Can we remove features that have zero-correlation with the target/label?

Can I drop these features to improve the accuracy of my classification problem?

If you are using a simple linear classifier, such as logistic regression then yes. That is because your plots are giving you a direct visualisation of how the model could make use of the data.

As soon as you start to use a non-linear classifier, that can combine features inside the learning model, then it is not so straightforward. Your plots cannot exclude a complex relationship that such a model might be able to exploit. Generally the only way to proceed is to train and test the model (using some form of cross-validation) with and without the feature.

A plot might visually show a strong non-linear relationship with zero linear correlation - e.g. a complete bell curve of feature versus target would have close to zero linear correlation, but suggest that something interesting is going on that would be useful in a predictive model. If you see plots like this, you can either try to turn them into linear relationships with some feature engineering, or you can treat it as evidence that you should use a non-linear model.

In general, this advice applies whether or not the features are derived features. For a linear model, a derived feature which is completely uncorrelated with the target is still not useful. A derived feature may or may not be easier for a non-linear model to learn from, you cannot easily tell from a plot designed to help you find linear relationships.

If I understand you well, you are asking if you can remove features having zero-correlation either :

1. With other features
2. With the label you want to predict

Those are two different cases :

1. We usually recommend to remove features having correlation between them (stabilize the model). If they are ZERO-correlated, you cannot conclude here. This is by training your model that you will see is the feature is worth or not.

Don't drop those ones.

2. If a feature is strongly correlated with your label, this means a linear function (or model) should be able to predict well the latter. Even if it is not correlated, it doesn't tell you that a non-linear model wouldn't perform well by using this feature.

Don't drop this one either !

I hope I answered your question.

These uncorrelated features might be important for target in connection with other non-target features. So, it might be not a good idea to remove them, especially if your model is a complex one.

It might be a good idea to remove one of the highly correlated between themselves non-target features, because they might be redundant.

Still, it might be better to use feature reduction technics like PCA, because PCA maximize variance, without removing the whole feature, but including it into principal component.

In case of ordinals or binary features, correlation won't tell you a lot. So I guess, the best way to test if a feature is important in case it's not correlated with target is to directly compare performance of a model with and without the feature. But still different features might have different importance for different algorithms.