More features, less F-Score Is there any rule about relationship between number of features and performance of the model? Recently, I did an experiment on 3 sets of features (all extracted from a same dataset). The strange point was that, the F-Score of all features together was way less than F-Score of each feature category. How I can explain such an observation? Is there any study about it?
 A: General answer
Yes, there is a relationship between the number of features and the performance of the model.
The more features you put into the model the better your model performs on the training set. However if you put more features into the model it generalizes worse on the test set. In other words there is a risk of overfitting. This phenomenon is called bias-variance tradeoff.
This phenomenon exists for all machine-learning algorithms (not only for classification and not only for supervised machine-learning algorithms).


Specific answer for Binary classification and $F_1$-Score
In binary classification the $F_1$ is computed as a harmonic mean of precision and recall:
$F_1$ = $(\frac{recall^{-1} + precision^{-1}}{2})^{-1}$ = $2* \frac{ precision * recall}{precision + recall}$.
You can reformulate this as a general formula in terms of Type I and Type II errors. 
$F_{\beta}$ = $\frac{(1 + \beta^2) * true positive}{(1 + \beta^2) * true positive + \beta^2 * false negative + false positive}$
So the higher the $F_1$ score the better the models fit. You can increase the $F_1$ score buy using a more complex classification model, but there is a risk of overfitting (bias-variance tradeoff). An other opportunity of increasing the $F_1$ score is adding more data. The smaller your dataset the higher the risk of overfitting. This is almost always a good idea (if you have more data and enough computing power of course). 
If the $F_1$ score for all features is less than the $F_1$ score for single features I would be very doubtful. One situation is explained in this question which is very similar to your question:
How can adding a feature reduce a model's performance?
Thank you @tavrock for your great answer. I am citing from you.

If you add it as a predictor to your model, you will most likely notice that your accuracy drops. This is because, while it is added information, it does not correlate well with the other information you have provided.
It may be difficult to distinguish weekends and holidays from the rest of the days of the week, and it just becomes noise. As a result, you may be able to get better results with weekend/holiday vs rest of the week binary data as a predictor for the crime.
It may also help to create a matrix plot of your data and see if any patterns emerge with "day of week" (and you may want to jitter that data, if possible).

