Milk can be classified in terms of its quality into three groups: low quality, medium quality, and high quality.
The central goal is to design a model that makes proper classifications for new milk samples. In other words, one which exhibits good generalization.
- Application type.
- Data set.
- Neural network.
- Training strategy.
- Model selection.
- Testing analysis.
- Model deployment.
1. Application type
This is a classification project. Indeed, the variable to be predicted is categorical (low, medium and high).
The objective is to model the quality of the milk by knowing its characteristics and thus be able to make future predictions.
2. Data set
The first step is to prepare the data set. This is the source of information for the classification problem. For that, we need to configure the following concepts:
- Data source.
The variables are:
- pH: This feature defines pH of the milk, which is in the range of 3 to 9.5.
- temperature: This feature defines the temperature of the milk, and its range is from 34’C to 90’C.
- taste: This feature defines the taste of the milk and takes the possible values: 1 (good) or 0 (bad).
- odor: This feature defines the odor of the milk and takes the possible values: 1 (good) or 0 (bad).
- fat: This feature defines the fat of the milk and takes the possible values: 1 (good) or 0 (bad).
- turbidity: This feature defines the turbidity of the milk and takes the possible values: 1 (good) or 0 (bad).
- colour: This feature defines the color of the milk, which is in the range of 240 to 255.
- grade: This is the target and takes the values: low_quality, medium_quality, or high_quality.
All variables in the study are inputs, except “grade”, which is the output that we want to extract from this machine learning study. Note that “grade” is categorical and can take the values low_quality, medium_quality, and high_quality.
The instances are divided into training, selection, and testing subsets. They represent 60.2% (637), 19.9% (211), and 19.9% (211) of the original instances, respectively, and are randomly split.
The milk dataset contains 429 instances of low quality, 374 instances of medium quality, and 256 instances of high quality. The next figure is the pie chart for the variable milk quality class, and it shows its distribution.
As we can see, the target is not well-distributed. Indeed, there are more samples of low_quality, with 40.5 % of the total samples and only 24.17% of the total samples of high_quality.
3. Neural network
The second step is to choose a neural network. For classification problems, it is usually composed by:
- A scaling layer.
- A perceptron layers.
- A probabilistic layer.
The neural network must have seven inputs since the data set has seven input variables.
The scaling layer normalizes the input values. As our inputs have different distributions, they are scaled with different methods:
- The variables pH, temperature, and colour are scaled with the mean and standard deviation scaling method.
- The variables taste, odor, fat, and turbidity are scaled with the minimum and maximum scaling method.
In this case, as first guest we only use one perceptron layer. This layer contains seven inputs, three neurons, and three outputs. For this example, the perceptron layer is a hyperbolic tangent activation function.
The neural network has three outputs because we have three different “grades”: low_quality, medium_quality and high_quality.
The next figure is a graphical representation of this classification neural network:
4. Training strategy
The next step is to set the training strategy, which is composed of:
- Loss index.
- Optimization algorithm.
The following chart shows how the training and selection errors decrease with the epochs during training.
The final values are training error = 0.252 NSE (blue), and selection error = 0.277 NSE (orange).
Is it important to have low selection error in our model, allowing us to generalize well the new data rather than simply memorizing the training data.
5. Model selection
We want to find a neural network with a selection error of less than 0.277 NSE, which is the value we have achieved so far.
Order selection algorithms train several network architectures with a different number of neurons and select that with the smallest selection error.
The incremental order method starts with a small number of neurons and increases the complexity at each iteration. The following chart shows the training error (blue) and the selection error (yellow) as a function of the number of neurons.
As we can see, the number of neurons that yield the minimum error is four. Therefore, we select the neural network with four neurons in the perceptron layer. The next chart show the new neural network architecture.
The following chart shows how the training and selection errors decrease with the epochs during training in the new neural network. The final values are training error = 0.0877 NSE (blue), and selection error = 0.107 NSE (orange).
With the new architecture of the neural network, we achieve around 50% less selection error.
6. Testing analysis
The purpose of the testing analysis is to validate the generalization performance of the model. Here we compare the neural network outputs to the corresponding targets in the testing instances of the data set.
