\n \uac00\uc6b0\uc2dc\uc548 \ud63c\ud569 \ubaa8\ub378(Gaussian Mixture Model, GMM)\uc740 \ud1b5\uacc4\uc801 \ubaa8\ub378\ub85c, \ub370\uc774\ud130\uac00 \uc5ec\ub7ec \uac1c\uc758 \uac00\uc6b0\uc2dc\uc548 \ubd84\ud3ec\uc758 \ud63c\ud569\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4\uace0 \uac00\uc815\ud569\ub2c8\ub2e4.
\n GMM\uc740 \ud074\ub7ec\uc2a4\ud130\ub9c1, \ubc00\ub3c4 \ucd94\uc815 \ubc0f \uc0dd\ubb3c\uc815\ubcf4\ud559\uacfc \uac19\uc740 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \ub110\ub9ac \uc0ac\uc6a9\ub429\ub2c8\ub2e4.
\n \uac01\uac01\uc758 \uac00\uc6b0\uc2dc\uc548 \ubd84\ud3ec\ub294 \ud3c9\uade0\uacfc \ubd84\uc0b0\uc73c\ub85c \uc815\uc758\ub418\uba70, \uc774\ub294 \ub370\uc774\ud130\uc758 \ud2b9\uc815 \ud074\ub7ec\uc2a4\ud130\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.\n <\/p>\n
\n GMM\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc218\uc2dd\uc73c\ub85c \ud45c\ud604\ub429\ub2c8\ub2e4: \n \ubcf8 \uc139\uc158\uc5d0\uc11c\ub294 PyTorch\ub97c \uc0ac\uc6a9\ud558\uc5ec GMM\uc744 \uad6c\ud604\ud558\ub294 \uacfc\uc815\uc744 \ub2e4\ub8f9\ub2c8\ub2e4. \n \uba3c\uc800 \uc608\uc2dc \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \n GMM\uc758 \uad6c\ud604\uc744 \uc704\ud574 \ud544\uc694\ud55c \ud074\ub798\uc2a4\uc640 \uba54\uc18c\ub4dc\ub97c \uc815\uc758\ud569\ub2c8\ub2e4.\n <\/p>\n \n \uc704\uc5d0\uc11c \uc815\uc758\ud55c \n GMM\uc740 \ub2e4\uc591\ud55c \ud074\ub7ec\uc2a4\ud130\uc758 \ud615\ud0dc\ub97c \uc798 \ubaa8\ud615\ud654\ud560 \uc218 \uc788\ub2e4\ub294 \uc7a5\uc810\uc774 \uc788\uc9c0\ub9cc, \ubaa8\ub378\uc758 \ubcf5\uc7a1\uc131\uacfc \ub370\uc774\ud130\uc758 \ucc28\uc6d0 \uc218\uac00 \uc99d\uac00\ud560\uc218\ub85d \ud559\uc2b5 \uc18d\ub3c4\uac00 \ub290\ub824\uc9c8 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \n GMM\uc740 \uac15\ub825\ud55c \ud074\ub7ec\uc2a4\ud130\ub9c1 \uae30\ubc95\uc73c\ub85c, \uc5ec\ub7ec \ubd84\uc57c\uc5d0\uc11c \uc0ac\uc6a9\ub418\uace0 \uc788\uc2b5\ub2c8\ub2e4. <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"
\n
\nP(x) = \u03a3\u2096 \u03c0\u2096 * N(x | \u03bc\u2096, \u03a3\u2096)<\/code>
\n
\n \uc5ec\uae30\uc11c:<\/p>\n\n
P(x)<\/code>: \ub370\uc774\ud130 \ud3ec\uc778\ud2b8 x<\/code>\uc758 \ud655\ub960<\/li>\n\u03c0\u2096<\/code>: \uac01 \ud074\ub7ec\uc2a4\ud130\uc758 \ud63c\ud569 \uacc4\uc218<\/li>\nN(x | \u03bc\u2096, \u03a3\u2096)<\/code>: \ud3c9\uade0 \u03bc\u2096<\/code>\uc640 \ubd84\uc0b0 \u03a3\u2096<\/code>\ub97c \uac00\uc9c0\ub294 \uac00\uc6b0\uc2dc\uc548 \ubd84\ud3ec<\/li>\n<\/ul>\n4. \ud30c\uc774\ud1a0\uce58(Pytorch)\ub85c GMM \uad6c\ud604\ud558\uae30<\/h2>\n
\n PyTorch\ub294 \ub525\ub7ec\ub2dd\uc744 \uc704\ud55c \uc778\uae30\uc788\ub294 \uba38\uc2e0\ub7ec\ub2dd \ub77c\uc774\ube0c\ub7ec\ub9ac\uc785\ub2c8\ub2e4.\n <\/p>\n4.1. \ud544\uc694\ud55c \ub77c\uc774\ube0c\ub7ec\ub9ac \uc124\uce58\ud558\uae30<\/h3>\n
!pip install torch matplotlib numpy<\/code><\/pre>\n4.2. \ub370\uc774\ud130 \uc0dd\uc131\ud558\uae30<\/h3>\n
\n \uc5ec\uae30\uc11c\ub294 2\ucc28\uc6d0 \ub370\uc774\ud130 \ud3ec\uc778\ud2b8\ub97c \uc0dd\uc131\ud558\uace0, \uc774\ub97c 3\uac1c\uc758 \ud074\ub7ec\uc2a4\ud130\ub85c \ub098\ub204\uaca0\uc2b5\ub2c8\ub2e4.\n <\/p>\n\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# Set random seed for reproducibility\nnp.random.seed(42)\n\n# Generate sample data for 3 clusters\nmean1 = [0, 0]\nmean2 = [5, 5]\nmean3 = [5, 0]\ncov = [[1, 0], [0, 1]] # covariance matrix\n\ncluster1 = np.random.multivariate_normal(mean1, cov, 100)\ncluster2 = np.random.multivariate_normal(mean2, cov, 100)\ncluster3 = np.random.multivariate_normal(mean3, cov, 100)\n\n# Combine clusters to create dataset\ndata = np.vstack((cluster1, cluster2, cluster3))\n\n# Plot the data\nplt.scatter(data[:, 0], data[:, 1], s=30)\nplt.title('Generated Data for GMM')\nplt.xlabel('X-axis')\nplt.ylabel('Y-axis')\nplt.show()\n <\/code><\/pre>\n4.3. \uac00\uc6b0\uc2dc\uc548 \ud63c\ud569 \ubaa8\ub378 \ud074\ub798\uc2a4 \uc815\uc758\ud558\uae30<\/h3>\n
