From 5542f6ba9d665838d273257859992efe958eca6a Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 22:18:48 +0530 Subject: [PATCH 01/13] Added K-Means --- .../machine-learning/K-Means_Clustering.md | 84 +++++++++++++++++++ 1 file changed, 84 insertions(+) create mode 100644 contrib/machine-learning/K-Means_Clustering.md diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md new file mode 100644 index 0000000..f90e290 --- /dev/null +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -0,0 +1,84 @@ +# K-Means Clustering +Unsupervised Learning Algorithm for Grouping Similar Data. +## Introduction +K-means clustering is a fundamental unsupervised machine learning algorithm that excels at grouping similar data points together. It's a popular choice due to its simplicity and efficiency in uncovering hidden patterns within unlabeled datasets. +## Unsupervised Learning +Unlike supervised learning algorithms that rely on labeled data for training, unsupervised algorithms, like K-means, operate solely on input data (without predefined categories). Their objective is to discover inherent structures or groupings within the data. +## The K-Means Objective +Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. + +![enter image description here](https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQnDTFfxrrAttYMwwjZV0RAA8J8rmUxgrnWc2gU_ArEqrxEMlHm) +## Clusters and Centroids +A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). +## Minimizing In-Cluster Variation +The K-means algorithm strategically assigns each data point to a cluster such that the total variation within each cluster (measured by the sum of squared distances between points and their centroid) is minimized. In simpler terms, K-means strives to create clusters where data points are close to their respective centroids. +## The Meaning Behind "K-Means" +The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. +## K-Means Algorithm in Action +![enter image description here](https://d3i71xaburhd42.cloudfront.net/2f49631bb3103a61fbc3045dd035c3d8f2175887/11-Figure2-1.png) +The K-means algorithm follows an iterative approach to optimize cluster formation: + +1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. +2. **Data Point Assignment:** Each data point is assigned to the closest centroid, effectively creating a preliminary clustering. +3. **Centroid Repositioning:** Once data points are assigned, the centroids are recalculated by averaging the positions of the points within their respective clusters. These new centroids represent the refined centers of the clusters. +4. **Iteration Until Convergence:** Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This criterion can be either: + - **Centroid Stability:** No significant change occurs in the centroids' positions, indicating successful clustering. + - **Reaching Maximum Iterations:** A predefined number of iterations is completed. + ## Code + Following is a simple implementation of K-Means. + + + # Generate and Visualize Sample Data + # import the necessary Libraries + + import numpy as np + import matplotlib.pyplot as plt + + # Create data points for cluster 1 and cluster 2 + X = -2 * np.random.rand(100, 2) + X1 = 1 + 2 * np.random.rand(50, 2) + + # Combine data points from both clusters + X[50:100, :] = X1 + + # Plot data points and display the plot + plt.scatter(X[:, 0], X[:, 1], s=50, c='b') + plt.show() + + # K-Means Model Creation and Training + from sklearn.cluster import KMeans + + # Create KMeans object with 2 clusters + kmeans = KMeans(n_clusters=2) + kmeans.fit(X) # Train the model on the data + + # Visualize Data Points with Centroids + centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) + + plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again + plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 + plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 + plt.show() # Display the plot with centroids + + # Predict Cluster Label for New Data Point + new_data = np.array([-3.0, -3.0]) + new_data_reshaped = new_data.reshape(1, -1) + predicted_cluster = kmeans.predict(new_data_reshaped) + print("Predicted cluster for new data:", predicted_cluster) + + ### Output: + Before Implementing K-Means Clustering : +![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) + + + After Implementing K-Means Clustering:![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) +## Conclusion +**K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. + + + + + + + + From 7259dc7047a0576721b852fc4aeb08ddf5bd8b84 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 22:24:02 +0530 Subject: [PATCH 02/13] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index f90e290..ab5fba9 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -67,11 +67,12 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio print("Predicted cluster for new data:", predicted_cluster) ### Output: - Before Implementing K-Means Clustering : + Before Implementing K-Means Clustering ![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) - After Implementing K-Means Clustering:![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) + After Implementing K-Means Clustering + ![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From e9eb68ab3832ec651264b967de709ee8ae41af5f Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 23:28:27 +0530 Subject: [PATCH 03/13] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index ab5fba9..c6aee6a 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -15,7 +15,6 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![enter image description here](https://d3i71xaburhd42.cloudfront.net/2f49631bb3103a61fbc3045dd035c3d8f2175887/11-Figure2-1.