[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6KJ5Y8PZQ2K8SW58SQ39WBZ":3,"skill-same:01M6KJ5Y8PZQ2K8SW58SQ39WBZ":53},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":15,"categories":16,"keywords":17,"publishedAt":26,"linkOnly":27,"markdownContent":28,"markdownBody":29,"frontMatter":30,"refName":31,"commitSha":32,"skillDirectory":33,"forksCount":34,"repositoryHtmlUrl":35,"repositoryHomepageUrl":36,"ownerHtmlUrl":37,"ownerBlogUrl":6,"ownerDescription":6,"updatedAt":38,"install":39,"resources":52},"01M6KJ5Y8PZQ2K8SW58SQ39WBZ","dbscan-anisotropic-distance",null,"Efficiently computing DBSCAN with a custom weighted (anisotropic) distance metric using coordinate scaling, avoiding the overhead of slow custom distance functions.","cxcscmu\u002FSkillLearnBench","cxcscmu","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F142838272?v=4","01M6KCQDFQWPDSN0MKZY96MSQP","01M6KCQDM7G70TKJ28NTSQC0RZ",93,"MIT","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fb3-teacher-feedback-gemini-3.1-pro-preview\u002Fdbscan-parameter-tuning\u002Frun1_dbscan-anisotropic-distance\u002FSKILL.md",[],[18,19,20,21,22,23,24,25],"dbscan anisotropic distance","functions","coordinate","scaling","with","overhead","metric","custom","2026-11-10 10:12:30",false,"---\nname: dbscan-anisotropic-distance\ndescription: Efficiently computing DBSCAN with a custom weighted (anisotropic) distance metric using coordinate scaling, avoiding the overhead of slow custom distance functions.\n---\n\n# Efficient Anisotropic Distance for DBSCAN\n\nWhen using scikit-learn's `DBSCAN`, passing a custom Python function to the `metric` argument forces the algorithm to bypass highly optimized C\u002FCython code, making it run extremely slowly (or requiring precomputing massive $N \\times N$ distance matrices).\n\nIf your custom distance metric takes the form:\n$d(a, b) = \\sqrt{(w_x \\cdot \\Delta x)^2 + (w_y \\cdot \\Delta y)^2}$\n\nThis is mathematically identical to performing a standard Euclidean distance search on **scaled coordinates**. By temporarily transforming the dataset, you can use the default `metric='euclidean'` in `DBSCAN` at full C-optimized speeds.\n\n### Implementation\n\n```python\nimport numpy as np\nfrom sklearn.cluster import DBSCAN\n\ndef get_cluster_centroids_weighted(df_points, min_samples, epsilon, shape_weight):\n    if len(df_points) == 0:\n        return []\n    \n    # 1. Extract coordinates\n    X = df_points[['x', 'y']].values.astype(float)\n    \n    # 2. Scale coordinates to represent the weighted Euclidean distance\n    # Example: d = sqrt((w * dx)^2 + ((2-w) * dy)^2)\n    # We multiply the x column by w, and the y column by (2 - w)\n    X_scaled = X.copy()\n    X_scaled[:, 0] *= shape_weight\n    X_scaled[:, 1] *= (2 - shape_weight)\n    \n    # 3. Run DBSCAN using standard Euclidean distance on the scaled data\n    db = DBSCAN(eps=epsilon, min_samples=min_samples, metric='euclidean')\n    labels = db.fit_predict(X_scaled)\n    \n    # 4. Compute centroids using the ORIGINAL (unscaled) coordinates\n    centroids = []\n    for k in set(labels):\n        if k == -1:\n            continue # Skip noise points\n        \n        cluster_mask = (labels == k)\n        # Always return the real-world spatial coordinates for the centroid!\n        cluster_centroid = X[cluster_mask].mean(axis=0)\n        centroids.append(cluster_centroid)\n        \n    return np.array(centroids)\n```","# Efficient Anisotropic Distance for DBSCAN\n\nWhen using scikit-learn's `DBSCAN`, passing a custom Python function to the `metric` argument forces the algorithm to bypass highly optimized C\u002FCython code, making it run extremely slowly (or requiring precomputing massive $N \\times N$ distance matrices).