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        "author": "Lifan Liang",
        "author_email": "lil115@pitt.edu",
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        "description": "# EM_BMF\n\nRobust Boolean matrix factorization via EM_BMF\nThe code is completely process-oriented. Sorry for contaminating your name space.\n\nDependency: (I think it will work as long as Annaconda on Python3 is installed)\n\nnumpy -- 1.11.3\n\nscipy -- 1.1.0\n\nnumba -- 0.40.0\n\n\n\nExample usage:\n\n```python\nimport numpy as np\nfrom boolem import boolem\n\ndef synthesis(shape, latent_size, P, noise_p=0.0):\n    '''\n    In this synthesis, the probability of X was sampled from the joint probability of the latent factors.\n    P is the parameter as Beta(1/(1-p),2) for generating the probability in latent factors.\n    '''\n\n    a = np.zeros((shape[0], latent_size))\n    b = np.zeros((latent_size, shape[1]))\n    X = np.zeros(shape)\n    for l in range(latent_size):\n        a[:,l] = np.random.binomial(1, P[l], shape[0])\n        b[l,:] = np.random.binomial(1, P[l], shape[1])\n        X += np.outer(a[:,l],b[l,:]) \n    X[X>1] = 1\n    flip = np.random.binomial(1, noise_p, X.shape)\n    X_noisy = np.abs(X-flip)\n    return X_noisy, X, a, b\n\n# Generate a Boolean matrice with heterogeneous Boolean factors and uniform noise.   \nX_noisy, X, a, b = synthesis((1000, 1000), 4, np.random.uniform(0.2,0.5,4), noise_p=0.2)\n\n# Feed the model with noisy matrix. \n# Latent_size: the dimension of latent Boolean factors. \n# alpha: the alpha for the beta prior. Default is recommended.\n# beta: the beta for the beta prior. Default is recommended.\n# mask: the matrix with the same shape as X. 0 means the correponding element in X is missing.\n# max_iter: the maximum iteration for gradient-based optimization\nmodel = boolem(np.int8(X_noisy), latent_size=5, alpha=0.95, beta=0.95, mask=np.ones(X.shape, dtype=np.int8), max_iter=200)\nmodel.run()\n\n# After running factorization, the model will contain several new attributes as the output:\n# model.U: the latent factor with the shape (X.shape[0], latent_size)\n# model.Z: the latent facotr with the shape (latent_size, X.shape[1])\n# model.X_hat: reconstructed Boolean matrix from U and Z. Note that values in X_hat is continuous within [0,1]\nprint('Reconstruction error:', np.abs((model.X_hat>0.5)-X).mean())\n```\n\n\n\n",
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