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -66,13 +65,13 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio predicted_cluster = kmeans.predict(new_data_reshaped) print("Predicted cluster for new data:", predicted_cluster) - ### Output: - Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) + ### Output: +![Before Implementing K-Means Clustering](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAxL0lEQVR4nO3df2xV933/8de1b6Fuwa5QCAzhpEmzRWrTkJWlGXGSkoQ0TbcMgpZt0qaRrooGgWyBrBOs0vLHFJEIlKxNsEk3KVSqIiJ5MyTtupCQQGLWrC2R25KNaSitQFATkqk29u4M2Pf7x+d7jW3uj88595zz+Zxzng/pimIuvude3Hze5/15v9+fQrlcLgsAAMCBFtcXAAAA8otABAAAOEMgAgAAnCEQAQAAzhCIAAAAZwhEAACAMwQiAADAGQIRAADgTNH1BdQzMTGhU6dOae7cuSoUCq4vBwAAWCiXyzp79qwWLVqklpb6OQ+vA5FTp06ps7PT9WUAAIAQTpw4ocWLF9d9jteByNy5cyWZN9Le3u74agAAgI3h4WF1dnZOruP1eB2IVLZj2tvbCUQAAEgZm7IKilUBAIAzBCIAAMAZAhEAAOAMgQgAAHCGQAQAADhDIAIAAJyJNRDp6enR9ddfP9l+u2zZMn3/+9+P8yUBAECKxBqILF68WE888YQOHz6sH//4x7rjjju0cuVKvfvuu3G+LAAA05RK0unT5lf4JdZA5N5779WXv/xl/fqv/7p+4zd+Q48//rjmzJmjt99+O86XBQBAktTfL61eLc2ZIy1caH5dvVo6dMj1laEisRqR8fFx7d69W6Ojo1q2bFnV54yNjWl4eHjaAwCAoEol6cknpVtvlV5+WZqYMF+fmDC/v/VWaedOt9cII/ZA5Gc/+5nmzJmj2bNna+3aterr69OnP/3pqs/dunWrOjo6Jh8ceAcACGJqBmTzZvO1CxemP+fCBalclh56iMyIDwrlcrkc5wucO3dOx48f19DQkHp7e/WP//iPOnjwYNVgZGxsTGNjY5O/rxyaMzQ0xFkzAIC6enqk9eul1tZLg49qikVp5Uqptzf+a8ub4eFhdXR0WK3fsQciM61YsUKf+tSn9NxzzzV8bpA3AgBoXqkkDQ9L7e1SW5vrq7HX3y/ddpvJdATR0iKNjKTrvaZBkPU78TkiExMT07IeAAD30l7U+dRTJhMS1MSECbzgTjHOb75lyxbdc889uuKKK3T27Fm98MILOnDggF555ZU4XxYAEMDULY2ZRZ179kjd3dLatU4vsa5SSdq79+K1B9HSYrI/SUpr1ikusWZE3n//ff3pn/6prr32Wt1555360Y9+pFdeeUV33XVXnC8LALDU32+CkHI5vUWdw8PhgpBiUbrvvuSCgbRnneKSeI1IENSIAEC8Vq82mY96xZ2+F3WWSmZRDxqMFArSW29JXV3xXNdUtQppi0VpfNz/rFNQXteIAAD8UNnSaNRhcuGC1Nfn71TStjYTKBUtiw2KRROEdHcnE4RkIesUJwIRAMipIFsavhd1btpkMguNFAomaHnrreQyEDaFtK2t0tNPJ3M9viEQAYCcam83xZo2XBR1BnHLLSbDUShcmhmpZECefFIaHTVbTElkQqTsZJ3iRCACADllu6WRdFFnWGvXmkzHypUXA6yWlosZkL/+6+TfQ5ayTnGJtX0XAOC3TZtMi2494+PSxo2JXE7TurrMI0yLbBxttZWsk00w4nvWKS5kRAAgx2y2NJIq6oxSW5u0YIFdQBFnW23Wsk5xIBABgJxrtKWRpbbSmXp6zGj4OE/otSmkTVPWKWrMEQEATMrT1E+b82mimjWyc6dp0WWOyKXIiAAAJgXZ0ki7JNtq85x1aoSMCAAgd4JMY436hN48ZJ2CrN90zQAAcidMW21UQUNbW3YDkDDYmgEA5E6Whrk1o1SSTp92O0iNQAQAkDt5b6v16SRgAhEACMGHO0k0Z9Mmu9HrWWurTaJlOQgCEQAIwKc7SRgEhfZ8PAmYQAQALPl2JxmVtC7kzQaFTz1ltzWTpVNxfTwJmPZdALCQ5PArW822gfb3m4Vp714TUFXmWjz6qP8j3Xt6zJ192AFhLtt3k1b5OfnIR6T585N5zww0A4CI+XQnGcX2UJqzO1FsL+ThVNyZPye2QYiU7HsmIwIADfh099xsJkDyM7sTxOrVJmCqV2haLJrsTm9v9T/36d80DrV+TmyREQEAj/hy9xxVoaFP2Z2gSiWzlWTT7dLXV7vuJe72XZd1N/V+Tmwk3bJMIAIADfgy/CqKACKqhdyVKIPCOE7F9aGryubnpJ6kTwImEAGABnwYfhVVAOFLdiesKIPCW24xW1mFwqX/tsWi+Xp3t/32lA91N7Y/J9WEec9RIBABAAtx3D0HEVUA4Ut2J6yog8KoTsX1ZT5HkJ8TyQQektuTgAlEAMBC1HfPQUUVQPiQ3WlW1EFhV5cpah0ZkQYHza+9vcH+LX2puwn6c/LBB+Hfc1QIRADAUlR3z2FEGUC4zu40K66gsK1NWrAgXGGqL3U3QX9O5s0L956jRCACAAFEcfccVlQBhOvsThRcBoUz+VZ3k7ZAk0AEAEIIe/fcjCgDCJ8W8rBcBoVT+VZ3k7ZAk0AEAFIkygDCl4W8WS6Cwpmv71vdTZoCTSarAkBKNXvWDKLj87RaFz8nTFYFgBxwnQnART5vh/j+c0IgAgAxcDniG5dK4t8jTdshPiEQAYAIJTnim2CnsaRHrmel7iZJBCIAEJGkRnz7cJ6JLZfBksuR675vh/iEQAQAIpDUiO9ai+tLL5k6hW9+s7nvHxXXwZIvI9fRGIEIAEQgiRHf9RbXygCrv/xL6QtfcLvA+nD4my8j19EY7bsA0KRSydzx20zXbGkxdQNhUvarV5vFvNEo8cpBZt3dyRdI+tDGmtS/B2qjfRcAEpTEiO8gx7uXy+62HnzIRPg2ch31EYgAQJOSGPEd9Hh3KfmtB18Of/Nt5DrqIxABgCYlMeI7yOJakcRpr1P5konwceR6GHlpzyYQAYAIxH3iqe3iOlOSWw8+ZSLSdgLtVK47jpJGIAIAEUhixLfN4jpTklsPbW3mc6gUy9aSRCbC55Hr9dh2HGUpW0IgAgARiXvE99TF1UbSWw89PdKbb9bvmJGSy0SkbeS6zeyTdetMe3aWsiW07wJADOI88fTQIenrX5cOHqz/vCRPe7Vp263o6Uk+CEjDScVB2rOnfs7FognuXLRr10L7LgA4FueI764u6cAB6Rvf8GfrwaZtVzJ38y4WS99Hrgdtz54q7ZNiCUQAIKX+4i/82HoIsoi+9VY26hqiFqY9eyabdm0fa0sIRAAgxXw47TVs226ci6KPC249YdqzZ6rXru1zJw6BCABkgMuth6Btu0eOxLco+rzg1hO2PXumau3aPpz9Uw/FqgCAptkUWhaL0nXXST/5idlGmPrcKAoue3pM10mY7+1DMWuQgt9aZp6d4+rsH4pVAQCJsplxcuGCNDBQvz01bMGlTetrte/tUwal3uwTG9XatX04+6cRAhEAyIk46yZsBojdcEPjBTbsohhmwfVxy6LW7JMvfKHx3505n8WXs38aIRABgIxL6q6/3gCx116TfvrTeBbFMAtu2AxKEqoVIB84YAKnIO3avpz90wiBCABkWNJ3/bW6eD7zmfgWxTALbhq2LGYWIAedFOvT2T/1UKwKABnlqlCxmlLJZGJsAoaZBZdRf+8zZ6T58+O5lqTYFtfaFhGvXGkCxqhQrAoAaOquP+p6Etv21DDn4wT93ufPp2PLoh7bdu00nEJMIAIAGRS2UDHOepI4F8Ug3zstWxZRSMMpxAQiAJBBYeom4q4niXNRDPK948zO+Mj3U4ipEQGADKnUDnzkI8HqIPbtk+66K5l6kkOHzHZQX5+5vpYWs+Bv3Jjc9/apfiZJSQ1uC7J+xxqIbN26Vf/8z/+so0