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Keras is a Python library for deep learning that wraps the efficient numerical libraries TensorFlow and Theano.

Keras allows you to quickly and simply design and train neural network and deep learning models.

In this post you will discover how to effectively use the Keras library in your machine learning project by working through a binary classification project step-by-step.

After completing this tutorial, you will know:

- How to load training data and make it available to Keras.
- How to design and train a neural network for tabular data.
- How to evaluate the performance of a neural network model in Keras on unseen data.
- How to perform data preparation to improve skill when using neural networks.
- How to tune the topology and configuration of neural networks in Keras.

Discover how to develop deep learning models for a range of predictive modeling problems with just a few lines of code in my new book, with 18 step-by-step tutorials and 9 projects.

Let’s get started.

**Update Oct/2016**: Updated for Keras 1.1.0 and scikit-learn v0.18.**Update Mar/2017**: Updated for Keras 2.0.2, TensorFlow 1.0.1 and Theano 0.9.0.**Updated Sep/2019**: Updated for Keras 2.2.5 API.

## 1. Description of the Dataset

The dataset we will use in this tutorial is the Sonar dataset.

This is a dataset that describes sonar chirp returns bouncing off different services. The 60 input variables are the strength of the returns at different angles. It is a binary classification problem that requires a model to differentiate rocks from metal cylinders.

You can learn more about this dataset on the UCI Machine Learning repository. You can download the dataset for free and place it in your working directory with the filename sonar.csv.

It is a well-understood dataset. All of the variables are continuous and generally in the range of 0 to 1. The output variable is a string “M” for mine and “R” for rock, which will need to be converted to integers 1 and 0.

A benefit of using this dataset is that it is a standard benchmark problem. This means that we have some idea of the expected skill of a good model. Using cross-validation, a neural network should be able to achieve performance around 84% with an upper bound on accuracy for custom models at around 88%.

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## 2. Baseline Neural Network Model Performance

Let’s create a baseline model and result for this problem.

We will start off by importing all of the classes and functions we will need.

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import pandas from keras.models import Sequential from keras.layers import Dense from keras.wrappers.scikit_learn import KerasClassifier from sklearn.model_selection import cross_val_score from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import StratifiedKFold from sklearn.preprocessing import StandardScaler from sklearn.pipeline import Pipeline ... |

Now we can load the dataset using pandas and split the columns into 60 input variables (X) and 1 output variable (Y). We use pandas to load the data because it easily handles strings (the output variable), whereas attempting to load the data directly using NumPy would be more difficult.

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... # load dataset dataframe = pandas.read_csv("sonar.csv", header=None) dataset = dataframe.values # split into input (X) and output (Y) variables X = dataset[:,0:60].astype(float) Y = dataset[:,60] |

The output variable is string values. We must convert them into integer values 0 and 1.

We can do this using the LabelEncoder class from scikit-learn. This class will model the encoding required using the entire dataset via the fit() function, then apply the encoding to create a new output variable using the transform() function.

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... # encode class values as integers encoder = LabelEncoder() encoder.fit(Y) encoded_Y = encoder.transform(Y) |

We are now ready to create our neural network model using Keras.

We are going to use scikit-learn to evaluate the model using stratified k-fold cross validation. This is a resampling technique that will provide an estimate of the performance of the model. It does this by splitting the data into k-parts, training the model on all parts except one which is held out as a test set to evaluate the performance of the model. This process is repeated k-times and the average score across all constructed models is used as a robust estimate of performance. It is stratified, meaning that it will look at the output values and attempt to balance the number of instances that belong to each class in the k-splits of the data.

To use Keras models with scikit-learn, we must use the KerasClassifier wrapper. This class takes a function that creates and returns our neural network model. It also takes arguments that it will pass along to the call to fit() such as the number of epochs and the batch size.

Let’s start off by defining the function that creates our baseline model. Our model will have a single fully connected hidden layer with the same number of neurons as input variables. This is a good default starting point when creating neural networks.

The weights are initialized using a small Gaussian random number. The Rectifier activation function is used. The output layer contains a single neuron in order to make predictions. It uses the sigmoid activation function in order to produce a probability output in the range of 0 to 1 that can easily and automatically be converted to crisp class values.

Finally, we are using the logarithmic loss function (binary_crossentropy) during training, the preferred loss function for binary classification problems. The model also uses the efficient Adam optimization algorithm for gradient descent and accuracy metrics will be collected when the model is trained.

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# baseline model def create_baseline(): # create model model = Sequential() model.add(Dense(60, input_dim=60, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model |

Now it is time to evaluate this model using stratified cross validation in the scikit-learn framework.

We pass the number of training epochs to the KerasClassifier, again using reasonable default values. Verbose output is also turned off given that the model will be created 10 times for the 10-fold cross validation being performed.

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... # evaluate model with standardized dataset estimator = KerasClassifier(build_fn=create_baseline, epochs=100, batch_size=5, verbose=0) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(estimator, X, encoded_Y, cv=kfold) print("Baseline: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Tying this together, the complete example is listed below.

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# Binary Classification with Sonar Dataset: Baseline from pandas import read_csv from keras.models import Sequential from keras.layers import Dense from keras.wrappers.scikit_learn import KerasClassifier from sklearn.model_selection import cross_val_score from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import StratifiedKFold # load dataset dataframe = read_csv("sonar.csv", header=None) dataset = dataframe.values # split into input (X) and output (Y) variables X = dataset[:,0:60].astype(float) Y = dataset[:,60] # encode class values as integers encoder = LabelEncoder() encoder.fit(Y) encoded_Y = encoder.transform(Y) # baseline model def create_baseline(): # create model model = Sequential() model.add(Dense(60, input_dim=60, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model # evaluate model with standardized dataset estimator = KerasClassifier(build_fn=create_baseline, epochs=100, batch_size=5, verbose=0) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(estimator, X, encoded_Y, cv=kfold) print("Baseline: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Running this code produces the following output showing the mean and standard deviation of the estimated accuracy of the model on unseen data.

**Note**: Your specific results may vary given the stochastic nature of the learning algorithm. Consider running the example a few times and compare the average performance.

