fundamentals of machine learning additionallythe following stricter normalization practice is common and can helpalthough it isn' always necessary (for exampleyou didn' do this in the digit-classification example)normalize each feature independently to have mean of normalize each feature independently to have standard deviation of this is easy to do with numpy arraysx - mean(axis= / std(axis= assuming is data matrix of shape (samplesfeatureshandling missing values you may sometimes have missing values in your data for instancein the house-price examplethe first feature (the column of index in the datawas the per capita crime rate what if this feature wasn' available for all samplesyou' then have missing values in the training or test data in generalwith neural networksit' safe to input missing values as with the condition that isn' already meaningful value the network will learn from exposure to the data that the value means missing data and will start ignoring the value note that if you're expecting missing values in the test databut the network was trained on data without any missing valuesthe network won' have learned to ignore missing valuesin this situationyou should artificially generate training samples with missing entriescopy some training samples several timesand drop some of the features that you expect are likely to be missing in the test data feature engineering feature engineering is the process of using your own knowledge about the data and about the machine-learning algorithm at hand (in this casea neural networkto make the algorithm work better by applying hardcoded (nonlearnedtransformations to the data before it goes raw datapixel grid into the model in many casesit isn' reasonable to expect machinelearning model to be able to learn from completely arbitrary data the better { { featuresy data needs to be presented to the clock hands{ { - coordinates model in way that will make the model' job easier let' look at an intuitive example theta theta even better theta theta suppose you're trying to develop featuresangles of model that can take as input an clock hands image of clock and can output the figure feature engineering for reading he ime on time of day (see figure clock licensed to