ePqq2tTTfffLOefPJJXXvttVZ/n0AEAOz095uakL17Ly7ACxZI779ff8uiUqhYyXwkWdQY56Jo87137jQtunFMebW9hqzyplj14MGDWr9+vd5++229+uqrOn/+vL74xS9qdHQ0zpcFgFyptaXSKAiRzJ8/9JCbwVdxno9j873j2rLwaVprGiS6NXPmzBldfvnlOnjwoG677baGzycjAgD12Z5P0to6PSiZetd/331mwbQ1OGgW+SyJKnvRzHk3WeJNRmSmoaEhSdK8efOSfFkAyCzbFt0FC2rf9eepi6SWKLIzPk9r9VmTBw7bm5iY0COPPKKuri5dd911VZ8zNjamsbGxyd8P+9i8DQCeqLToNipIHR83WYwzZ8wMjZl3/ZUuEtsakbzVO9iqBIX1PsPK3JYsFcA2K7GMyPr163XkyBHt3r275nO2bt2qjo6OyUdnZ2dSlwcAqRO0Rff8+dp3/WkYfOWzOA+Yi/OwQh8kEohs2LBB3/3ud/XGG29o8eLFNZ+3ZcsWDQ0NTT5OnDiRxOUBQCpFuaWShsFXPovjgLm8FL3GGoiUy2Vt2LBBfX19ev3113XVVVfVff7s2bPV3t4+7QEAqC7qwVy+D75qxGXmIOo6m6QPK3Qp1kBk/fr1+s53vqMXXnhBc+fO1eDgoAYHB1XKan4JABIW9ZZKrdNzfc6E+JA5iDIozFvRa6yBSE9Pj4aGhrR8+XL92q/92uTjxRdfjPNlASA34tpSiXPGR5R8yhxEFRQ2c1hhGjHiHQAyIM6x6b7ycUx7s9NaSyWT0bEdzT8y4mew6O0cEQBAPNK4pdIsHzMHzdbZxFH06jsyIgCA1ElD5iDMtNY0vC8bZEQAAJmWhsxBmDqbqDuh0oBABACQOlkeSx/ncDkfh6MRiAAAUifLmYM4OqF8aHGuhUAEABLg451o2mV5LH2Uw+V8anGuhkAEAGLk852oDZ8DqDjH0vvwvqPohErDcDQCEQCISa070ZdeMouo6zvRetISQEU9lt7H993McDkfW5xnon0XAGJgM2xLMnfs69Ylc022enrMXXTYoVyuhGmXnSqt77sWl63AtO8CgGM2d6KSSYv7lBlJQyq/lmYyB2l+37WkocVZIhABgMiVStLevZcuaLX4tMClIZUfhyy+77S0OBOIAEDEgtyJSmYR8GGBsw2gLlwwZ9r4WMAaRlbfd1panAlEACBiQe5EJVN/4MMCl5ZUftSy/L7T0OJMIAIAEavcidrUiFT4sMClJZUftSy/7zhbnKNCIAIAMbC5E53KhwUuLan8qGX9fUfd4hw1AhEAiMEtt5h2UBs+LXBpSOXHIevvO4rhaHEhEAGAmKxdK+3Y0fh5Pi1waUjlxyEv77uZFue4EIgAQIweeshkRgqFS2tGfF3g6qXyX3vNZG9cF9bGwfctjKxisioAWGh2auehQ6ZFt6/PFKa2tJgFfeNGv4KQmSrv+8gRk93Zu/fi9a9cKT36qN/XH1az/955F2T9JhABgDr6+82wq1oLcNAFK40LXNZGnyN+BCIAEIF6C/CFC9INN0g//Wm2MwQ2Z+YUCmbrIkvvG83hrBkAaFKjs0ckaWBg+qm6L78s3XqrX2fHNCuLo8/hFwIRAKjC9tC6qdJ6OFotWR19Dr8QiADADEEPrZspKxmCLI8+hz8IRABghqCH1s2UlQxBlkefwx8EIgAwQ9BD66rJQoYg66PP4QcCEQCYwXYBricrGYKsjz6HewQiAFBF0EPrpspShiAvo8/hDoEIAFRRWYDDSDpDUCpJp0/HV5PC6HPEiUAEAGq47rpgz086Q9DfL61eLc2ZIy1caH5dvTqe1mGfT29FuhGIAEANTz1lXyeSdIagp8dMPH355WSHqvl4eiuCiTuDFhSBCABUEWSWSEuLdOZMchmCRlNfszRUDdFJMoMWBIEIAFQRdJjX+fPxXs9UUY9d9+0OGdFzlUGzQSACAFX4OswryrHrvt4hI1q+Z9AIRACgCl+HeUU1dt3nO2REy/eDCwvlcr3Dnd0KcowwAEStv98s1vX+K1komALVpLpHSiWTubAJRlpaTHfLzCDJx/flo1LJBHLt7ektzo3i5yWMIOs3GREAqMHHYV5RZGp8v0N2LUtbVmk4uJBABADq8HGYVzNj16OsMcmirG1Z+VrrNO11k39JAEgX34Z5NZOpScMdsiu+F3WG4Wut01QEIgBgyadhXmEzNWm4Q3Ylq1tWvh9cSLEqAKRc0KLK1avNVkO97Zli0QQ1vb3RXafPXBV1JmXnTpPNaW2d/u9eLJogpLs72m1GilUBIEeCZmp8v0N2IetbVj7WOlVYnqIAAMiKSo1JozvkPLXuVrasbDMiaUzSd3WZh29tyWREACCH4rpDTuu4+DQUdUbFp1oniUAEAHIrym6gLMzeYMvKDQIRAMi5Zu+Q0zJ7o1G2xscBdnlAIAIACC0NszeCZGtqbVn97u+6L+rMKopVAQChVWZv1GsFrszecJFJ6OkxgVJr66XZmj17qretdnWZAOr8+YtZnpdeMhmRyp8jOswRAQCE4vvsjbCH+00NXpKYuZFFzBEBAMTO99kbYSalpmGrKWsIRAAAofg8Lj7s4X5ZHfPuMwIRAEAoPs/eCJOt4WRiNwhEAACh+Tp7I0y2xvetpqwiEAEAhGY7e+Nzn0t24mqYbI3PW01ZRiACAGhKvXHxzz4r7dvnZuJq0GyNz1tNWUYgAgBNcHm2ik/nulQbF3/nndKGDe4mroaZlOrrVlOWEYgAQAguz1bx+VyXyrj4w4f9aIMNergfY96Tx0AzAAjI5cCrtAzbWr3aZD7qdaAUiyYg6O1N5ppKJVNg2t7eeFvl0CHTotvXZ7I4LS1mO2bjRoIQG0HW71gDkTfffFPbtm3T4cOH9ctf/lJ9fX1atWqV9d8nEAHgm7DTOtP+2kH4PnE1iCDBCy7yZrLq6OiolixZoh07dsT5MgCQGJcDr9IybCtLbbDNnkyMxhLbmikUCmREAKSayzv9NGUZ0nStiIc3GZGgxsbGNDw8PO0BAL5weaefpiwDbbAIwqtAZOvWrero6Jh8dHZ2ur4kAJjkcuBV2oZt0QYLW14FIlu2bNHQ0NDk48SJE64vCQAmubzTT1uWgTZY2PIqEJk9e7ba29unPQDAJy7v9NOWZQg6wwP55FUgAgC+c3mnn8YsQ7WJq729fl0j3Io1EBkZGdHAwIAGBgYkST//+c81MDCg48ePx/myABArl3f6ac0y0AaLWmJt3z1w4IBuv/32S76+Zs0a7dq1q+Hfp30XgO9cDrxi2BZ8FWT9blD21Jzly5fL4wnyANC0tjZ3QYDL1waiQo0IAABwhkAEAAA4QyACAACcIRABAADOEIgAAABnCEQAAIAzBCIAAMAZAhEAAOAMgQgAAHCGQAQAADhDIAIAAJwhEAEAAM4QiAAAAGcIRAAAgDMEIgAAwBkCEQAA4AyBCAAAcIZABAAAOEMgAgAAnCEQAQAAzhCIAAAAZwhEAACAMwQiAADAGQIRAADgDIEIAABwhkAEAAA4QyACAACcIRABAADOEIgAAABnCEQAAIAzBCIAAMAZAhEAAOAMgQgAAHCGQAQAADhDIAIAAJwhEAEAAM4QiAAAAGcIRAAAgDMEIgAAwBkCEQAA4AyBCAAAcIZABAAAOEMgAgAAnCEQAQAAzhCIAAAAZwhEAACAMwQiAADAGQIRAADgDIEIAABwhkAEAAA4QyACAACcIRABAADOEIgAAABnCEQAAIAzBCIAAMAZAhEAAOAMgUjOlErS6dPmVwAAXEskENmxY4c++clP6qMf/ahuuukm/fCHP0ziZTFFf7+0erU0Z460cKH5dfVq6dAh11cGAMiz2AORF198UZs2bdJjjz2md955R0uWLNHdd9+t999/P+6Xxv/X0yPddpv08svSxIT52sSE+f2tt0o7d7q9PgBAfhXK5XI5zhe46aabdOONN+rZZ5+VJE1MTKizs1MPP/ywNm/eXPfvDg8Pq6OjQ0NDQ2pvb4/zMjOrv98EIfX+lQsF6a23pK6u5K4LAJBdQdbvWDMi586d0+HDh7VixYqLL9jSohUrVugHP/jBJc8fGxvT8PDwtAea89RTUmtr/ee0tkpPP53M9QAAMFWsgcgHH3yg8fFxLViwYNrXFyxYoMHBwUuev3XrVnV0dEw+Ojs747y8zCuVpL17pQsX6j/vwgWpr48CVgBA8rzqmtmyZYuGhoYmHydOnHB9Sak2PHyxJqSRiQnzfAAAklSM85tfdtllam1t1enTp6d9/fTp01q4cOElz589e7Zmz54d5yXlSnu71NJiF4y0tJjnAwCQpFgzIrNmzdLSpUu1f//+ya9NTExo//79WrZsWZwvDUltbdLKlVKxQbhZLEr33Wee7xNmngBA9sW+NbNp0yb9wz/8g7797W/rP//zP7Vu3TqNjo7qK1/5StwvDUmbNknj4/WfMz4ubdyYzPXYYOYJAORH7IHIH/7hH2r79u3627/9W91www0aGBjQv/7rv15SwIp43HKL1N1tWnRnZkaKRfP17m5/WneZeQIA+RL7HJFm+DpHpFQyhZ3t7f5tZ9Ry6JBp0e3rMwt7S4vZjtm40Z8ghJknAJAN3swRyYpKrcL+/endMujqknp7pZERaXDQ/Nrb69eCzswTAMgfMiJ19PebxXHv3tqdJ8WiqbHo7pbWrk32+rKkVDKBnW2Hz8hIerJRAJA3ZEQiUK1WoZoLF8xWwkMPpSMz4itmngBAPhGIVNHfL61fbwKMRlNJK9gyaE5l5okNZp4AQHYQiFRhU6swU5Rj0vM4PyPtM08AAOEQiMxgez5LNc1uGeR9fkYaZ57EKY8BKYD8IRCZIUitwkzNbBkwPyN9M0/ikveAFEC+EIjMEKRWYapmtgzq1aTkrRh27VozJ2Tlyov/Di0t5vdvvZX9ziQCUgB5Q/