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Baseline: 81.68% (7.26%) |

This is an excellent score without doing any hard work.

## 3. Re-Run The Baseline Model With Data Preparation

It is a good practice to prepare your data before modeling.

Neural network models are especially suitable to having consistent input values, both in scale and distribution.

An effective data preparation scheme for tabular data when building neural network models is standardization. This is where the data is rescaled such that the mean value for each attribute is 0 and the standard deviation is 1. This preserves Gaussian and Gaussian-like distributions whilst normalizing the central tendencies for each attribute.

We can use scikit-learn to perform the standardization of our Sonar dataset using the StandardScaler class.

Rather than performing the standardization on the entire dataset, it is good practice to train the standardization procedure on the training data within the pass of a cross-validation run and to use the trained standardization to prepare the “unseen” test fold. This makes standardization a step in model preparation in the cross-validation process and it prevents the algorithm having knowledge of “unseen” data during evaluation, knowledge that might be passed from the data preparation scheme like a crisper distribution.

We can achieve this in scikit-learn using a Pipeline. The pipeline is a wrapper that executes one or more models within a pass of the cross-validation procedure. Here, we can define a pipeline with the StandardScaler followed by our neural network model.

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... # evaluate baseline model with standardized dataset estimators = [] estimators.append(('standardize', StandardScaler())) estimators.append(('mlp', KerasClassifier(build_fn=create_baseline, epochs=100, batch_size=5, verbose=0))) pipeline = Pipeline(estimators) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(pipeline, X, encoded_Y, cv=kfold) print("Standardized: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Tying this together, the complete example is listed below.

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# Binary Classification with Sonar Dataset: Standardized from pandas import read_csv from keras.models import Sequential from keras.layers import Dense from keras.wrappers.scikit_learn import KerasClassifier from sklearn.model_selection import cross_val_score from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import StratifiedKFold from sklearn.preprocessing import StandardScaler from sklearn.pipeline import Pipeline # load dataset dataframe = read_csv("sonar.csv", header=None) dataset = dataframe.values # split into input (X) and output (Y) variables X = dataset[:,0:60].astype(float) Y = dataset[:,60] # encode class values as integers encoder = LabelEncoder() encoder.fit(Y) encoded_Y = encoder.transform(Y) # baseline model def create_baseline(): # create model model = Sequential() model.add(Dense(60, input_dim=60, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model # evaluate baseline model with standardized dataset estimators = [] estimators.append(('standardize', StandardScaler())) estimators.append(('mlp', KerasClassifier(build_fn=create_baseline, epochs=100, batch_size=5, verbose=0))) pipeline = Pipeline(estimators) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(pipeline, X, encoded_Y, cv=kfold) print("Standardized: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Running this example provides the results below.

**Note**: Your specific results may vary given the stochastic nature of the learning algorithm. Consider running the example a few times and compare the average performance.

We do see a small but very nice lift in the mean accuracy.

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Standardized: 84.56% (5.74%) |

## 4. Tuning Layers and Number of Neurons in The Model

There are many things to tune on a neural network, such as the weight initialization, activation functions, optimization procedure and so on.

One aspect that may have an outsized effect is the structure of the network itself called the network topology. In this section, we take a look at two experiments on the structure of the network: making it smaller and making it larger.

These are good experiments to perform when tuning a neural network on your problem.

### 4.1. Evaluate a Smaller Network

I suspect that there is a lot of redundancy in the input variables for this problem.

The data describes the same signal from different angles. Perhaps some of those angles are more relevant than others. We can force a type of feature extraction by the network by restricting the representational space in the first hidden layer.

In this experiment, we take our baseline model with 60 neurons in the hidden layer and reduce it by half to 30. This will put pressure on the network during training to pick out the most important structure in the input data to model.

We will also standardize the data as in the previous experiment with data preparation and try to take advantage of the small lift in performance.

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... # smaller model def create_smaller(): # create model model = Sequential() model.add(Dense(30, input_dim=60, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model estimators = [] estimators.append(('standardize', StandardScaler())) estimators.append(('mlp', KerasClassifier(build_fn=create_smaller, epochs=100, batch_size=5, verbose=0))) pipeline = Pipeline(estimators) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(pipeline, X, encoded_Y, cv=kfold) print("Smaller: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Tying this together, the complete example is listed below.

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# Binary Classification with Sonar Dataset: Standardized Smaller from pandas import read_csv from keras.models import Sequential from keras.layers import Dense from keras.wrappers.scikit_learn import KerasClassifier from sklearn.model_selection import cross_val_score from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import StratifiedKFold from sklearn.preprocessing import StandardScaler from sklearn.pipeline import Pipeline # load dataset dataframe = read_csv("sonar.csv", header=None) dataset = dataframe.values # split into input (X) and output (Y) variables X = dataset[:,0:60].astype(float) Y = dataset[:,60] # encode class values as integers encoder = LabelEncoder() encoder.fit(Y) encoded_Y = encoder.transform(Y) # smaller model def create_smaller(): # create model model = Sequential() model.add(Dense(30, input_dim=60, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model estimators = [] estimators.append(('standardize', StandardScaler())) estimators.append(('mlp', KerasClassifier(build_fn=create_smaller, epochs=100, batch_size=5, verbose=0))) pipeline = Pipeline(estimators) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(pipeline, X, encoded_Y, cv=kfold) print("Smaller: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Running this example provides the following result. We can see that we have a very slight boost in the mean estimated accuracy and an important reduction in the standard deviation (average spread) of the accuracy scores for the model.

**Note**: Your specific results may vary given the stochastic nature of the learning algorithm. Consider running the example a few times and compare the average performance.

This is a great result because we are doing slightly better with a network half the size, which in turn takes half the time to train.

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Smaller: 86.04% (4.00%) |

### 4.2. Evaluate a Larger Network

A neural network topology with more layers offers more opportunity for the network to extract key features and recombine them in useful nonlinear ways.

We can evaluate whether adding more layers to the network improves the performance easily by making another small tweak to the function used to create our model. Here, we add one new layer (one line) to the network that introduces another hidden layer with 30 neurons after the first hidden layer.

