diff --git a/docs/prediction/weights_of_evidence.md b/docs/prediction/weights_of_evidence.md
new file mode 100644
index 00000000..e642df88
--- /dev/null
+++ b/docs/prediction/weights_of_evidence.md
@@ -0,0 +1,3 @@
+# Weights of evidence
+
+::: eis_toolkit.prediction.weights_of_evidence
diff --git a/eis_toolkit/exceptions.py b/eis_toolkit/exceptions.py
index b3fb4248..6dec2159 100644
--- a/eis_toolkit/exceptions.py
+++ b/eis_toolkit/exceptions.py
@@ -2,6 +2,10 @@ class CoordinatesOutOfBoundsException(Exception):
"""Exception error class for out of bound coordinates."""
+class ClassificationFailedException(Exception):
+ """Exception error class for classification failures."""
+
+
class EmptyDataFrameException(Exception):
"""Exception error class raised if the dataframe is empty."""
diff --git a/eis_toolkit/prediction/weights_of_evidence.py b/eis_toolkit/prediction/weights_of_evidence.py
new file mode 100644
index 00000000..7f668ee1
--- /dev/null
+++ b/eis_toolkit/prediction/weights_of_evidence.py
@@ -0,0 +1,418 @@
+from numbers import Number
+
+import geopandas as gpd
+import numpy as np
+import pandas as pd
+import rasterio
+from beartype import beartype
+from beartype.typing import Dict, List, Literal, Optional, Sequence, Tuple
+
+from eis_toolkit import exceptions
+from eis_toolkit.vector_processing.rasterize_vector import rasterize_vector
+
+CLASS_COLUMN = "Class"
+PIXEL_COUNT_COLUMN = "Pixel count"
+DEPOSIT_COUNT_COLUMN = "Deposit count"
+WEIGHT_PLUS_COLUMN = "W+"
+WEIGHT_S_PLUS_COLUMN = "S_W+"
+WEIGHT_MINUS_COLUMN = "W-"
+WEIGHT_S_MINUS_COLUMN = "S_W-"
+CONTRAST_COLUMN = "Contrast"
+S_CONTRAST_COLUMN = "S_Contrast"
+STUDENTIZED_CONTRAST_COLUMN = "Studentized contrast"
+GENERALIZED_CLASS_COLUMN = "Generalized class"
+GENERALIZED_WEIGHT_PLUS_COLUMN = "Generalized W+"
+GENERALIZED_S_WEIGHT_PLUS_COLUMN = "Generalized S_W+"
+
+VALID_DF_COLUMNS = [
+ CLASS_COLUMN,
+ PIXEL_COUNT_COLUMN,
+ DEPOSIT_COUNT_COLUMN,
+ WEIGHT_PLUS_COLUMN,
+ WEIGHT_S_PLUS_COLUMN,
+ WEIGHT_MINUS_COLUMN,
+ WEIGHT_S_MINUS_COLUMN,
+ CONTRAST_COLUMN,
+ S_CONTRAST_COLUMN,
+ STUDENTIZED_CONTRAST_COLUMN,
+ GENERALIZED_CLASS_COLUMN,
+ GENERALIZED_WEIGHT_PLUS_COLUMN,
+ GENERALIZED_S_WEIGHT_PLUS_COLUMN,
+]
+
+DEFAULT_METRICS_UNIQUE = [CLASS_COLUMN, WEIGHT_PLUS_COLUMN, WEIGHT_S_PLUS_COLUMN]
+DEFAULT_METRICS_CUMULATIVE = [
+ CLASS_COLUMN,
+ WEIGHT_PLUS_COLUMN,
+ WEIGHT_S_PLUS_COLUMN,
+ GENERALIZED_WEIGHT_PLUS_COLUMN,
+ GENERALIZED_S_WEIGHT_PLUS_COLUMN,
+]
+
+
+def _read_and_preprocess_evidence(
+ raster: rasterio.io.DatasetReader, nodata: Optional[Number] = None, band: int = 1
+) -> np.ndarray:
+ """Read raster data and handle NoData values."""