tuFatXm//wB9meaWbQls3rFYtmMe7tDf79w/BhaJsP15AkBroByArad5tkU6tQ0eyWgW1NSpTFsPX4tC3Q1iYtWBAuCEljfQUD3QDkEYFIFfVqFQqFi/87ii0Dn+ZnZGFbwKdAKgjfAlIASAqBSA21ahVWrzaj3qMak+7L/Iws1KmkOZDyKSAFgCQ1mNqQbY1qELq6zCNIrULQuobK/AzbGpG4aiUq2wL1rqG1Vdq+XbrmGv/qNhoFUpIJpD77Wb/qKyo/Lx/5iAk0bUfcM9ANQFbkMiMSNH1vU6vQzJaA6/kZQbYF9uzxc8sjbfUVM39e5s83P2ON3gMD3QBkTtljQ0NDZUnloaGhyL5nd3e5XCiUy8ViuWzun82jWDRf7+lx8z17eqK/LluDg9Nf0/aRxLXZ+N//LZdbWuyuuaXFPN+lWj8vra2Nr79QKJf7+91ePwA0EmT9zlVGJI46iKi+p8v5GWFnp/hSO5Km+op6Py9Ts2IzMyN5GugGIF9yFYjEkb6P8nt2dZni15GR6Iphbdie81KL6y0PXwp+bdj+vCxYkM+BbgDyJzcDzUolsx9vWww4MmJXmBr193TFZphWPa7fn49D4WYK+vNy5ox0/rx/hcEA0AgDzaqII32fpi2BRurNTrHh+v25Lvi1EfTn5fz58APdACAtchOIxJG+T9OWgI1qdSq2XL+/NByY194+fSBePa4/TwBISm4CEds6iCDtkXF8T9c+9zlpxw6zLTA4KP3e76Xn/fl+YN7hw3ZbX62tfnyeAJCE3AQiUjzp+zRsCdioNtdi3Trp7rvT9f5cFfzasClUlfz6PAEgbrkKROJI36dhS6CReqPRN2yQ/uiP0vf+mjkwLw6VoXE2hykWCiYzBQB5kKtARIonfe/7lkA9NnNQdu822zVpfH++CFKoWi77XdgMAFHK5VkzYc6QcfE9k2B7xsz+/WaLI23vzxeVwmbOkgGA6XKXEZkqjvS9b1sC9YQ5ej5N788nWSxsBoAo5DoQybsszUFJg6wUNgNAlAhEcixrc1B8l4XCZgCIGoFIjqV5u6BUkk6fNr+mSZoLmwEgDgQiOZe27YKZ807mzDG/d3n6b1A+zzoBgKQRiMQkLXfsadouqDfv5NZbpZ073V5fUBT+AgCBSOTSeMeehu0Cm3knDz3k9+cMALhUoVwOe/B7/IIcI+yDnh6zWM6cy1Esmu2N7u5kF/UwMz98nBNSKkm///vSvn31W42LRRM89fYmd20AgEsFWb/JiETEpzv2ZrIyPm0XVN7Hxz8u/cu/BJt3AgBIBwKRiNgcaNbaKj39dLzXkZU6iqnvI0jOjnknAJAubM1EoFQyWQfb8d0jI/FkHPr7zeJd71+0UDB1Hz4Un9Zi8z5qifPzBQDYYWsmYb5MKPUlK9Msm/dRjY/zTgAA9ZERiYAPGREfriEKQd7HTGnI9gBAHpARSZgPE0p9ycpMFWaWSpD3UeHbvBMAgD0CkYhs2tS4qyPOCaU+nRvTTNdOkPch+TfvBAAQDIFIBPr7TV1DoVD9z5O4Y/chKyM137Vj+z5aW6Xf+R3GowNA2hGINKlRm2mhkNwdu+tzY6KapWLzPiYmpC1b/KxzAQDYIxBpQr2Fd6qNG5O5Y3d9bkxUXTuu3wcAIDkEIk3wsV3W1bkxpZK0d29000/TcP4NAKB5tO+GlIZ22STPjTl92hSm2hocNKPkbfh4/g0AoLYg63eDkkDUEqZdNulFtK0tudesdLvYBmZB4sok3wcAIFlszYTkU7tsNWFmeDTDl64dAEC6EIiE5OvC28wMj2a57toBAKQPgUgTfFt4XZ+8m6Zul6QzRgCA6ghEmuDTwhvVDI9m+d7t4jJjBAC4FF0zETh0yLTo9vWZDERLi9mOSWp+iGQW05dfrt8+WyyagKC3N5lr8q3bpafHBGutrdM/p2LRZK66u90HSgCQBUHWbwKRCLlaeKNsJfYteIhKf7/Ztqr3087pvQAQDU7fdaStzczGSHoBj+Lk3axvWfg4fA4AQCCSCc22Ersuco1b1FNfbV6PQlgAsEMgkgHNtBL7UuQapygyRjaynlUCgDgQiGRE2FbiPGxZJDF8LutZJQCIC4FIRoRpJU56y8KVuIfP5SGrBABxIRDJkKAzPJLasvBBnMPnbLJKLS3S9u3BvzcAZF1sgcjjjz+um2++WR/72Mf0iU98Iq6XwQxdXWZOyMiIOeF2ZMT8vlpLqu/n5USp2eFztQpQbbNK4+PSnj0mKCQzAgAXxRaInDt3Tvfff7/WrVsX10ugDptWYl/Py4lLmKmvjQpQg2SVJOl736NmBACmin2g2a5du/TII4/oV7/6VeC/m7aBZmmU10FfNoPbbCaxrlljP0xuqix+pgBQkdqBZmNjYxoeHp72QLx8Oi8nSY0yRrYFqO+8Y5dVmintnUgAEBWvApGtW7eqo6Nj8tHZ2Rnr6zF4yqi2ZVEoSHffLb32Wj7PXwnS1mxTCDtT2juRACAqgQKRzZs3q1Ao1H0cPXo09MVs2bJFQ0NDk48TJ06E/l71MHjqUpUi1337pC9/2QQi3/uedNdd+ftsgrY1L116MavUKHiZKu2dSAAQhUA1ImfOnNGHH35Y9zlXX321Zs2aNfl732pEOIG1Nj4b4/RpE6DaGhw02zyHDpkW3T177P5eowMIASCtgqzfgXa258+fr/nz5zd1cS412veXzL7/Zz+bvZqIRvhsLqq0NdueZlz5/1hXl3msXGmySfW2a4pF8zyCEAB5F1uNyPHjxzUwMKDjx49rfHxcAwMDGhgY0MjISFwv2VAexpmHFfazyWKdTbNtzV/7WuMgJuzwNADImtjadx944AF9+9vfvuTrb7zxhpYvX271PaLcmimV7Nss85YyD/PZHD5sgpe9e83fq8zjePTRbGRMmm1r3rnTZJDyvs0FIJ+8aN/dtWuXyuXyJQ/bICRqeRpnHlTQz+ab38z+AW/NtjWHGZ4GAHkU+0CzZpARCc9mYNfU5wb5bBo9L0vDug4dMttRfX0XMz/33We2VWzfX5B/CwDIAi8yIr7JyzjzMK3JQT6bhQsbP29qLUnaa0iCnN1Ti824fQDIq9wEIlK8J7D6oKcn/JaJ7Wfzy1/az9dYuTI7s1oIJgAgHrkKRLI8ztx2JHmtQMDms3niifrFm1NNTJgW1qzWkAAAopGrQETKbhFhFK3JjT6bhx+++HUbMzMsNgERACBfclOsWk1WigjjKMSd+tlIF//3H/+xyWw02p6ppzLMq7c3/PcAAPiLYlVLWdn3j6M1ua1N+u//NoHH1DqPDz9sLgiROPANAHBRwMPL4aOwI8nrmXruzNQ6j3/7t4vPKRanByWtrfan0FYCorQHgQCA5uQ6I5IVUbcm25w7I5mi3qm1JPfea4pabdgGRACAbCMQSQGbWRxRtibbFL4Wi9Jll02fr9HXJ61alf1ZLQCA6BCIeCzIcLKoWpNLJXN+jO2sEGl6nU3WZ7UAAKJFIOKpMMPJomhNbrbwNcuzWgAA0ct1+66vmj35VQrfmhxVK3AUZ7QAANIpyPpN14yHKjUa9bZHKsPJai3qbW3hajAqha+NZoVUZoHUeo2uLvPIyqwWAEA82JrxTNAajThmcURZ55GVWS0AgHgQiHgmjuFkQVHnAQBICoGIZyrDyWzEOYsjTOGrTZsxAABTEYh4JurhZM3o6jLnwUydFdLbe2kmJEibMQAAUxGIeMi3WRz16jzCtBkDAFBBIOKhtNRoNBoFXy5LDz1EZgQAUBuBiKeiGE4WN5tR8JU2Y9ihzgZA3jDQLAV8nMUR1eAzGP39JrDbu/fiALiVK6VHH3Wf+QKAoIKs32REUsCHWRwz79R9aDPOCupsAOQZgQjqqtUR8+674dqM2XqYjjobAHlHIIKa6t2pr1ghXX+9fZvx4cO0+FZDnQ2AvKNGBFXZHLxno1Aw7cjVzs8pFk0bcne3H8W3SaPOBkBWUSOCptncqReL0m/+Zv0240oQYrP1kLdtG+psAIBABFUEOXjvJz+RXnutdpvxe+81DmhaWqQ/+IP8bdv4Ms4fAFwiEKkjb3foFUHv1D/zmeqj4D/3ObuAZnxcOnUqfx0jPo3zBwBXCESqyPvZKWHv1Ge2GQcJaGbKS8eIb+P8ASBpuQ1EamU7mOkQ3Z16kICmlqx3jKRlnD8AxCV3gUi9bAczHS6K4k7dNqCp58IFqa8v29tjaRjnDwBxyVX7bk+PCTRqtZEuWSIdOVK/pqFYNAtEb++lfxbXKHZXI9537jSBVzNtt1G1AQ8Omm2frPNxnD8ABEX7bhU22Y6BAbtOkZl36HHVlLiuVYniTr3e1oMtXzpGkihe9mGcPwAkKTeBiM1cDFtTZzpUakpeeinamhJfalW6uqp3xASpWagV0CxaZDerxHXHiOuAEACyLBdbM0EmWNqoTLl8/nmTZamnUDCLcJCF22Y7I8z39cHUrYfDh/1/n4228/I6FRYA6mFrZoZm2khnqtyh79rVOAiRTNAStOsjy+ePTN168L1jhOJlAIhfLgKRKNpIK8bHpTvuMAuQ7fP/6Z+k11+3e36QqaZZ6CbxuWMkywEhAPgiF4FIkLkYjc5O6e42I82D1pusWGFX15HH80eiqEOJWt4CQgBwJReBiGQ/F+OZZ+rfoa9ZYxaoRt9rJts0fp7PH/GpYySPASEAuJCbQCRIPUK9O/Rm6k1s0vicP+KHPAeEAJCk3AQiUvB6hGp36M3Um9im8ZM4fySvB/rZIiAEgGTkKhCRmq9HaHZsuU0aP85ukpkzMT7+cfN+6Py4FAfSAUD8cheIVDRTj2CzQNVim8aPo5uk2vC1ctn8/pZbpK99Lfj3zDLf24sBIAtyMdAsDrXOYamn3jk19URx/ojtmS9/9VfStm3hXiOrDh0ytT19fSaAa2kx2zEbN7rv7OFcGgA+YqBZAqplLBoJm8aPopvkqafsrnP7drZpZvKtvZiR8wCyhECkCZUFat8+6Z57aj/PdRq/MhPDdjtp+/Z4ryetfGgv9uUMIgCICoFIk3p6pLvukl59tfqfFwrup4QGbTl+6SW6aXzEyHkAWUQg0oR6C0NFuey+lqC93QREthjQ5SdGzgPIIgKRJtgsDMWi+4WhrU2691775zOgyz+MnAeQVQQiIaVtYbBtzW1tZUCXjxg5DyCrCERCStvCcMst0qOPNn7exAQDunzEyHkAWUUgEpLPC0Ot8e3bt5s5IdW0tjKgy2eMnAeQVQQiIfm4MNjMl9i2zTxv1arpE1tXrXLb2YPGGDkPIIuYrNoEm2mlhYJZ4OPOMvT0mA6emZNei0WzOHV3XxpkMJkzfWpN9K337wwASWOyakJ8OYsk7HwJHwZ0IZg4ziACAJdCniGLirVrpc9+9tKzSFauTG5+SKWNuF4HT2W+BPUf6dfVZR5ktABkQWxbM7/4xS/0d3/3d3r99dc1ODioRYsW6U/+5E/09a9/XbNmzbL6Hr5vzczkYmEolUwtiE0HT0uLOSeFRQsAEKcg63dsGZGjR49qYmJCzz33nK655hodOXJEDz74oEZHR7U9o4eZtLUlv8iHaSMmEAEA+CLRYtVt27app6dH7733ntXz05YRcYGMCADAN94Wqw4NDWnevHk1/3xsbEzDw8PTHqjPxzZiAABsJRaIHDt2TM8884z+/M//vOZztm7dqo6OjslHZ2dnUpeXasyXAACkVeBAZPPmzSoUCnUfR48enfZ3Tp48qS996Uu6//779eCDD9b83lu2bNHQ0NDk48SJE8HfUQ750kYMAEBQgWtEzpw5ow8//LDuc66++urJzphTp05p+fLl+u3f/m3t2rVLLbZz0UWNSFCHDl3aRnzffcm1EQMAIAVbv2MtVj158qRuv/12LV26VN/5znfU2toa6O8TiITDfAkAgEtetO+ePHlSy5cv15VXXqnt27frzJkzk3+2cOHCuF4WctNGDABAGLEFIq+++qqOHTumY8eOafHixdP+zOPjbQAAQIJi65p54IEHVC6Xqz4AAAAkDr0DAAAOEYgAAABnCEQAAIAzBCIAAMAZAhEAAOAMgQgAAHAmtjkiUai0+nIKLwAA6VFZt21GdngdiJw9e1aSOIUXAIAUOnv2rDo6Ouo+J9azZpo1MTGhU6dOae7cuSoUCqG/z/DwsDo7O3XixAnOrIkZn3Vy+KyTxeedHD7rZMXxeZfLZZ09e1aLFi1qeNit1xmRlpaWS8bDN6O9vZ0f6oTwWSeHzzpZfN7J4bNOVtSfd6NMSAXFqgAAwBkCEQAA4EwuApHZs2frscce0+zZs11fSubxWSeHzzpZfN7J4bNOluvP2+tiVQAAkG25yIgAAAA/EYgAAABnCEQAAIAzBCIAAMCZXAUiv/jFL/TVr35VV111ldra2vSpT31Kjz32mM6dO+f60jLp8ccf180336yPfexj+sQnPuH6cjJnx44d+uQnP6mPfvSjuummm/TDH/7Q9SVl0ptvvql7771XixYtUqFQ0J49e1xfUmZt3bpVN954o+bOnavLL79cq1at0n/913+5vqzM6unp0fXXXz85yGzZsmX6/ve/n/h15CoQOXr0qCYmJvTcc8/p3Xff1dNPP62dO3fqb/7mb1xfWiadO3dO999/v9atW+f6UjLnxRdf1KZNm/TYY4/pnXfe0ZIlS3T33Xfr/fffd31pmTM6OqolS5Zox44dri8l8w4ePKj169fr7bff1quvvqrz58/ri1/8okZHR11fWiYtXrxYTzzxhA4fPqwf//jHuuOOO7Ry5Uq9++67iV5H7tt3t23bpp6eHr333nuuLyWzdu3apUceeUS/+tWvXF9KZtx000268cYb9eyzz0oy5zJ1dnbq4Ycf1ubNmx1fXXYVCgX19fVp1apVri8lF86cOaPLL79cBw8e1G233eb6cnJh3rx52rZtm7761a8m9pq5yohUMzQ0pHnz5rm+DMDauXPndPjwYa1YsWLyay0tLVqxYoV+8IMfOLwyIFpDQ0OSxH+jEzA+Pq7du3drdHRUy5YtS/S1vT70Lm7Hjh3TM888o+3bt7u+FMDaBx98oPHxcS1YsGDa1xcsWKCjR486uiogWhMTE3rkkUfU1dWl6667zvXlZNbPfvYzLVu2TP/3f/+nOXPmqK+vT5/+9KcTvYZMZEQ2b96sQqFQ9zHzP9AnT57Ul770Jd1///168MEHHV15+oT5rAEgqPXr1+vIkSPavXu360vJtGuvvVYDAwP693//d61bt05r1qzRf/zHfyR6DZnIiDz66KN64IEH6j7n6quvnvzfp06d0u23366bb75Z3/rWt2K+umwJ+lkjepdddplaW1t1+vTpaV8/ffq0Fi5c6OiqgOhs2LBB3/3ud/Xmm29q8eLFri8n02bNmqVrrrlGkrR06VL96Ec/0je+8Q0999xziV1DJgKR+fPna/78+VbPPXnypG6//XYtXbpUzz//vFpaMpEUSkyQzxrxmDVrlpYuXar9+/dPFk1OTExo//792rBhg9uLA5pQLpf18MMPq6+vTwcOHNBVV13l+pJyZ2JiQmNjY4m+ZiYCEVsnT57U8uXLdeWVV2r79u06c+bM5J9xJxm948eP63/+5390/PhxjY+Pa2BgQJJ0zTXXaM6cOW4vLuU2bdqkNWvW6Ld+67f0+c9/Xn//93+v0dFRfeUrX3F9aZkzMjKiY8eOTf7+5z//uQYGBjRv3jxdccUVDq8se9avX68XXnhBe/fu1dy5czU4OChJ6ujoUFtbm+Ory54tW7bonnvu0RVXXKGzZ8/qhRde0IEDB/TKK68keyHlHHn++efLkqo+EL01a9ZU/azfeOMN15eWCc8880z5iiuuKM+aNav8+c9/vvz222+7vqRMeuONN6r+HK9Zs8b1pWVOrf8+P//8864vLZP+7M/+rHzllVeWZ82aVZ4/f375zjvvLO/bty/x68j9HBEAAOAOBRIAAMAZAhEAAOAMgQgAAHCGQAQAADhDIAIAAJwhEAEAAM4QiAAAAGcIRAAAgDMEIgAAwBkCEQAA4AyBCAAAcIZABAAAOPP/AKwWRRDiBzjkAAAAAElFTkSuQmCC) - After Implementing K-Means Clustering - ![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) + + ![After Implementing K-Means Clustering](data:image/png;base64,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+ Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. 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z!s>5(N}+(ZYo14FzRtNg^TU^uiyqHBaGpQV4i=4`3*N;iYFt-VS!I<~R#|10RaRLg arT+(~s&-lbfZ;O$0000 Date: Tue, 4 Jun 2024 23:41:27 +0530 Subject: [PATCH 05/13] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index c6aee6a..82a5c83 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![enter image description here](https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQnDTFfxrrAttYMwwjZV0RAA8J8rmUxgrnWc2gU_ArEqrxEMlHm) +![image](assets/Knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,6 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action +![image](assets/Km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -66,11 +67,11 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio print("Predicted cluster for new data:", predicted_cluster) ### Output: -![Before Implementing K-Means Clustering](data:image/png;base64,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) + Before Implementing K-Means Clustering +![Before Implementing K-Means Clustering](assets/Km_2.png) - - - ![After Implementing K-Means Clustering](data:image/png;base64,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) + After Implementing K-Means Clustering + ![After Implementing K-Means Clustering](assets/Km_3.png) Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From d65dce72e10873a2554cbc37b00fab868fdfb0d5 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 23:46:20 +0530 Subject: [PATCH 06/13] update k-means --- contrib/machine-learning/K-Means_Clustering.