In the confusion matrix, the rows represent the targets (or real values) and the columns the corresponding outputs (or predictive values).
|Predicted low_quality||Predicted medium_quality||Predicted high_quality||Total|
|Real low_quality||49 (23.2%)||0||4 (1.9%)||53 (23.7%)|
|Real medium_quality||1 (0.5%)||92 (43.6%)||0||93 (43.6%)|
|Real high_quality||0||0||65 (30.8%)||65 (32.7%)|
|Total||50 (23.7%)||92 (43.6%)||69 (32.7%)||211 (100%)|
The number of correctly classified samples is 206, and the number of misclassified samples is 5.
The confusion matrix allows us to calculate the model’s accuracy and error:
- Classification accuracy: 97.6%.
- Error rate: 2.4%.
7. Model deployment
The neural network is now ready to predict outputs for inputs that it has never seen. This process is called model deployment.
To classify a sample of milk, we calculate the neural network outputs. For instance, consider a sample with the following features:
- ph: 6.63
- temperature: 39.2
- taste: 0
- odor: 1
- fat: 1
- turbidity: 1
The neural network outputs for this features are:
- high_quality: 91.2%
- medium_quality: 8.73%
- low_quality: 0.07%
For this particular case, the neural network would classify the sample of milk as being of high_quality since it has the highest probability.
The mathematical expression of the trained neural network is listed below.
scaled_pH = (pH-6.630119801)/1.399680018; scaled_temperature = (temperature-44.22660065)/10.09840012; scaled_taste = taste*(1+1)/(1-(0))-0*(1+1)/(1-0)-1; scaled_odor = odor*(1+1)/(1-(0))-0*(1+1)/(1-0)-1; scaled_fat = fat*(1+1)/(1-(0))-0*(1+1)/(1-0)-1; scaled_turbidity = turbidity*(1+1)/(1-(0))-0*(1+1)/(1-0)-1; scaled_colour = (colour-251.8399963)/4.30742979; perceptron_layer_1_output_0 = tanh( -0.058706 + (scaled_pH*-3.09864) + (scaled_temperature*-2.08141) + (scaled_taste*0.0928608) + (scaled_odor*1.25385) + (scaled_fat*2.07282) + (scaled_turbidity*0.00868495) + (scaled_colour*0.344164) ); perceptron_layer_1_output_1 = tanh( 0.23707 + (scaled_pH*-0.124321) + (scaled_temperature*2.62452) + (scaled_taste*0.903015) + (scaled_odor*0.730532) + (scaled_fat*0.447419) + (scaled_turbidity*0.235073) + (scaled_colour*1.864) ); perceptron_layer_1_output_2 = tanh( 1.37137 + (scaled_pH*3.56574) + (scaled_temperature*-5.7119) + (scaled_taste*-0.719459) + (scaled_odor*0.622088) + (scaled_fat*-1.22018) + (scaled_turbidity*-1.07232) + (scaled_colour*-0.576336) ); perceptron_layer_1_output_3 = tanh( -0.937949 + (scaled_pH*5.19285) + (scaled_temperature*-1.96228) + (scaled_taste*0.552014) + (scaled_odor*1.22828) + (scaled_fat*1.60562) + (scaled_turbidity*1.39285) + (scaled_colour*0.712061) ); probabilistic_layer_combinations_0 = -2.21108 +3.43582*perceptron_layer_1_output_0 -0.0137288*perceptron_layer_1_output_1 -0.730089*perceptron_layer_1_output_2 +5.37976*perceptron_layer_1_output_3 probabilistic_layer_combinations_1 = 2.80993 -2.64362*perceptron_layer_1_output_0 +1.6769*perceptron_layer_1_output_1 -2.2073*perceptron_layer_1_output_2 -0.471236*perceptron_layer_1_output_3 probabilistic_layer_combinations_2 = -0.469866 -0.676177*perceptron_layer_1_output_0 -1.55635*perceptron_layer_1_output_1 +2.90799*perceptron_layer_1_output_2 -4.70235*perceptron_layer_1_output_3 sum = exp(probabilistic_layer_combinations_0) + exp(probabilistic_layer_combinations_1) + exp(probabilistic_layer_combinations_2); high_quality = exp(probabilistic_layer_combinations_0)/sum; low_quality = exp(probabilistic_layer_combinations_1)/sum; medium_quality = exp(probabilistic_layer_combinations_2)/sum;
We can implement this expression in any programming language to obtain the output for our input.
- Kaggle. Machine learning and data science community: Milk Dataset.