# Does it make sense using Machine Learning techniques on a sparse features matrix?

I am trying to predict the sentiment (neg/neutral/pos) of a given text. To do so I use a LDA model (Latent Dirichlet Allocation) that is a topic discovery model.

The LDA model works as follows: given a number N (the model will have to define N topics) and a training corpus, it returns N weighted combination of words that are the respective topics.

Once trained, and given a document, the LDA model will then return a vector of the topic loadings for that document. I apply that to my testing set which gives me my matrix of features X.

I then try to use a machine learning tool to train and predict the sentiment (this is my label vector Y).

Problem with LDA is that depending on your parameters, each document can have a very concentrated distribution across the topics (for instance a document could be fully explained by 2 or 3 topics). This then gives me a very sparse matrix. To give you an example, I usually set N to 200 and each document is fully explained by 2 to 5 topics, so each column of X will have about 195 to 198 zeros.

It seems to me counter intuitive to use ML techniques on such a matrix. The first example that comes randomForest that will be bagging my observations and randomly picking a few features, leading to a lot of zeros in the observations.

It appears that in my case, logistic regression is doing better than any of the more complex classification methods I tried (random forest, adaptative and gradient boosting, KNN and SVM).

Is it a result that makes sense or am I missing something that could make ML more useful in this case? Many thanks for your advice!

• It sounds like most of the problem originates with attempting to use some method after LDA. Have you tried working with the raw data, or an alternative, non-LDA source derived from the raw data?
– Sycorax
Mar 26 '18 at 15:09

Logistic regression is a good example of a method that can incorporate sparsity. If you use $l_1$ penalty (adding $\lambda \|w\|_1 = \sum_{i}|w_i|$ to the error term) you can enforce $w$ to be sparse.