\n\nIf your custom distance metric takes the form:\n$d(a, b) = \\sqrt{(w_x \\cdot \\Delta x)^2 + (w_y \\cdot \\Delta y)^2}$\n\nThis is mathematically identical to performing a standard Euclidean distance search on **scaled coordinates**. By temporarily transforming the dataset, you can use the default `metric='euclidean'` in `DBSCAN` at full C-optimized speeds.\n\n### Implementation\n\n```python\nimport numpy as np\nfrom sklearn.cluster import DBSCAN\n\ndef get_cluster_centroids_weighted(df_points, min_samples, epsilon, shape_weight):\n    if len(df_points) == 0:\n        return []\n    \n    # 1. Extract coordinates\n    X = df_points[['x', 'y']].values.astype(float)\n    \n    # 2. Scale coordinates to represent the weighted Euclidean distance\n    # Example: d = sqrt((w * dx)^2 + ((2-w) * dy)^2)\n    # We multiply the x column by w, and the y column by (2 - w)\n    X_scaled = X.copy()\n    X_scaled[:, 0] *= shape_weight\n    X_scaled[:, 1] *= (2 - shape_weight)\n    \n    # 3. Run DBSCAN using standard Euclidean distance on the scaled data\n    db = DBSCAN(eps=epsilon, min_samples=min_samples, metric='euclidean')\n    labels = db.fit_predict(X_scaled)\n    \n    # 4. Compute centroids using the ORIGINAL (unscaled) coordinates\n    centroids = []\n    for k in set(labels):\n        if k == -1:\n            continue # Skip noise points\n        \n        cluster_mask = (labels == k)\n        # Always return the real-world spatial coordinates for the centroid!\n        cluster_centroid = X[cluster_mask].mean(axis=0)\n        centroids.append(cluster_centroid)\n        \n    return np.array(centroids)\n```",{"name":5,"description":7},"main","726e1f79b96b0cb3d729d0e55a1c847e0b5353ae","skills\u002Fb3-teacher-feedback-gemini-3.1-pro-preview\u002Fdbscan-parameter-tuning\u002Frun1_dbscan-anisotropic-distance",7,"https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench","https:\u002F\u002Fcxcscmu.github.io\u002FSkillLearnBench","https:\u002F\u002Fgithub.com\u002Fcxcscmu","2026-10-02 22:55:36",{"source":8,"skillName":5,"commands":40,"prompt":50,"zipAvailable":51},[41,44,47],{"tool":42,"command":43},"npx","npx skills add cxcscmu\u002FSkillLearnBench --skill dbscan-anisotropic-distance",{"tool":45,"command":46},"bunx","bunx skills add cxcscmu\u002FSkillLearnBench --skill dbscan-anisotropic-distance",{"tool":48,"command":49},"pnpm","pnpm dlx skills add cxcscmu\u002FSkillLearnBench --skill dbscan-anisotropic-distance","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fb3-teacher-feedback-gemini-3.1-pro-preview\u002Fdbscan-parameter-tuning\u002Frun1_dbscan-anisotropic-distance\u002FSKILL.md",true,[],[54,72,97,115,135,146],{"skillNo":55,"name":56,"nameZh":6,"description":57,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":58,"categories":59,"keywords":65,"publishedAt":26},"01M6KM5KH175P5ABP5JMX2SBDQ","object_counter","Count occurrences of an object in the image using computer vision algorithm.","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fhuman_authored\u002Fvideo-object-counting\u002Fobject_counter\u002FSKILL.md",[60],{"categoryNo":61,"categoryName":62,"taxonomyType":63,"taxonomyTypeDesc":64},"01JBSEEDCAT000000000000016","图像与多媒体","SCENARIO","使用场景",[66,67,68,69,70,71],"object counter","object","vision","computer","Computer Vision","image",{"skillNo":73,"name":74,"nameZh":6,"description":75,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":76,"categories":77,"keywords":81,"publishedAt":26},"01M6KM51TMVXG79MMPCS6Y8G86","travel-planning-workflow","Invoke