Description Of UCI Datasets And Files ✓ Solved

Description of UCI Datasets The files in the UCI datasets di

The files in the UCI datasets directory contain training files and test files for three datasets. Both the training file and the test file are text files, containing data in tabular format. Each value is a number, and values are separated by white space. The i-th row and j-th column contain the value for the j-th dimension of the i-th object. The only exception is the LAST column, that stores the class label for each object.

Make sure you do not use data from the last column (i.e., the class labels) as parts of the input vector. The datasets are copied from the UCI repository of machine learning datasets. Here are some details on each dataset:

• The pendigits dataset:
  • 7494 training objects.
  • 3498 test objects.
  • 16 dimensions.
  • 10 classes.
• The satellite dataset:
  • 4435 training objects.
  • 2000 test objects.
  • 36 dimensions.
  • 6 classes.
• The yeast dataset:
  • 1000 training objects.
  • 484 test objects.
  • 8 dimensions.
  • 10 classes.

For each dataset, a training file and a test file are provided. The name of each file indicates what dataset the file belongs to, and whether the file contains training or test data. Note that, for the purposes of your assignments, it does not matter at all where the data come from. The methods that you are asked to implement should work on all three datasets, as well as ANY other datasets following the same format.

Feature Scaling for Both Question-1 and Question-2: Training data should be normalized, separately from all other dimensions. Each feature should be transformed using function F(v) = (v – mean) / std, using the mean and std (standard deviation) of the values of that feature on the training data.

Question-2: Linear Regression

You must implement a Python executable file called linear_regression that uses linear regression to fit a polynomial function to the data. Your function should be invoked as follows: linear_regression with following three command line arguments: .

• : The path name of the training file, where the training data is stored.
• : The path name of the test file, where the test data is stored.
• : An integer between 1 and 10.

Suppose you have an input vector x = (x1, x2, ..., xD)T. If the degree is 1, then φ(x) = (1, x1, x2, ..., xD)T. If the degree is 2, then φ(x) = (1, x1, (x1)², x2, (x2)²..., xD, (xD)²)T. If the degree is 3, then φ(x) = (1, x1, (x1)², (x1)³, x2, (x2)², (x2)³, ..., xD, (xD)², (xD)³)T.

Training Stage for Linear Regression

At the end of the training stage, your program should print out the values of the weights that you have estimated. The output of the training phase should be a sequence of lines such as: 𜃠0=%.4f 𜃠1=%.4f 𜃠2=%.4f ...

Test Stage for Linear Regression

After the training stage, your function should be applied to the test data. For each test object, you should print a line containing the object ID, output, target value, and squared error.

This is simply the squared difference between the output that your function produces for the test object and the target output for that object. The output of the test stage should be a sequence of lines like: ID=%5d, output=%14.4f, target value = %10.4f, squared error = %.4f.

Paper For Above Instructions

The implementation of linear regression is a widely studied topic in machine learning and statistical modeling. In this paper, we will focus on how to work with UCI datasets, perform data normalization, and implement a linear regression model that can fit polynomial functions to the data. Our approach will follow the specifics outlined in the prompt, addressing each requirement comprehensively.

Understanding the Datasets

We are provided with three UCI datasets: pendigits, satellite, and yeast. Each dataset contains a training and test file formatted as plain text, where data is organized into rows and columns. The training and test files must remain separate, and it is essential to exclude the last column (which contains class labels) when training our model.

Data Preprocessing

Before training the linear regression model, data preprocessing is crucial. We need to ensure that each feature in the training data is normalized. Normalization improves the performance of gradient descent algorithms by scaling the inputs to a similar range. The normalization function used follows the formula:

F(v) = (v – mean) / std

Where mean and std are the mean and standard deviation calculated from the training dataset for each feature. This ensures that the model is not biased toward any particular feature with wider ranges.

Implementing Linear Regression

The next step involves implementing the linear regression function. To accomplish this, we will create a Python script named `linear_regression.py`. The script will accept three arguments: the training file, the test file, and the degree of polynomial to fit.

The format of the polynomial basis functions is defined as:

• For degree 1: ϕ(x) = (1, x1, x2, ..., xD)T
• For degree 2: ϕ(x) = (1, x1, (x1)², x2, (x2)²..., xD, (xD)²)T
• For degree 3: ϕ(x) = (1, x1, (x1)², (x1)³, x2, (x2)², (x2)³..., xD, (xD)², (xD)³)T

As the degree parameter increases, the model can capture more complexity in the data, but care must be taken to avoid overfitting.

Training the Model

During the training phase, we will use linear regression to estimate the weights for polynomial functions based on the training data. Our script will compute the weights using a form of gradient descent or direct computation via linear algebra. After training, it will output the estimated weights in the specified format.

Testing the Model

In the test phase, we will apply our model on the test dataset. For every object in the test file, the script will calculate the predicted values based on the learned weights and also compute the squared error, which is defined as:

Squared Error = (output - target)²

Our output for the test stage will include the object ID, predicted output, target value, and squared error, formatted as specified.

Conclusion

In summary, we have detailed the process of working with UCI datasets for linear regression tasks, including preprocessing, model implementation, training, and testing. The models we build can be easily adapted to new datasets following the same structural format, thereby enhancing their utility in a wide range of applications.

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