principal Component Analysis (PCA) applied to this data identifies the combination of attributes (principal components, or directions in the feature space) that account for the most variance in the data. Here we plot the different samples on the 2 first principal components.
Linear Discriminant Analysis (LDA) tries to identify attributes that account for the most variance between classes. In particular, LDA, in contrast to PCA, is a supervised method, using known class labels.
Related
I am currently working on a project that uses Linear Discriminant Analysis to transform some high-dimensional feature set into a scalar value according to some binary labels.
So I train LDA on the data and the labels and then use either transform(X) or decision_function(X) to project the data into a one-dimensional space.
I would like to understand the difference between these two functions. My intuition would be that the decision_function(X) would be transform(X) + bias, but this is not the case.
Also, I found that those two functions give a different AUC score, and thus indicate that it is not a monotonic transformation as I would have thought.
In the documentation, it states that the transform(X) projects the data to maximize class separation, but I would have expected decision_function(X) to do this.
I hope someone could help me understand the difference between these two.
LDA projects your multivariate data onto a 1D space. The projection is based on a linear combination of all your attributes (columns in X). The weights of each attribute are determined by maximizing the class separation. Subsequently, a threshold value in 1D space is determined which gives the best classification results. transform(X) gives you the value of each observation in this 1D space x' = transform(X). decision_function(X) gives you the log-likelihood of an attribute being a positive class log(P(y=1|x')).
I am classifying data with categorical variables. It is data where people have provided information.
My training dataset is of varying quality. I have a greater confidence in some of the data i.e. I have a higher confidence that people have provided correct information whereas in some the data I am not so sure.
How can I pass this information into a classification algorithm such as Naive Bayes or K nearest neighbour?
Or should I instead look to another algorithm?
I think what you want to do, is to provide individual weights (for the importance/confidence) for each data point you have.
For instance, if you are very certain that one data point is of higher quality and should have a higher weight than others, in which you are less confident in, you can specify that when fitting your classifier.
Sklearn provides for instance the Gaussian Naive Bayes classifier (GaussianNB) for that.
Here, you can specify sample_weights when calling the fit() method.
I'm using GradientBoostingClassifier for my unbalanced labeled datasets. It seems like class weight doesn't exist as a parameter for this classifier in Sklearn. I see I can use sample_weight when fit but I cannot use it when I deal with VotingClassifier or GridSearch. Could someone help?
Currently there isn't a way to use class_weights for GB in sklearn.
Don't confuse this with sample_weight
Sample Weights change the loss function and your score that you're trying to optimize. This is often used in case of survey data where sampling approaches have gaps.
Class Weights are used to correct class imbalances as a proxy for over \ undersampling. There is no direct way to do that for GB in sklearn (you can do that in Random Forests though)
Very late, but I hope it can be useful for other members.
In the article of Zichen Wang in towardsdatascience.com, the point 5 Gradient Boosting it is told:
For instance, Gradient Boosting Machines (GBM) deals with class imbalance by constructing successive training sets based on incorrectly classified examples. It usually outperforms Random Forest on imbalanced dataset For instance, Gradient Boosting Machines (GBM) deals with class imbalance by constructing successive training sets based on incorrectly classified examples. It usually outperforms Random Forest on imbalanced dataset.
And a chart shows that the half of the grandient boosting model have an AUROC over 80%. So considering GB models performances and the way they are done, it seems not to be necessary to introduce a kind of class_weight parameter as it is the case for RandomForestClassifier in sklearn package.
In the book Introduction To Machine Learning with Pyhton written by Andreas C. Müller and Sarah Guido, edition 2017, page 89, Chapter 2 *Supervised Learning, section Ensembles of Decision Trees, sub-section Gradient boosted regression trees (gradient boosting machines):
They are generally a bit more sensitive to
parameter settings than random forests, but can provide better accuracy if the parameters are set correctly.
Now if you still have scoring problems due to imbalance proportions of categories in the target variable, it is possible you should see if your data should be splited to apply different models on it, because they are not as homogeneous as it seems to be. I mean it may have a variable you have not in your dataset train (an hidden variable clearly) that influences a lot the model results, then it is difficult even for the greater GB to give correct scoring because it misses a huge information that you cannot make appear in the matrix to compute sometimes for many reasons.
Some updates:
I found, by random, there are libraries that implement it as parameters of their gradient boosting instance objects. It is the case of H2O where for the parameter balance_classes it is told:
Balance training data class counts via over/under-sampling (for
imbalanced data).
Type: bool (default: False).
If you want to keep with sklearn you should do as HakunaMaData told: over/under-sampling because that's what other libraries finally do when the parameter exist.
I'm looking at this example code given on Scikit Kmeans digit example
There is the following code in this script :
# in this case the seeding of the centers is deterministic, hence we run the
# kmeans algorithm only once with n_init=1
pca = PCA(n_components=n_digits).fit(data)
bench_k_means(KMeans(init=pca.components_, n_clusters=n_digits, n_init=1),
name="PCA-based",
data=data)
Why are the eigen vectors used as initial centers and is there any intuition for this?
There is a stackexchange link here, and also some discussion on the PCA wikipedia.
There is also an informative mailing list discussion about the creation of this example.
All of these threads point back to this paper among others. In a brief, this paper says that there is a strong relationship between the subspace found by SVD (as seen in PCA) and the optimal cluster centers we seek in K-means, along with associated proofs. The key sentence comes in the lower right of the first page - "We prove that principal
components are actually the continuous solution of the cluster membership indicators in the K-means clustering method, i.e., the PCA dimension reduction automatically performs data clustering according to the K-means objective function".
What this amounts to is that SVD/PCA eigenvectors should be very good initializers for K-Means. The authors of this paper actually take things a step further, and project the data into the eigenspace for both of their experiments, then cluster there.
I am working with sklearn's implementation of KNN. While my input data has about 20 features, I believe some of the features are more important than others. Is there a way to:
set the feature weights for each feature when "training" the KNN learner.
learn what the optimal weight values are with or without pre-processing the data.
On a related note, I understand generally KNN does not require training but since sklearn implements it using KDTrees, the tree must be generated from the training data. However, this sounds like its turning KNN into a binary tree problem. Is that the case?
Thanks.
kNN is simply based on a distance function. When you say "feature two is more important than others" it usually means difference in feature two is worth, say, 10x difference in other coords. Simple way to achive this is by multiplying coord #2 by its weight. So you put into the tree not the original coords but coords multiplied by their respective weights.
In case your features are combinations of the coords, you might need to apply appropriate matrix transform on your coords before applying weights, see PCA (principal component analysis). PCA is likely to help you with question 2.
The answer to question to is called "metric learning" and currently not implemented in Scikit-learn. Using the popular Mahalanobis distance amounts to rescaling the data using StandardScaler. Ideally you would want your metric to take into account the labels.