Our network now has the topology:

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60 inputs -> [60 -> 30] -> 1 output |

The idea here is that the network is given the opportunity to model all input variables before being bottlenecked and forced to halve the representational capacity, much like we did in the experiment above with the smaller network.

Instead of squeezing the representation of the inputs themselves, we have an additional hidden layer to aid in the process.

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... # larger model def create_larger(): # create model model = Sequential() model.add(Dense(60, input_dim=60, activation='relu')) model.add(Dense(30, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model estimators = [] estimators.append(('standardize', StandardScaler())) estimators.append(('mlp', KerasClassifier(build_fn=create_larger, epochs=100, batch_size=5, verbose=0))) pipeline = Pipeline(estimators) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(pipeline, X, encoded_Y, cv=kfold) print("Larger: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Tying this together, the complete example is listed below.

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# Binary Classification with Sonar Dataset: Standardized Larger from pandas import read_csv from keras.models import Sequential from keras.layers import Dense from keras.wrappers.scikit_learn import KerasClassifier from sklearn.model_selection import cross_val_score from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import StratifiedKFold from sklearn.preprocessing import StandardScaler from sklearn.pipeline import Pipeline # load dataset dataframe = read_csv("sonar.csv", header=None) dataset = dataframe.values # split into input (X) and output (Y) variables X = dataset[:,0:60].astype(float) Y = dataset[:,60] # encode class values as integers encoder = LabelEncoder() encoder.fit(Y) encoded_Y = encoder.transform(Y) # larger model def create_larger(): # create model model = Sequential() model.add(Dense(60, input_dim=60, activation='relu')) model.add(Dense(30, activation='relu')) model.add(Dense(1, activation='sigmoid')) # Compile model model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) return model estimators = [] estimators.append(('standardize', StandardScaler())) estimators.append(('mlp', KerasClassifier(build_fn=create_larger, epochs=100, batch_size=5, verbose=0))) pipeline = Pipeline(estimators) kfold = StratifiedKFold(n_splits=10, shuffle=True) results = cross_val_score(pipeline, X, encoded_Y, cv=kfold) print("Larger: %.2f%% (%.2f%%)" % (results.mean()*100, results.std()*100)) |

Running this example produces the results below.

**Note**: Your specific results may vary given the stochastic nature of the learning algorithm. Consider running the example a few times and compare the average performance.

We can see that we do not get a lift in the model performance. This may be statistical noise or a sign that further training is needed.

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Larger: 83.14% (4.52%) |

With further tuning of aspects like the optimization algorithm and the number of training epochs, it is expected that further improvements are possible. What is the best score that you can achieve on this dataset?

## Summary

In this post, you discovered the Keras Deep Learning library in Python.

You learned how you can work through a binary classification problem step-by-step with Keras, specifically:

- How to load and prepare data for use in Keras.
- How to create a baseline neural network model.
- How to evaluate a Keras model using scikit-learn and stratified k-fold cross validation.
- How data preparation schemes can lift the performance of your models.
- How experiments adjusting the network topology can lift model performance.

Do you have any questions about Deep Learning with Keras or about this post? Ask your questions in the comments and I will do my best to answer.

Excellent post with straightforward examples. Thanks for posting Jason!

You’re very welcome Matt.

Hi Jason,

How can we use a test dataset here, I am new to machine Learning and so far I have only come across k-fold methods for accuracy measurements, but I’d like to predict on a test set, can you share an example of that.

Thank you.

Hi Shanky,

There is an example of evaluating a neural network on a manual verification dataset while the model is being fit here:

http://machinelearningmastery.com/evaluate-performance-deep-learning-models-keras/

You can use the model.evaluate() function to evaluate your fit model on new data, there is an example at the end of this deep learning tutorial:

http://machinelearningmastery.com/tutorial-first-neural-network-python-keras/

You can learn more about test options for evaluating machine learning algorithms here:

http://machinelearningmastery.com/how-to-choose-the-right-test-options-when-evaluating-machine-learning-algorithms/

Hi Jason,

After following this tutorial successfully I started playing with the model to learn more.

Eventually I got to the point where I added model.predict inside the baseline.

However when I print back the predicted Ys they are scaled. Is there a way to use standard scalar and then get your prediction back to binary?

Thanks

Hi Paul, I would advise you to scale your data before hand and keep the coefficients used to scale, then reuse them later to reverse the scaling of predictions.

Hi Jason,

great post! Very helpful introduction to binary classification in Keras.

I was wondering, how would one print the progress of the model training the way Keras usually does in this example particularly?

Thanks Cedric.

You can print progress with an epoch by setting verbose=1 in the call to model.fit(). You can just see progress across epochs by setting verbose=2 and turin off output with verbose=0.

Progress is turned off here because we are using k-fold cross validation which results in so many more models being created and in turn very noisy output.

Hello Jason,

Excellent tutorial. Consider a situation now. Suppose the data set loaded by you is the training set and the test set is given to you separately. I created the model as you described but now I want to predict the outcomes for test data and check the prediction score for the test data. How can I do that ?

You can use model.predict() to make predictions and then compare the results to the known outcomes.

This post provides an example of what you want:

http://machinelearningmastery.com/5-step-life-cycle-neural-network-models-keras/

Dear Jason,

Thanks for this excellent tutorial , may I ask you regarding this network model; to which deep learning models does it belong? is it Deep Belief Network, CNN, stacked auto-encoder or other?

Thanks in advance

It is a deep neural network.

Note that the DBN and autoencoders are generally no longer mainstream for classification problems like this example.

CNN are state of the art and used with image data.

I hope this helps.

Hello Dr. Brownlee,

I’m sorry that I don’t get your point on the statement “…DBN and autoencoders are generally no longer mainstream for classification problems…”. I read on paper where they have used DBN for prediction of success of movies. They mentioned that they used a 2-layer DBN that yielded best accuracy.

Yes, my understanding is that CNNs are currently state of the art for text-classification.

That does not stop new papers coming out on old methods.

