The objective is to create a higher dimension by using a polynomial mapping. The output is equal to the dot product of the new feature map. From the method above, you need to: Transform x1 and x2 into a new dimension Compute the dot product: common to all kernels Transform x1 and x2 into a new dimension You can use the function created above to compute the higher dimension. You see the problem, you need to store in memory a new feature map to compute the dot product.
If you have a dataset with millions of records, it is computationally ineffective. Instead, you can use the polynomial kernel to compute the dot product without transforming the vector. This function computes the dot product of x1 and x2 as if these two vectors have been transformed into the higher dimension. Said differently, a kernel function computes the results of the dot product from another feature space.
You can write the polynomial kernel function in Python as follow. Below, you return the second degree of the polynomial kernel.
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The output is equal to the other method. This is the magic of the kernel. The simplest is the linear kernel. This function works pretty well for text classification. TensorFlow has a build in estimator to compute the new feature space. This function is an approximation of the Gaussian kernel function. This function computes the similarity between the data points in a much higher dimensional space. Train Gaussian Kernel classifier with TensorFlow The objective of the algorithm is to classify the household earning more or less than 50k.
You will evaluate a logistic regression to have a benchmark model. After that, you will train a Kernel classifier to see if you can get better results. A good practice is to standardize the values of the continuous variables. You can use the function StandardScaler from sci-kit learn.
You create a user-defined function as well to make it easier to convert the train and test set. It will give you a baseline accuracy. The objective is to beat the baseline with a different algorithm, namely a Kernel classifier.
It will make sure all variables are dense numeric data. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Loss for final step: In the next section, you will try to beat the logistic classifier with a Kernel classifier Step 7 Construct the Kernel classifier The kernel estimator is not so different from the traditional linear classifier, at least in term of construction.
The idea behind is to use the power of explicit kernel with the linear classifier. You need two pre-defined estimators available in TensorFlow to train the Kernel Classifier: RandomFourierFeatureMapper KernelLinearClassifier You learned in the first section that you need to transform the low dimension into a high dimension using a kernel function. More precisely, you will use the Random Fourier, which is an approximation of the Gaussian function.
The model can be trained using the estimator KernelLinearClassifier. To build the model, you will follow these steps: Set the high dimension Kernel function Set the L2 hyperparameter Build the model Train the model Evaluate the model Step A Set the high dimension Kernel function The current dataset contains 14 features that you will transform to a new high dimension of the 5. You use the random Fourier features to achieve the transformation.
If you recall the Gaussian Kernel formula, you note that there is the standard deviation parameter to define. This parameter controls for the similarity measure employs during the classification.
You set the L2 hyperparameter to 0. You use the build-in estimator KernelLinearClassifier. Note that you add the kernel mapper defined previously and change the model directory. Instructions for updating: Please switch to tf.
Instructions for updating: Please replace uses of any Estimator from tf. Instructions for updating: When switching to tf. Estimator, use tf. RunConfig instead. INFO:tensorflow:Using default config. INFO:tensorflow:Loss for final step: 0. Cathy O'Neill. Data Mining Techniques. Enterprise Data Architecture.
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