\nimport torch\n\nclass GaussianMixtureModel:\n def __init__(self, n_components, n_iterations=100):\n self.n_components = n_components\n self.n_iterations = n_iterations\n self.means = None\n self.covariances = None\n self.weights = None\n\n def fit(self, X):\n n_samples, n_features = X.shape\n\n # Initialize parameters\n self.means = X[np.random.choice(n_samples, self.n_components, replace=False)]\n self.covariances = [np.eye(n_features)] * self.n_components\n self.weights = np.ones(self.n_components) \/ self.n_components\n\n # EM algorithm\n for _ in range(self.n_iterations):\n # E-step\n responsibilities = self._e_step(X)\n \n # M-step\n self._m_step(X, responsibilities)\n\n def _e_step(self, X):\n likelihood = np.zeros((X.shape[0], self.n_components))\n for k in range(self.n_components):\n likelihood[:, k] = self.weights[k] * self._multivariate_gaussian(X, self.means[k], self.covariances[k])\n total_likelihood = np.sum(likelihood, axis=1)[:, np.newaxis]\n return likelihood \/ total_likelihood\n\n def _m_step(self, X, responsibilities):\n n_samples = X.shape[0]\n for k in range(self.n_components):\n N_k = np.sum(responsibilities[:, k])\n self.means[k] = (1 \/ N_k) * np.sum(responsibilities[:, k, np.newaxis] * X, axis=0)\n self.covariances[k] = (1 \/ N_k) * np.dot((responsibilities[:, k, np.newaxis] * (X - self.means[k])).T, (X - self.means[k]))\n self.weights[k] = N_k \/ n_samples\n\n def _multivariate_gaussian(self, X, mean, cov):\n d = mean.shape[0]\n diff = X - mean\n return (1 \/ np.sqrt((2 * np.pi) ** d * np.linalg.det(cov))) * np.exp(-0.5 * np.sum(np.dot(diff, np.linalg.inv(cov)) * diff, axis=1))\n\n def predict(self, X):\n responsibilities = self._e_step(X)\n return np.argmax(responsibilities, axis=1)\n <\/code><\/pre>\n4.4. \ubaa8\ub378 \ud559\uc2b5 \ubc0f \uc608\uce21\ud558\uae30<\/h3>\n
GaussianMixtureModel<\/code> \ud074\ub798\uc2a4\ub97c \uc774\uc6a9\ud558\uc5ec \ubaa8\ub378\uc744 \ud559\uc2b5\uc2dc\ud0a4\uace0 \ud074\ub7ec\uc2a4\ud130\ub97c \uc608\uce21\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.\n <\/p>\n\n# Create GMM instance and fit to the data\ngmm = GaussianMixtureModel(n_components=3, n_iterations=100)\ngmm.fit(data)\n\n# Predict clusters\npredictions = gmm.predict(data)\n\n# Plot the data and the predicted clusters\nplt.scatter(data[:, 0], data[:, 1], c=predictions, s=30, cmap='viridis')\nplt.title('GMM Clustering Result')\nplt.xlabel('X-axis')\nplt.ylabel('Y-axis')\nplt.show()\n <\/code><\/pre>\n5. GMM\uc758 \uc7a5\ub2e8\uc810<\/h2>\n
\n \ub610\ud55c, \ucd08\uae30\ud654\uc5d0 \ub530\ub77c \uacb0\uacfc\uac00 \ub2ec\ub77c\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c \uc801\uc808\ud55c \ucd08\uae30\ud654\ub97c \uc704\ud574 \uc5ec\ub7ec \ubc88 \uc2dc\ub3c4\ub97c \ud574\ubcf4\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.\n <\/p>\n6. \uacb0\ub860<\/h2>\n
\n PyTorch\ub97c \uc774\uc6a9\ud558\uc5ec GMM\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc744 \uc54c\uc544\ubcf4\uc558\uc73c\uba70, \uac01 \ub2e8\uacc4\ub9c8\ub2e4 \ud544\uc694\ud55c \uc218\ud559\uc801 \ubc30\uacbd\uc744 \uc774\ud574\ud558\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.
\n \uc55e\uc73c\ub85c GMM\uc758 \ub2e4\uc591\ud55c \uc751\uc6a9\uacfc \ud655\uc7a5 \ubc29\ubc95\uc5d0 \ub300\ud574 \ub354 \uae4a\uc774 \uc788\ub294 \uc5f0\uad6c\ub97c \ud574\ubcf4\uae38 \ubc14\ub78d\ub2c8\ub2e4.\n <\/p>\n