Thanks Jason for you reply, I have another question regarding this example. How can I know the reduced features after making the network smaller as in section 4.1. you have obliged the network to reduce the features in the hidden layer from 60 to 30. how can I know which features are chosen after this step? also can I know the weight that each feature got in participation in the classification process?

Hi Sally,

The features are weighted, but the weighting is complex, because of the multiple layers. It would not be accurate to take just the input weights and use that to determine feature importance or which features are required.

The hidden layer neurons are not the same as the input features, I hope that is clear. Perhaps I misunderstand your question and you can elaborate what you mean?

Hi Jason,

My case is as follows: I have something similar to your example. I have a deep Neural network with 11 features. I used a hidden layer to reduce the 11 features to 7 and then fed it to a binary classifier to classify the values to A class or B class. The first thing I need to know is that which 7 features of the 11 were chosen? can I have a way in the code to list them? the second thing I need to know is the average value for each feature in the case of classifying the record as class A or B. In more details; when feature 1 have an average value of 0.5 , feature 2 have average value of 0.2, feature 3 value of 0.3 ,,, etc. then the record is classified as class A. I need something like that; how can I have such value ?

Hi Sally,

The number of nodes in a hidden layer is not a subset of the input features. They are an entirely new nonlinear recombination of input data. You cannot list out which features the nodes in a hidden layer relate to, because they are new features that relate to all input features. Does that make sense?

Oh Yup!! I thought it is a kind of features selection that is done via the hidden layers!! so that if I need to make a feature selection I have to do it before creating the model. The second question that I did not get answer for it, is how can I measure the contribution of each feature at the prediction? in another words; how can I get the ” _features_importance_” . I tried to do it in the code but it is not applied to the “pipeline” model in line 16. Where can I use the function of “features_importance “to view each feature contribution in the prediction

Hi Sally, you may be able to calculate feature importance using a neural net, I don’t know. You may have to research this question yourself sorry.

I search it but unfortunately I did not get it 🙁 .. Thanks for your cooperation

Hi Jason,

Excellent tutorial indeed!!!

While using PyDev in eclipse I ran into trouble with following imports …

from keras.models import Sequential

from keras.layers import Dense

I downloaded latest keras-master from git and did

sudo python setup.py install because my latest PIP install of keras gave me import errors. [Had to remove it.]

Hope it helps someone. My two cents, contributing to your excellent post.

Thanks a ton! Once again.

Warm regards,

Sunil M

Thanks for the note Sunil.

I’m not an IDE user myself, command line all the way.

Dear Jason,

I have another question regarding this example. As you know; deep learning performs well with large data-sets and mostly overfitts with small data-sets. The dataset in this example have only 208 record, and the deep model achieved pretty good results. How can this meet the idea of deep learning with large datasets?

Hi Sally,

Don’t read too much into it. It is a demonstration of an MLP on a small binary classification problem.

MLPs scale. If the problem was sufficiently complex and we had 1000x more data, the model performance would continue to improve.

Thanks Jason for the reply, but could you please explain me how you find out that the data is 1000x ?? you have 208 record with 60 input value for each? did you multiply them to get this number? so that we can have the determine that a data is complex or not? another this could you help me by published articles that approve that MLP scale if the problem was complex?? Sorry for all these question but I am working on some thing relevant on my project and I need to prove and cite it

Sorry, no, I meant if we had one thousand times the amount of data.

In multiple category classification like MNIST we have 10 outputs for everyone of 0 to 9.

Why in binary classification we have only 1 output? We should have 2 outputs for each 0 and 1. Can you explain.

Great question Sidharth.

We can use two output neurons for binary classification.

Alternatively, because there are only two outcomes, we can simplify and use a single output neuron with an activation function that outputs a binary response, like sigmoid or tanh.

They are generally equivalent, although the simpler approach is preferred as there are fewer weights to train.

Finally, you can one output neuron for a multi-class classification if you like and design a custom activation function or interpret a linear output value into the classes. This approach often does not capture sufficient complexity in the problem – e.g. like the network wanting to suggest an input may have potential membership in more than one class (a confusing input pattern) and it assumes an ordinal relationship between classes which is often invalid.

I dont get it, how and where you do that.

Do you use 1 output node and if the sigmoid output is =0.5) is considered class B ??

Is that correct? Where in the code do you do that?

Hi Jason. Thanks. Your tutorials are really helpful!

I made a small network(2-2-1) which fits XOR function.

I found that without numpy.random.seed(seed) accuracy results can vary much.

Sometimes it learns quickly but in most cases its accuracy just remain near 0.25, 0.50, 0.75 etc…

So I needed to try several times to find some proper seed value which leads to high accuracy.

Is it common to try several times with the same model until it succeeds?

Also there was a case where it’s trapped in the local optimum but after a long time it gets out of it and accuracy reach 1.0

What if there’s a very big network and it takes 2~3 weeks to train it?

Do people just start training and start it again if there is not much improvement for some time?

Do people run the same model with different initialization values on different machines?

Is there any method to know if its accuracy will go up after a week?

Thank you!

Great questions, see this post on randomness and machine learning:

http://machinelearningmastery.com/randomness-in-machine-learning/

I hope that helps as a start.

Hi Jason. Thanks for the tutorial.

I want to implement autoencoder to do image similarity measurement. Cloud you please provide some tips/directions/suggestions to me how to figure this out ? Thanks

Sorry, I do not have an example of using autoencoders.

Hi Brownlee:

How would I save and load the model of KerasRegressor.

estimator = KerasRegressor(…)

I use estimator.model.save(), it works,

but it should call estimator.fit(X, Y) first, or it would throw “no model” error.

Besides, I have no idea about how to load the model to estimator.

It is easier to use normal model of Keras to save/load model, while using Keras wrapper of scikit_learn to save/load model is more difficult for me.

Would you please tell me how to do this.

Thanks a lot.

Hi Chan, you could try pickle?

I find it easier to use KerasClassifier to explore models and tuning, and then using native Keras with save/load for larger models and finalizing the model.

Awesome tutorial, one of the first I’ve been able to follow the entire way through.

I would love to see a tiny code snippet that uses this model to make an actual prediction. I figured it would be as easy as using

`estimator.predict(X[0])`

, but I’m getting errors about the shape of my data being incorrect (None, 60) vs (60, 1).I’m glad to hear it Emerson.

