{
  "analysis_id": "uci-seeds-scaled-pca",
  "analysis_scope": "Descriptive PCA of the complete UCI Seeds dataset. No population inference, classifier evaluation, or causal claim is made.",
  "counts": {
    "features": 7,
    "kernels": 210,
    "kernels_by_variety": {
      "Canadian": 70,
      "Kama": 70,
      "Rosa": 70
    },
    "missing_measurement_cells": 0
  },
  "figures": {
    "fig-wheat-kernel-all-features.png": {
      "dimensions": [
        2400,
        2400
      ],
      "plotting_note": "Boxplots plus all observations with deterministic jitter from NumPy seed 236",
      "question": "How are all seven original measurements distributed within each recorded variety?",
      "sha256": "66f65468cf83297c681a660533a0ead591225fa5cc60ae055e77ab99db20d3c4"
    },
    "fig-wheat-kernel-correlations.png": {
      "dimensions": [
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      ],
      "question": "Which pairs of original measurements have strong linear correlations?",
      "sha256": "ba62a90e5ecfcfee6bcc0373274168abb8b90e1c6fbf6234186f5a3a5197be89"
    },
    "fig-wheat-kernel-feature-space.png": {
      "dimensions": [
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        1000
      ],
      "question": "What is visible in two of the seven original measurements?",
      "sha256": "71cb776e5e575200795f9ee203dc371247c5032dfb91fe8b2d5827bde90e379b"
    },
    "fig-wheat-kernel-loadings.png": {
      "dimensions": [
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      ],
      "question": "Which principal-axis coefficients define PC1 and PC2?",
      "sha256": "0986e90f9a7007f83a9b516174bacf0d1639b94fbe86116d83e63ba885d14418"
    },
    "fig-wheat-kernel-pca.png": {
      "dimensions": [
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      ],
      "question": "Where do kernels land on PC1 and PC2, and how much variance do all components represent?",
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    },
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      "dimensions": [
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      "question": "What is the page's central real-data example?",
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  "original_feature_correlations": {
    "area": {
      "area": 1.0,
      "asymmetry_coefficient": -0.229572,
      "compactness": 0.608288,
      "kernel_groove_length": 0.863693,
      "kernel_length": 0.949985,
      "kernel_width": 0.970771,
      "perimeter": 0.994341
    },
    "asymmetry_coefficient": {
      "area": -0.229572,
      "asymmetry_coefficient": 1.0,
      "compactness": -0.331471,
      "kernel_groove_length": -0.011079,
      "kernel_length": -0.171562,
      "kernel_width": -0.258037,
      "perimeter": -0.21734
    },
    "compactness": {
      "area": 0.608288,
      "asymmetry_coefficient": -0.331471,
      "compactness": 1.0,
      "kernel_groove_length": 0.226825,
      "kernel_length": 0.367915,
      "kernel_width": 0.761635,
      "perimeter": 0.529244
    },
    "kernel_groove_length": {
      "area": 0.863693,
      "asymmetry_coefficient": -0.011079,
      "compactness": 0.226825,
      "kernel_groove_length": 1.0,
      "kernel_length": 0.932806,
      "kernel_width": 0.749131,
      "perimeter": 0.890784
    },
    "kernel_length": {
      "area": 0.949985,
      "asymmetry_coefficient": -0.171562,
      "compactness": 0.367915,
      "kernel_groove_length": 0.932806,
      "kernel_length": 1.0,
      "kernel_width": 0.860415,
      "perimeter": 0.972422
    },
    "kernel_width": {
      "area": 0.970771,
      "asymmetry_coefficient": -0.258037,
      "compactness": 0.761635,
      "kernel_groove_length": 0.749131,
      "kernel_length": 0.860415,
      "kernel_width": 1.0,
      "perimeter": 0.944829
    },
    "perimeter": {
      "area": 0.994341,
      "asymmetry_coefficient": -0.21734,
      "compactness": 0.529244,
      "kernel_groove_length": 0.890784,
      "kernel_length": 0.972422,
      "kernel_width": 0.944829,
      "perimeter": 1.0
    }
  },
  "pca": {
    "coefficient_terminology": "Values called loadings in legacy artifact names are principal-axis coefficients, equivalently entries of the right singular vectors; they are not feature-component correlation loadings",
    "explained_variance_ratio": {
      "PC1": 0.718743,
      "PC2": 0.171082,
      "PC3": 0.096858,
