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    # exercise 2.2.2
    
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    from dtuimldmtools import similarity
    
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    # Generate two data objects with M random attributes
    M = 5
    x = np.random.rand(1, M)
    y = np.random.rand(1, M)
    
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    # Check the statements in the exercise
    print(
        "Cosine scaling: %.4f "
        % (similarity(x, y, "cos") - similarity(a * x, y, "cos"))[0, 0]
    )
    print(
        "ExtendedJaccard scaling: %.4f "
        % (similarity(x, y, "ext") - similarity(a * x, y, "ext"))[0, 0]
    )
    print(
        "Correlation scaling: %.4f "
        % (similarity(x, y, "cor") - similarity(a * x, y, "cor"))[0, 0]
    )
    print(
        "Cosine translation: %.4f "
        % (similarity(x, y, "cos") - similarity(b + x, y, "cos"))[0, 0]
    )
    print(
        "ExtendedJaccard translation: %.4f "
        % (similarity(x, y, "ext") - similarity(b + x, y, "ext"))[0, 0]
    )
    print(
        "Correlation translation: %.4f "
        % (similarity(x, y, "cor") - similarity(b + x, y, "cor"))[0, 0]
    )
    
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    print("Ran Exercise 2.2.2")