Yes, you can make a prediction with:

You may need to reshape your data into a 2D array:

Hi Jason, such an amazing post, congrats! I have some doubts regarding Emerson’s question and your answer.

I want to separate cross-validation and prediction in different stages basically because they are executed in different moments, for that I will receive to receive a non-standardized input vector X with a single sample to predict. I was able to save the model using callbacks so it can be reused to predict but I’m a bit lost on how to standardize the input vector without loading the entire dataset before predicting, I was trying to pickle the pipeline state but nothing good came from that road, is this possible? do you have any example on how to do it? Thanks!

To standardize all you need is the mean and standard deviation of the training data for each variable.

Fantastic tutorial Jason, thank you. Here’s my Jupyter notebook of it: https://github.com/ChrisCummins/phd/blob/master/learn/keras/Sonar.ipynb

Nice work Chris.

I have a difficult question. I have google weekly search trends data for NASDAQ companies, over 2 year span, and I’m trying to classify if the stock goes up or down after the earnings based on the search trends, which leads to104 weeks or features. I ran this data and received no signal Results: 48.55% (4.48%).

However, in my non machine learning experiments i see signal. If i take the diffs (week n – week n+1), creating an array of 103 diffs. I then average out all the stocks that went up and average out all the stocks that went down. When i predict a new stock for the same 2 year time period, I compare in a voting like manner week n of new stock to week n of stocks labeled up, and labeled down. Whoever has more votes wins. In this simple method i do see signal.

Thoughts?

Short term movements on the stock market are a random walk. The best you can do is a persistence forecast as far as I know.

But I’m not comparing movements of the stock, but its tendency to have an upward day or downward day after earnings, as the labeled data, and the google weekly search trends over the 2 year span becoming essentially the inputs for the neural network. So then it becomes a classification problem.

As described above in the 2nd paragraph i see signal, based on taking the average of the weeks that go up after earnings vs ones that go down, and comparing the new week to those 2 averages. I’m just not sure how to interpret that into a neural network.

BTW, awesome tutorial, i will follow all of your tutorials.

I meant to say i take the average of each week for all the labeled companies that go up after earnings creating an array of averages, and same for the companies that go down after earnings. I then compare the weeks of the new stock, over the same time period to each of the prior arrays. An i do see signal, but how to make that work with neural networks.

Another question. Using this methodology but with a different set of data I’m getting accuracy improvement with each epoch run. But in the end i get Results: 52.64% (15.74%). Any idea why? I thought results were related to the average accuracy.

Epoch 1/10

0s – loss: 1.1388 – acc: 0.5130

Epoch 2/10

0s – loss: 0.6415 – acc: 0.6269

Epoch 3/10

0s – loss: 0.4489 – acc: 0.7565

Epoch 4/10

0s – loss: 0.3568 – acc: 0.8446

Epoch 5/10

0s – loss: 0.3007 – acc: 0.8808

Epoch 6/10

0s – loss: 0.2611 – acc: 0.9326

Epoch 7/10

0s – loss: 0.2260 – acc: 0.9430

Epoch 8/10

0s – loss: 0.1987 – acc: 0.9689

Epoch 9/10

0s – loss: 0.1771 – acc: 0.9741

Epoch 10/10

0s – loss: 0.1556 – acc: 0.9741

Results: 52.64% (15.74%)

Perhaps the model is overfitting the training data?

Consider slowing down learning with some regularization methods like dropout.

Hi Jason,

Can this type of classifier (which described in this tutorial) can be used for ordinal classification (with binary classification)?

Thanks,

I would use the network as is or phrase the problem as a regression problem and round results.

Hello Jason,

How can I save the pipelined model?

I mean in the past it was easy when we only implemented a model and we fit it …

but now how can I save this in order to load it and make predictions later on?

I believe you cannot save the pipelined model.

You must use the Keras API alone to save models to disk. At least as far as I know.

Hi Jason,

“You must use the Keras API alone to save models to disk” –> any chance you’d be willing to elaborate on what you mean by this, please? I’ve been trying to save the model from your example above using pickle, the json-method you explained here: https://machinelearningmastery.com/save-load-keras-deep-learning-models/ , as well the joblib method you explained here: https://machinelearningmastery.com/save-load-machine-learning-models-python-scikit-learn/ . However, none of them work. Pickle gives the following error:

_pickle.PicklingError: Can’t pickle : attribute lookup module on builtins failed

Using json gives this error:

AttributeError: ‘Pipeline’ object has no attribute ‘to_json’

… and for the joblib approach I get the error message

TypeError: can’t pickle SwigPyObject objects

I have tried googling the SwigPyObject for more info, but haven’t found anything useful. Any advice you’d be able to offer would be great.

Thanks in advance.

As far as I know, we cannot save a sklearn wrapped keras model. We must use the Keras API directly to save/load the model.

Thanks a lot for this great post! I am trying to learn more about machine learning and your blog has been a huge help.

Any idea why I would be getting very different results if I train the model without k-fold cross validation? e.g. If I run

model = create_baseline()

model.fit(X, encoded_Y, epochs=100, batch_size=5, validation_split=0.3)

It outputs a val_acc of around 0.38. But if I run your code using k-fold I am getting an accuracy of around 75%

Full code snippet is here https://gist.github.com/robianmcd/e94b4d393346b2d62f9ca2fcecb1cfdf

Any idea why this might be happening?

Hi Rob, yes neural networks are stochastic. See this post:

http://machinelearningmastery.com/randomness-in-machine-learning/

See here for how to get a more robust estimate of neural network model skill:

http://machinelearningmastery.com/evaluate-skill-deep-learning-models/

I ran it many times and I was consistently getting around 75% accuracy with k-fold and 35% without it. Turns out I wasn’t shuffling the array when I wasn’t using k-fold so the validation target set was almost all 1s and the training set was mostly 0s. I added

`numpy.random.shuffle(dataset)`

and it’s all good now.I’m glad to hear you got to the bottom of it Rob!