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 82a5c83..bf72ffd 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![image](assets/Knm.png) +![image](assets\knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,7 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![image](assets/Km_.png) +![image](assets\km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -68,10 +68,10 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio ### Output: Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](assets/Km_2.png) +![Before Implementing K-Means Clustering](assets\km_2.png) After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets/Km_3.png) + ![After Implementing K-Means Clustering](assets\km_3.png) Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From 7bc7b0621eb59fa6e85c076885d1e18d2f103847 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Wed, 5 Jun 2024 11:26:57 +0530 Subject: [PATCH 07/13] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index bf72ffd..859636b 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![image](assets\knm.png) +![image](assets/knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,7 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![image](assets\km_.png) +![image](assets/km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -68,10 +68,11 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio ### Output: Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](assets\km_2.png) +![Before Implementing K-Means Clustering](assets/km_2.png) After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets\km_3.png) + ![After Implementing K-Means Clustering](assets/km_3.png) + Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From c2c84a09d21445382fc535a99d2745d8a8be0a29 Mon Sep 17 00:00:00 2001 From: Kosuri Indu Date: Sat, 8 Jun 2024 19:10:46 +0530 Subject: [PATCH 08/13] Added Splay Trees in DSA section --- contrib/ds-algorithms/index.md | 3 +- contrib/ds-algorithms/splay-trees.md | 162 +++++++++++++++++++++++++++ 2 files changed, 164 insertions(+), 1 deletion(-) create mode 100644 contrib/ds-algorithms/splay-trees.md diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..e099f97 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [Splay Trees](splay-trees.md) \ No newline at end of file diff --git a/contrib/ds-algorithms/splay-trees.md b/contrib/ds-algorithms/splay-trees.md new file mode 100644 index 0000000..ee900ed --- /dev/null +++ b/contrib/ds-algorithms/splay-trees.md @@ -0,0 +1,162 @@ +# Splay Tree + +In Data Structures and Algorithms, a **Splay Tree** is a self-adjusting binary search tree with the additional property that recently accessed elements are quick to access again. It performs basic operations such as insertion, search, and deletion in O(log n) amortized time. This is achieved by a process called **splaying**, where the accessed node is moved to the root through a series of tree rotations. + +## Points to be Remembered + +- **Splaying**: Moving the accessed node to the root using rotations. +- **Rotations**: Tree rotations (left and right) are used to balance the tree during splaying. +- **Self-adjusting**: The tree adjusts itself with each access, keeping frequently accessed nodes near the root. + +## Real Life Examples of Splay Trees + +- **Cache Implementation**: Frequently accessed data is kept near the top of the tree, making repeated accesses faster. +- **Networking**: Routing tables in network switches can use splay trees to prioritize frequently accessed routes. + +## Applications of Splay Trees + +Splay trees are used in various applications in Computer Science: + +- **Cache Implementations** +- **Garbage Collection Algorithms** +- **Data Compression Algorithms (e.g., LZ78)** + +Understanding these applications is essential for Software Development. + +## Operations in Splay Tree + +Key operations include: + +- **INSERT**: Insert a new element into the splay tree. +- **SEARCH**: Find the position of an element in the splay tree. +- **DELETE**: Remove an element from the splay tree. + +## Implementing Splay Tree in Python + +```python +class SplayTreeNode: + def __init__(self, key): + self.key = key + self.left = None + self.right = None + +class SplayTree: + def __init__(self): + self.root = None + + def insert(self, key): + self.root = self.splay_insert(self.root, key) + + def search(self, key): + self.root = self.splay_search(self.root, key) + return self.root + + def splay(self, root, key): + if not root or root.key == key: + return root + + if root.key > key: + if not root.left: + return root + if root.left.key > key: + root.left.left = self.splay(root.left.left, key) + root = self.rotateRight(root) + elif root.left.key < key: + root.left.right = self.splay(root.left.right, key) + if root.left.right: + root.left = self.rotateLeft(root.left) + return root if not root.left else self.rotateRight(root) + + else: + if not root.right: + return root + if root.right.key > key: + root.right.left = self.splay(root.right.left, key) + if root.right.left: + root.right = self.rotateRight(root.right) + elif root.right.key < key: + root.right.right = self.splay(root.right.right, key) + root = self.rotateLeft(root) + return root if not root.right else self.rotateLeft(root) + + def splay_insert(self, root, key): + if not root: + return SplayTreeNode(key) + + root = self.splay(root, key) + + if root.key == key: + return root + + new_node = SplayTreeNode(key) + + if root.key > key: + new_node.right = root + new_node.left = root.left + root.left = None + else: + new_node.left = root + new_node.right = root.right + root.right = None + + return new_node + + def splay_search(self, root, key): + return self.splay(root, key) + + def rotateRight(self, node): + temp = node.left + node.left = temp.right + temp.right = node + return temp + + def rotateLeft(self, node): + temp = node.right + node.right = temp.left + temp.left = node + return temp + + def preOrder(self, root): + if root: + print(root.key, end=' ') + self.preOrder(root.left) + self.preOrder(root.right) + +#Example usage: +splay_tree = SplayTree() +splay_tree.insert(50) +splay_tree.insert(30) +splay_tree.insert(20) +splay_tree.insert(40) +splay_tree.insert(70) +splay_tree.insert(60) +splay_tree.insert(80) + +print("Preorder traversal of the Splay tree is:") +splay_tree.preOrder(splay_tree.root) + +splay_tree.search(60) + +print("\nSplay tree after search operation for key 60:") +splay_tree.preOrder(splay_tree.root) +``` + +## Output + +```markdown +Preorder traversal of the Splay tree is: +50 30 20 40 70 60 80 + +Splay tree after search operation for key 60: +60 50 30 20 40 70 80 +``` + +## Complexity Analysis + +The worst-case time complexities of the main operations in a Splay Tree are as follows: + +- **Insertion**: (O(n)). In the worst case, insertion may take linear time if the tree is highly unbalanced. +- **Search**: (O(n)). In the worst case, searching for a node may take linear time if the tree is highly unbalanced. +- **Deletion**: (O(n)). In the worst case, deleting a node may take linear time if the tree is highly unbalanced. + +While these operations can take linear time in the worst case, the splay operation ensures that the tree remains balanced over a sequence of operations, leading to better average-case performance. \ No newline at end of file From aefb52e5b3e6a81e55dce1a22f4870b3ef0e2c69 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Sun, 9 Jun 2024 11:48:46 +0530 Subject: [PATCH 09/13] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 859636b..83fbd80 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -76,6 +76,10 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. +## Reference +[[Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] + +[[A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] From bb38f8fb5a9418a359635dcbec275e77e364c6fa Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Wed, 12 Jun 2024 21:57:30 +0530 Subject: [PATCH 10/13] Update K-Means_Clustering.md --- .../machine-learning/K-Means_Clustering.md | 96 ++++++++++--------- 1 file changed, 53 insertions(+), 43 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 83fbd80..ee615c3 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -1,19 +1,25 @@ # K-Means Clustering Unsupervised Learning Algorithm for Grouping Similar Data. + ## Introduction K-means clustering is a fundamental unsupervised machine learning algorithm that excels at grouping similar data points together. It's a popular choice due to its simplicity and efficiency in uncovering hidden patterns within unlabeled datasets. + ## Unsupervised Learning Unlike supervised learning algorithms that rely on labeled data for training, unsupervised algorithms, like K-means, operate solely on input data (without predefined categories). Their objective is to discover inherent structures or groupings within the data. + ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. ![image](assets/knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). + ## Minimizing In-Cluster Variation The K-means algorithm strategically assigns each data point to a cluster such that the total variation within each cluster (measured by the sum of squared distances between points and their centroid) is minimized. In simpler terms, K-means strives to create clusters where data points are close to their respective centroids. + ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. + ## K-Means Algorithm in Action ![image](assets/km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: @@ -24,62 +30,66 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio 4. **Iteration Until Convergence:** Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This criterion can be either: - **Centroid Stability:** No significant change occurs in the centroids' positions, indicating successful clustering. - **Reaching Maximum Iterations:** A predefined number of iterations is