this skill when performing travel planning. It defines a structured workflow for generating itineraries. Following this workflow is essential to ensure the final plan satisfies user requirements.","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fhuman_authored\u002Ftravel-planning\u002Ftravel-planning-workflow\u002FSKILL.md",[78],{"categoryNo":79,"categoryName":80,"taxonomyType":63,"taxonomyTypeDesc":64},"01JBSEEDCAT000000000000023","Skill与智能体开发",[82,83,84,85,86,87,88,89,90,91,92,93,94,95,96],"workflow","planning","planning workflow","travel","travel planning","travel planning workflow","structured","performing","plan","for","user","it","requirements","essential","itineraries",{"skillNo":98,"name":99,"nameZh":6,"description":100,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":101,"categories":102,"keywords":103,"publishedAt":26},"01M6KM4DY820XHS9YTSK5QP5HD","bundled-dataset-search-tool","invoke this skill when you need to perform database search for travel planning. This skill provides some useful pre-packaged tools to look up accommodations, attractions, cities, driving distance, flights, and restaurants from the bundled dataset.","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fhuman_authored\u002Ftravel-planning\u002Fbundled-dataset-search-tool\u002FSKILL.md",[],[104,105,106,107,108,109,110,85,111,112,86,113,91,114,83],"search","tool","dataset","bundled dataset search tool","restaurants","Tools","up","look","flights","you","database",{"skillNo":116,"name":117,"nameZh":6,"description":118,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":119,"categories":120,"keywords":121,"publishedAt":26},"01M6KM465BB9PQ0B548HQSVAWZ","glm-output","Output-processing guidance for GLM tasks. Especially useful after glm-basics and glm-calibration when you need verifier-matching metrics from output.nc and a final \u002Froot\u002Fmetrics.json.","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fhuman_authored\u002Ftemperature-simulation\u002Fglm-output\u002FSKILL.md",[],[122,123,124,91,125,126,127,128,129,130,131,132,113,133,134],"glm output","output","glm","tasks","metrics","json","basics","guidance","matching","verifier","processing","root","calibration",{"skillNo":136,"name":137,"nameZh":6,"description":138,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":139,"categories":140,"keywords":142,"publishedAt":26},"01M6KM40KY3QWDW5W97S39R2BC","glm-calibration","Calibration guidance for GLM tasks. Often most effective after glm-basics has clarified the setup; glm-output is the companion skill for exact final metric computation.","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fhuman_authored\u002Ftemperature-simulation\u002Fglm-calibration\u002FSKILL.md",[141],{"categoryNo":79,"categoryName":80,"taxonomyType":63,"taxonomyTypeDesc":64},[143,134,124,123,129,128,125,144,145,91,24],"glm calibration","setup","companion",{"skillNo":147,"name":148,"nameZh":6,"description":149,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":150,"categories":151,"keywords":152,"publishedAt":26},"01M6KM3VHHVSGMGHJQB3PPT6YG","glm-basics","A good starting point for GLM calibration tasks. Use to inspect glm3.nml, confirm how GLM runs, and identify the relevant files before moving on to calibration and output evaluation.","https:\u002F\u002Fgithub.com\u002Fcxcscmu\u002FSkillLearnBench\u002Fblob\u002Fmain\u002Fskills\u002Fhuman_authored\u002Ftemperature-simulation\u002Fglm-basics\u002FSKILL.md",[],[153,124,128,154,143,134,91,123,155,156,157,158,159,160,125],"glm basics","inspect","relevant","files","good","use","how","Evaluation"]