Hi Jason,

In this post you mentioned the ability of hidden layers with less neurons than the number of neurons in the previous layers to extract key features.

Is it possible to visualize or get list of these selected key features in Keras? (For exmaple, for networks with high number of features)?

Thanks,

Michael

You may, I am not aware if an example sorry.

Hi I would love to see object location / segmentation network for identifying object locations and labeling them.

Thanks for the suggestion joseph.

Hi Jason, how do we know which structure is best for a neural network? Any resources you could point me to?( I don’t mind going through the math)

Nope. There is no good theory for this.

Copy other designs, use trial and error. Design robust experiments to test many structures.

Thanks for your sharing.

I’m glad it helped!

Thank you for sharing, but it needs now a bit more discussion –

see http://www.cloudypoint.com/Tutorials/discussion/python-solved-can-i-send-callbacks-to-a-kerasclassifier/

Glad to hear it.

Hi Jason! Thanks so much for this very concise and easy to follow tutorial! One question: if you call native Keras model.fit(X,y) you can also supply validation_data, such that validation score is printed during training (if verbose=1). Do you know how to switch this feature on in the pipeline? sklearn creates the split automatically within the cross_val_score step, but how to pass this on to the Keras fit method…?

Thanks a lot!

No and I would not recommend it. I think it would cause more problems.

Hi Jason,

Is there any way to use class_weight parameter in this code?

Thanks,

Biswa

Yes, set class_weight in the fit() function.

More help here:

https://keras.io/models/sequential/

Thanks for the great post Jason!

How to use class_weight when I use cross_val_score and I don’t use fit(), as you did in this post?

Thanks,

Don

Sorry, I don’t have examples of using weighted classes.

Good day interesting article. I am currently doing an investigation, it is a comparative study of three types of artificial neural network algorithms: multilayer perceptron, radial and recurrent neural networks. Well I already work the algorithms and I’m in training time, everything is fine until I start this stage unfortunately I can not generalize the network, and try changing parameters such as learning reason and number of iterations, but the result remains the same. The input data (dataset) that input are binary ie a pattern for example has (1,0,0,1,1,0,0,1,0,1,1,1) the last indicator being the desired output , I also noticed that when the weights converge and I use them in the validation stage, all the results are almost the same is as if there would be no difference in the patterns. Well now I am doing cross validation hoping to solve this problem or to realize what my error may be. I would appreciate your help or advice

Generally, I would recommend this process for evaluating your model:

https://machinelearningmastery.com/evaluate-skill-deep-learning-models/

Perhaps you can calculate some diagnostics like learning rate on a training and validation datasets?

Hi Jason or anyone active here:

could you please advise on what would be considered good performance of binary classification regarding precision and recall? I have got:

class precision recall f1-score support

0 0.88 0.94 0.91 32438

1 0.80 0.66 0.72 11790

avg / total 0.86 0.86 0.86 44228

Accuracy: 0.864520213439

I wish to improve recall for class 1. Would appreciate if anyone can provide hints.

Thanks in advance.

A “good” result is really problem dependent and relative to other algorithm performance on your problem.

Thanks Jason,

actually i have binary classification problem, i have written my code, just i can see the accuracy of my model, so if i want to see the output of my model what should i add to my code? i mean when it recieves 1 or 0 , at the end it shows to me that it is 1 or 0?

You can make predictions with your final model as follows:

Does that help?

Hi,

I am trying to classify an image. I have used classifier as softmax, loss as categorical_crossentropy. while I am testing the model I am getting the probabilities but all probabilities is equal to 1. But I want to get the probability of classes independently. I have tried with sigmoid and loss as binary_crossentropy. here i am getting the accuracy 85% but its not giving the probabilities independently like clarifai website.

How do I can achieve? can you please suggest ?

Perhaps check-out this tutorial:

http://machinelearningmastery.com/object-recognition-convolutional-neural-networks-keras-deep-learning-library/

Thanks for the great tutorial. I wanted to mention that for some newer versions of Keras the above code didn’t work correctly (due to changes in the Keras API).

The most notable change that took me a while to debug is that “nb_epoch=100” has to be changed to “epoch=100” or the cross validation steps will only go for 1 epoch resulting in poor model performance overall (~55% instead of 81%). Turns out that “nb_epoch” has been depreciated. Hope this comment helps someone.

It should work with Keras 2.1.2.

@Cody is right, “b_epoch” has to be changed with “epochs”, otherwise it will be ignored, and the training will run just for 1 epoch for each fold (Keras 2.1.3)

Fixed, thanks.

My loss value keep on constant its not even decreasing after 4 epochs and accuracy not even increasing,which parameters i have update to tune the RNN binary classification probelm.

Please help in that .

model = Sequential()

model.add(LSTM(100, input_shape=(82, 1),activation=’relu’))

#model.add(Dense(60, input_dim=60, kernel_initializer=’normal’, activation=’relu’))

model.add((Dense(80,activation=’tanh’)))

model.add((Dense(40,activation=’tanh’)))

model.add((Dense(20,activation=’tanh’)))

model.add(Dense(1,activation=’sigmoid’))

model.compile(loss=’binary_crossentropy’, optimizer=’adam’,metrics=[“accuracy”])

#print(model.summary())

model.fit(trainX,trainY, nb_epoch=200, batch_size=4, verbose=2,shuffle=False)

Please suggest me in this scenario .

Perhaps try training for longer, 100s of epochs.

Perhaps spot check on less data.

Here are more ideas to try:

http://machinelearningmastery.com/improve-deep-learning-performance/

which optmizer is suitable for binary classification i am giving rmsprop .

i am having less no of samples with me.

can i train with more epochs and less batch size ,is it suitable to increase my accuracy of model.

Perhaps try it and see.

Hi Jason, when testing new samples with a trained binary classification model, do the new samples need to be scaled before feeding into the model? What if there is only one sample? Thanks David

Yes, data must be prepared in exact same way. Even a single sample.

Hi Jason! It is really kind of you to contribute this article. Albeit how do I classify a new data set (60 features)? I think there is no code snippet for this. I mean really using the trained model now.

Once you train your final model you can make predictions by calling model.predict(X).

