Machine Learning: Feature Comparison I am working on a machine learning algorithm which performs a binary classification. I have different features, and I would like to know which of them are better for the classification, I mean what of them really make a difference between classes and what of them are not important.
I have thought of computing the normal distribution of every feature in class A and B and getting the overlap between them. If they have a big area in common the feature is not good.
I have also heard about Principal Component Analysis. I do not know what is the best way of determining which are the best features, so I ask or your help.
Thanks a lot!!!!
 A: As I continue to investigate this subject I found out that there are different methods to compare features, I am going to post some of them, just in case someone has the same problem than me:
1.-Kolmogorov-Smirnov compares the maximum distance between two cumulative distribution functions and returns a value meaning the similarity between the functions. If you compare the feature from sample A and B gives you an idea, if they are close is not a good feature.
2.-Compute overlap between distribution functions, the bigger the overlap the worse the feature is to differenciate the classes, code:
# compute overlap between the 2 distributions
ker_sick = stats.gaussian_kde(sick)
ker_healthy = stats.gaussian_kde(healthy)
min_point, max_point = aux.get_min_max(sick, healthy)
points_range = np.linspace(min_point, max_point, 100)
sick_points = ker_sick(points_range)
healthy_points = ker_healthy(points_range)
min_points = aux.min_between_two_list(sick_points, healthy_points)


def y_pts(pt):
    y_pt = min(ker_sick(pt), ker_healthy(pt))
    return y_pt


overlap = integrate.quad(y_pts, a=-np.inf, b=np.inf)
print("overlap: ", overlap)
overlap_list.append(overlap[0])

# plot distributions (healthy, sick) and the overlap between them
fig = plt.figure()
ax = fig.add_subplot(121)
ax = sns.kdeplot(sick, shade=True, cut=0, label="healthy", color='g')
ax = sns.kdeplot(healthy, shade=True, cut=0, label="sick", color='r')
ax.plot(points_range, min_points, color="y", alpha=1)
ax.fill_between(points_range, 0, min_points)
ax.set(xlabel='value', ylabel='probability', title=name)

3.- Previous methods are bit more homemade, scikit also includes some module for feature selection using different methods to compare features and let you know which one is better, Scikit feature selection
I tried these 3 methods, including several variatons of the scikit feature selection, and they always matched in which was the best feature, so I guess everyone of them is working properly.
Thanks a lot and I hope this ends up being helpful!
A: First off, principal component analysis is not necessarily what you want. PCA is a method of dimensionality reduction, meaning that it reduces the dimensions of your data. This may be good for you, but you should know that the algorithm will change the value of the components in each dimension. See this: http://setosa.io/ev/principal-component-analysis/
Your thought about distributions is a very good idea! So good, actually, that staticians have been doing something similar for a long time. Try computing the Kullback-Leibler divergence of the distributions of your two classes for each dimension in your data. Don't just do it, understand what it means: https://www.countbayesie.com/blog/2017/5/9/kullback-leibler-divergence-explained
or look at my own post https://github.com/abrhor/Momentum-Neural-Networks/blob/master/Distributions/Conditional%20Distribution%20of%20RSI%20Notebook.ipynb which is not as informative and also has some finance and a lot of code.
KL divergence will give you information about your data, but won't help simplify the computation of the actual classifier like PCA does: 
Finally, just a convention, you don't mean computing the normal distributions. "Normal" is a term for a regular distribution/histogram if the plot is or is approximately symmetrical, because it has certain resulting statistical characteristics.
A: I am no expert in machine learning, but there is a method similar to what you have described called the "Receiver Operator Characteristic" (ROC), which evaluates the the ability of a continuous variable to distinguish between binary outcomes.
Bellow I have linked a video that carefully explains how the ROC curve works, as well as the Wikipedia page, which gives a good description of the method.
https://www.youtube.com/watch?v=pYIIZR_XIyY
https://en.wikipedia.org/wiki/Receiver_operating_characteristic
The ROC curve is easy to request in most statistical software packages. I have personally used it more often in behavioral and social sciences, but I have been told that it is quite useful in machine learning. The area under the ROC curve is a decent metric of how well a factor is able to classify your binary variable, so you could compare separate factors or models using this metric. 