      "PC4": 0.009766,
      "PC5": 0.002673,
      "PC6": 0.000762,
      "PC7": 0.000116
    },
    "first_two_components_combined": 0.889825,
    "loadings_ordered_by_absolute_value": {
      "PC1": [
        {
          "feature": "area",
          "label": "Area",
          "loading": 0.444474
        },
        {
          "feature": "perimeter",
          "label": "Perimeter",
          "loading": 0.441571
        },
        {
          "feature": "kernel_width",
          "label": "Kernel width",
          "loading": 0.432819
        },
        {
          "feature": "kernel_length",
          "label": "Kernel length",
          "loading": 0.423563
        },
        {
          "feature": "kernel_groove_length",
          "label": "Kernel-groove length",
          "loading": 0.387161
        },
        {
          "feature": "compactness",
          "label": "Compactness",
          "loading": 0.277017
        },
        {
          "feature": "asymmetry_coefficient",
          "label": "Asymmetry coefficient",
          "loading": -0.118692
        }
      ],
      "PC2": [
        {
          "feature": "asymmetry_coefficient",
          "label": "Asymmetry coefficient",
          "loading": -0.716882
        },
        {
          "feature": "compactness",
          "label": "Compactness",
          "loading": 0.529151
        },
        {
          "feature": "kernel_groove_length",
          "label": "Kernel-groove length",
          "loading": -0.377193
        },
        {
          "feature": "kernel_length",
          "label": "Kernel length",
          "loading": -0.205975
        },
        {
          "feature": "kernel_width",
          "label": "Kernel width",
          "loading": 0.11669
        },
        {
          "feature": "perimeter",
          "label": "Perimeter",
          "loading": -0.084003
        },
        {
          "feature": "area",
          "label": "Area",
          "loading": -0.026564
        }
      ]
    },
    "method": "singular value decomposition of the centered, scaled matrix",
    "sign_orientation": [
      "PC1 is oriented so area has a positive principal-axis coefficient",
      "PC2 is oriented so compactness has a positive principal-axis coefficient",
      "PC3 is oriented so asymmetry coefficient has a positive principal-axis coefficient",
      "PC4 is oriented so kernel-groove length has a positive principal-axis coefficient",
      "PC5 is oriented so kernel length has a positive principal-axis coefficient",
      "PC6 is oriented so kernel width has a positive principal-axis coefficient",
      "PC7 is oriented so area has a positive principal-axis coefficient"
    ],
    "variety_score_centroids": {
      "Canadian": {
        "PC1": -2.317316,
        "PC2": -0.607992
      },
      "Kama": {
        "PC1": -0.364914,
        "PC2": 1.017664
      },
      "Rosa": {
        "PC1": 2.68223,
        "PC2": -0.409671
      }
    }
  },
  "preprocessing": {
    "aggregation": "none",
    "feature_means": {
      "area": 14.847524,
      "asymmetry_coefficient": 3.700201,
      "compactness": 0.870999,
      "kernel_groove_length": 5.408071,
      "kernel_length": 5.628533,
      "kernel_width": 3.258605,
      "perimeter": 14.559286
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    "feature_standard_deviations": {
      "area": 2.902763,
      "asymmetry_coefficient": 1.499973,
      "compactness": 0.023573,
      "kernel_groove_length": 0.490309,
      "kernel_length": 0.442007,
      "kernel_width": 0.376814,
      "perimeter": 1.302846
    },
    "imputation": "none; the source table contains no missing values",
    "scaling": "for each feature, subtract the full-dataset mean and divide by the full-dataset population standard deviation (ddof=0)"
  },
  "provenance": {
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  "source": {
    "committed_source": "seeds_dataset.txt",
    "dataset": "Seeds",
    "dataset_page": "https://archive.ics.uci.edu/dataset/236/seeds",
    "doi": "10.24432/C5H30K",
    "download_url": "https://archive.ics.uci.edu/ml/machine-learning-databases/00236/seeds_dataset.txt",
    "license": "CC BY 4.0",
    "repository": "UCI Machine Learning Repository",
    "row_definition": "one measured wheat kernel",
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      "3": "Canadian"
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}