Perhaps this post will make it clearer:

https://machinelearningmastery.com/train-final-machine-learning-model/

Thank you very much for this. This is an excellent introduction to Keras for me and I adapted this code in minutes without any problems. The explanation was perfect too. Much appreciated.

I’m glad it helped.

Great article, thanks!

I’m glad it helped.

Hi Jason,

Thank you very for the great tutorial, it helps me a lot.

Please I have two questions,

1- I have a binary classification problem, please any idea how to choose the right architecture of neural network , RNN or CNN or …. ?

2- Is there any to way use machine learning classifier like K-Means, DecisionTrees, excplitly in your code above? because you used KerasClassifier but I don’t know which algorithm is used for classification.

Thank you again

Use an MLP, more here:

https://machinelearningmastery.com/when-to-use-mlp-cnn-and-rnn-neural-networks/

You can use sklearn to test a suite of other algorithms, more here:

https://machinelearningmastery.com/spot-check-classification-machine-learning-algorithms-python-scikit-learn/

Thank you very much again M.Jason.

You’re welcome.

This article was very helpful! 🙂

I have a question. In this article you have used all continuous variables to predict a binary variable. How to proceed if the inputs are a mix of categorical and continuous variables?

Categorical inputs can be integer encoded, one hot encoded or some other encoding prior to modeling.

Hello,

I have a question. I am using Functional API of keras (using dense layer) & built a single fully connected NN. I see that the weight updates happens based on several factors like optimization method, activation function, etc. etc. Suppose, assume that I am using a real binary weight as my synapse & i want to use a binary weight function to update the weight such that I check weight update (delta w) in every iteration & when it is positive I decide to increase the weight & when it is negative I want to decrease the weight. How can it be done using keras ??

I read that keras is very limited to do this. Is it true ?? FYI, I use the syntax dense to define my layers & input to define the inputs. Is it possible to add a binary weight deciding function using dense layers in keras ?

Thanks in advance 🙂

Hi Jason,

Thanks for the post. A couple of questions.

1) The data has 260 rows. If i look at the number of params in the deeper network it is 6000+ . Shouldn’t the number of rows be greater than the number of params?

2) How can we use the cross-validated model to predict. Do we just take the last model and predict ?

No, we can over-specify the model and still achieve low generalization error. This is also true for statistical methods through the use of regularization.

We do not use CV to predict. CV is only used to estimate the generalization error of the model. Learn more here:

https://machinelearningmastery.com/faq/single-faq/how-do-i-make-predictions

Hello Jason,

I am new to Deep Learning, here is my deep learning first program is Sonar data with keras , while fitting the model i got an error i’m unable to understanding that:

‘ValueError: Error when checking input: expected dense_13_input to have shape (20,) but got array with shape (60,)’

could please help me where did i make mistake… Thank you Jason…here is my program code:

The error suggests the expectations of the model and the actual data differ. You can change the model or change the data.

hi sir …

sir is it possible that every line should contain some brief explanation for example

import numpy :(numpy is library of scientific computation etc.

so i can understand the functionality of every line easily.

thanks.

Thanks for the suggestion.

Hola Jason:

Thank you. I could not have enough time to go through your tutorial , but from other logistic regression (binary classification)tutorials of you, I have a general question:

1) As in multi-class classification we put as many units on the last or output layers as numbers of classes , could we replace the single units of the last layer with sigmoid activation by two units in the output layer with softmax activation instead of sigmoid, and the corresponding arguments of loss for categorical_crossentropy instead of binary_cross entropy in de model.compilation?

1.1) If it is possible this method, is it more efficient than the “classical” of unit only in the output layer?

many thanks

Yes, you can have 2 nodes with softmax for binary classification.

It often does not make a difference and we have less complexity by using a single node.

‘encoded_Y’ is ‘Y’? Is not defined before.

It is defined in section 2 of the post.

Hi Jason.

Thank you for an interesting and informative article.

I am new to ANN and am not a Python programmer, so cannot “look inside” those Keras functions you used. But I have a general (and I am sure very basic) question about your example.

If I understand correctly, you constructed a neural net with 60 nodes (same as the number of predictor variables) in the input layer, a single hidden layer and an output layer with just one node for the predicted binary variable. It seems to me then that you needed to train your net for each record in your dataset separately. And as a result obtain as many sets of optimal node weights as there are records in the dataset (208 total). How then can you integrate them into just one final set? If you do something like averaging all 208 weights for each node, how then can the resultant net perform well? And without it, how can the net be tested and later used for actual predictions? I am truly confused.

Do my questions make any sense?

Thank you,

Igor

Not really, a single set of weights is updated during training.

Perhaps this will make things clearer:

https://machinelearningmastery.com/implement-backpropagation-algorithm-scratch-python/

thank you for the good explain

how i can save a model create baseline() plz answer me?

Yes, this post shows you how to save a model:

https://machinelearningmastery.com/save-load-keras-deep-learning-models/

for binary claasificaiton why we have to give 1 in output layer and sigmoid layer as activation function ,is their any particular reason .

Yes, it can predict the probability directly. It’s efficient and effective.

Hi Jason

Thanks for your excellent post.

I just want to start DNN with Keras . Would you please introduce me a practical tutorial according to Keras library most in case of classification?

Cheers

S

Yes, you can get started here:

https://machinelearningmastery.com/start-here/#deeplearning

Hi Jason

Thanks for this tutoriel but what about the test phase ?

You can use model.evaluate() to estimate the performance of the model on unseen data.

Does that help?

Sir, the result from this code is around 55% not 81%, without optimizing the NN.

Here my code for checking errors or what else:

I expect normalizing the data first might help.

Hi Jason,

I have a binary classification problem where classes are unbalanced. For example, 72000 records belongs to one class and 3000 records to the other. Is there a way to mark some kind of weights between classes in order to give more relevance to the less common class?

I’ve found class_weights but I doesn’t work with 3D data.

Could you give and idea to solve the problem?

Thank you in advanced!

Yes, I have some ideas here that might help:

https://machinelearningmastery.com/tactics-to-combat-imbalanced-classes-in-your-machine-learning-dataset/

Thank you Jason!