completed. - ## Code - Following is a simple implementation of K-Means. + +## Code +Following is a simple implementation of K-Means. - - # Generate and Visualize Sample Data - # import the necessary Libraries - - import numpy as np - import matplotlib.pyplot as plt +```python +# Generate and Visualize Sample Data +# import the necessary Libraries - # Create data points for cluster 1 and cluster 2 - X = -2 * np.random.rand(100, 2) - X1 = 1 + 2 * np.random.rand(50, 2) - - # Combine data points from both clusters - X[50:100, :] = X1 - - # Plot data points and display the plot - plt.scatter(X[:, 0], X[:, 1], s=50, c='b') - plt.show() +import numpy as np +import matplotlib.pyplot as plt - # K-Means Model Creation and Training - from sklearn.cluster import KMeans - - # Create KMeans object with 2 clusters - kmeans = KMeans(n_clusters=2) - kmeans.fit(X) # Train the model on the data +# Create data points for cluster 1 and cluster 2 +X = -2 * np.random.rand(100, 2) +X1 = 1 + 2 * np.random.rand(50, 2) - # Visualize Data Points with Centroids - centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) +# Combine data points from both clusters +X[50:100, :] = X1 + +# Plot data points and display the plot +plt.scatter(X[:, 0], X[:, 1], s=50, c='b') +plt.show() - plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again - plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 - plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 - plt.show() # Display the plot with centroids +# K-Means Model Creation and Training +from sklearn.cluster import KMeans - # Predict Cluster Label for New Data Point - new_data = np.array([-3.0, -3.0]) - new_data_reshaped = new_data.reshape(1, -1) - predicted_cluster = kmeans.predict(new_data_reshaped) - print("Predicted cluster for new data:", predicted_cluster) +# Create KMeans object with 2 clusters +kmeans = KMeans(n_clusters=2) +kmeans.fit(X) # Train the model on the data - ### Output: - Before Implementing K-Means Clustering +# Visualize Data Points with Centroids +centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) + +plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again +plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 +plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 +plt.show() # Display the plot with centroids + +# Predict Cluster Label for New Data Point +new_data = np.array([-3.0, -3.0]) +new_data_reshaped = new_data.reshape(1, -1) +predicted_cluster = kmeans.predict(new_data_reshaped) +print("Predicted cluster for new data:", predicted_cluster) +``` + +### Output: +Before Implementing K-Means Clustering ![Before Implementing K-Means Clustering](assets/km_2.png) - After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets/km_3.png) +After Implementing K-Means Clustering +![After Implementing K-Means Clustering](assets/km_3.png) + +Predicted cluster for new data: `[0]` - Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. -## Reference -[[Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] -[[A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] +## References + +- [Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) +- [A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) From cf01273be27a0d9f82c45a41e505fde46360b749 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Wed, 12 Jun 2024 21:58:13 +0530 Subject: [PATCH 11/13] Update and rename K-Means_Clustering.md to kmeans.md --- contrib/machine-learning/{K-Means_Clustering.md => kmeans.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/machine-learning/{K-Means_Clustering.md => kmeans.md} (100%) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/kmeans.md similarity index 100% rename from contrib/machine-learning/K-Means_Clustering.md rename to contrib/machine-learning/kmeans.md From 8f0e9808356ae8a02937d490f8952f3de28a42e4 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Wed, 12 Jun 2024 22:16:20 +0530 Subject: [PATCH 12/13] Update index.md --- contrib/machine-learning/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index b6945cd..6227561 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -16,3 +16,4 @@ - [Types_of_Cost_Functions](cost-functions.md) - [Clustering](clustering.md) - [Grid Search](grid-search.md) +- [K-Means](kmeans.md) From 51011db02b624db7723f246984e3a2d9644c5d57 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Thu, 13 Jun 2024 00:38:06 +0530 Subject: [PATCH 13/13] Update kmeans.md --- contrib/machine-learning/kmeans.md | 8 -------- 1 file changed, 8 deletions(-) diff --git a/contrib/machine-learning/kmeans.md b/contrib/machine-learning/kmeans.md index ee615c3..52db92e 100644 --- a/contrib/machine-learning/kmeans.md +++ b/contrib/machine-learning/kmeans.md @@ -90,11 +90,3 @@ Predicted cluster for new data: `[0]` - [Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) - [A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) - - - - - - - -

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