Hello Jason,

I wonder if the options you mention in the above link can be used with time series as some of them modify the content of the dataset. I’m not sure what to use.

Thank you.

Not really, I expect you may need specialized methods for time series.

And what specialized methods can I use to solve the problem for time series?

Sorry, I don’t have many tutorials on time series classification, I do have a few here:

https://machinelearningmastery.com/start-here/#deep_learning_time_series

Hello Jason, I enjoy your tutorials to learn ML and feel you are very helpful to us. I saw that in this post you have used LabelEncoder. If you use this, then doesn’t it mean that when you assign values to categorical labels then there is a meaning between intergers i.e. 0 < 1 is interpreted by the model.

While reading elsewhere, I saw that when you have labels where the order of integers is unimportant, then you must use OneHotEncoder. I am not sure if it makes any difference here, please clarify if you are aware.

https://medium.com/@contactsunny/label-encoder-vs-one-hot-encoder-in-machine-learning-3fc273365621

Yes, if the input is integer encoded then the model may infer an ordinal relationship between the values.

If no such relationship is real, it is recommended to use a OHE.

Thanks. 🙂

Hi Jason,

Thank you for your nice explanations!

I have a question about the cross-validation part in your code, which gives us a good view of the generalization error.

Does the use of cross-validation enable us to select the right weights for the neural network? Is it like using CV for a logistic regression, which would select the right complexity of the model in order to reach bias-variance tradeoff? What is the CV doing precisely for your neural network?

About the process, I guess that the network trains itself on the whole training data. Then, the network can be validated on 10 randomly shuffled pieces of the training dataset (10-fold CV). Am I right? Then, I get the accuracy score of the classification performance of the model, as well as its standard deviation?

So, if I want to test my model on new data, then I can do what Aakash Nain and you have nicely proposed?

Thank you!

Best,

Jonathan

Yes, we can use CV to estimate the performance of a specific model/config, as we do for other algorithms.

You can learn how CV works here:

https://machinelearningmastery.com/k-fold-cross-validation/

If you want to make predictions, you must fit the model on all available data first:

https://machinelearningmastery.com/train-final-machine-learning-model/

Then use that model to make predictions:

https://machinelearningmastery.com/how-to-make-classification-and-regression-predictions-for-deep-learning-models-in-keras/

Thank you Jason.

Another question, does it make sense to use like 75% of my data for training and CV, and then the remaining 25% for testing my model ?

I am making a MLP for classification purpose. In my case, doing CV would evaluate the performance. However, making a separated test set would be better if I want to give to the model unseen data, right ?

Thanks!

Jonathan

Perhaps. It really depends on the problem and how representative the 25% is of the broader problem. If it’s too small it might give misleading/optimistic results.

Hi,

Why isn’t there a .fit() method used here?

We are using the sklearn wrapper instead.

Thank you :). One more question, cause it may be me being blind. The only way I see the data set linked to the model is through cross validation that takes the X and endoded_Y. What is it that I am missing here?

R

A model learns to map input to output.

Most models achieve this by taking input, making a prediction, and comparing the prediction to the expected values, then updating the model toward making predictions closer to the expected values. Repeat.

Does that help?

Jason,

It does indeed – the inner workings of this model are clear. I am wondering if you have a model as a function here, how would you serialise it?

You must use the Keras API directly in order to save the model:

https://machinelearningmastery.com/save-load-keras-deep-learning-models/

I have a mixed data-set(categorical and numerical features). Does this method will be suitable with such data?

Yes, although you may need to integer encode or one hot encode the categorical data first.

Why do you use accuracy to evaluate the model in this dataset? Is it not an imbalanced dataset?

It is imbalanced, but not severely. Accuracy is reasonable as long as it is compared to a baseline/naive result.

How to determine the no of neurons to build our layer with? Does it depend on the no of features?? Say i have 40 features.. what should be the optimal no of neurons ?

This is a common question that I answer here:

https://machinelearningmastery.com/faq/single-faq/how-many-layers-and-nodes-do-i-need-in-my-neural-network

Hey

How can we implement neural networks on 6 million binary data with 128 columns?

I mean what will be the units, the activation function, batch size and the epochs?

Thanks in advance

Start with a smaller sample of the dataset, more details here:

https://machinelearningmastery.com/faq/single-faq/how-to-i-work-with-a-very-large-dataset

Hi Jason,

I’ve read many of your posts, which are all excellent, congrat!

I’ve a question regarding the probabilities output in the case of binary classification with binary_crossentropy + sigmoid with Keras/TF

I’ve read many time this is the way of doing to have real (calibrated) probabilities as an output.

In order to verify this, I’ve applied the calibration curve to my model, and probabilities results are not meeting my expectations. Especially I don’t understand the fact that on training data this does not give a nearly perfect curve.

Pseudo code I use for calibration curve of training data:

model.fit(X, Y, epochs=nb_epochs, batch_size=5, verbose=2)

..

predictions = model.predict_classes(X)

…

calibration_curve(Y, predictions, n_bins=100)

The results (with calibration curve on test) to be found here:

https://we.tl/t-WwJKqXQFVB

I was wondering If you had any advice on this.

Thanks in advance

Perhaps this tutorial will help in calibrating the predicted probabilities from your model:

https://machinelearningmastery.com/calibrated-classification-model-in-scikit-learn/

Hi Jason, another great tutorial and thank you for that! I have 2 questions in this regards, though:

1) What if my output is a binary image of size 160×160 which includes facial landmarks. Can I use this model but the output should be 160×160 =25600 rather than only one neuron?

2) The paper says they used a shallow MLP with ReLU. This means their model doesn’t have any hidden layers. So, I just need to directly connect the input face features to the output layer to construct landmarks mask?

Thank you so much

If you are predicting an image, you might want to use a different model, like a U-Net.

I don’t know about the paper you’re referring to, perhaps contact the authors?

Thank you for the suggestion, dear Jason. I’ll look into it. This is the paper:

“Synthesizing Normalized Faces from Facial Identity Features”

They create facial landmarks for neutral faces using a MLP. Thank you!