+
+ array = np.array(raster.read(band), dtype=np.float32)
+
+ if nodata is not None:
+ array[array == nodata] = np.nan
+ elif raster.meta["nodata"] is not None:
+ array[array == raster.meta["nodata"]] = np.nan
+
+ return array
+
+
+def _calculate_metrics_for_class(
+ deposits: np.ndarray, evidence: np.ndarray
+) -> Tuple[float, float, float, float, float, float, float, float, float, float, float]:
+ """Calculate weights/metrics for given data."""
+ A = np.sum(np.logical_and(deposits == 1, evidence == 1))
+ B = np.sum(np.logical_and(deposits == 1, evidence == 0))
+ C = np.sum(np.logical_and(deposits == 0, evidence == 1))
+ D = np.sum(np.logical_and(deposits == 0, evidence == 0))
+
+ # If data has no deposits or every evidence pixel has a deposit
+ if A == 0 or C + D == 0:
+ return A, B, C, D, 0, 0, 0, 0, 0, 0, 0
+
+ p_A_nominator = A
+ p_C_nominator = C
+ B_adjusted = B
+ D_adjusted = D
+
+ if B == 0:
+ p_A_nominator -= 0.99
+ B_adjusted = 0.99
+
+ if D == 0:
+ p_C_nominator -= 0.99
+ D_adjusted = 0.99
+
+ p_A = p_A_nominator / (A + B) # probability of presence of evidence given the presence of mineral deposit
+ p_C = p_C_nominator / (C + D) # probability of presence of evidence given the absence of mineral deposit
+
+ # Calculate metrics
+ w_plus = np.log(p_A / p_C) if p_C != 0 else 0 # Check
+ w_minus = np.log((1 - p_A) / (1 - p_C))
+ contrast = w_plus - w_minus
+
+ # Calculate signifigance metrics
+ s_w_plus = np.sqrt((1 / p_A_nominator) + (1 / p_C_nominator))
+ s_w_minus = np.sqrt((1 / B_adjusted) + (1 / D_adjusted))
+
+ s_contrast = np.sqrt(s_w_plus**2 + s_w_minus**2)
+ studentized_contrast = contrast / s_contrast
+
+ return A, B, C, D, w_plus, s_w_plus, w_minus, s_w_minus, contrast, s_contrast, studentized_contrast
+
+
+def _unique_weights(deposits: np.ndarray, evidence: np.ndarray) -> dict:
+ """Calculate unique weights for each class."""
+ classes = np.unique(evidence)
+ return {cls: _calculate_metrics_for_class(deposits, evidence == cls) for cls in classes}
+
+
+def _cumulative_weights(deposits: np.ndarray, evidence: np.ndarray, ascending: bool = True) -> dict:
+ """Calculate cumulative weights (ascending or descending) for each class."""
+ classes = sorted(np.unique(evidence), reverse=not ascending)
+ cumulative_classes = [classes[: i + 1] for i in range(len(classes))]
+ return {
+ cls[i]: _calculate_metrics_for_class(deposits, np.isin(evidence, cls))
+ for i, cls in enumerate(cumulative_classes)
+ }
+
+
+def _generalized_classes_categorical(df: pd.DataFrame, studentized_contrast_threshold: Number) -> pd.DataFrame:
+ gen_df = df.copy()
+ gen_df[GENERALIZED_CLASS_COLUMN] = gen_df[CLASS_COLUMN]
+
+ reclassified = False
+ for i in range(0, len(gen_df.index)):
+ if abs(gen_df.loc[i, STUDENTIZED_CONTRAST_COLUMN]) < studentized_contrast_threshold:
+ gen_df.loc[i, GENERALIZED_CLASS_COLUMN] = 99
+ reclassified = True
+
+ if not reclassified:
+ raise exceptions.ClassificationFailedException(
+ "Failed to create generalized classes with given studentized contrast treshold ({})".format(
+ studentized_contrast_threshold
+ )
+ )
+
+ gen_df = gen_df.sort_values(by=GENERALIZED_CLASS_COLUMN, ascending=True)
+
+ return gen_df
+
+
+def _generalized_weights_categorical(df: pd.DataFrame, deposits) -> pd.DataFrame:
+ """Calculate generalized weights for categorical weights type. Assumes class 99 exists as the general class."""
+ gen_df = df.copy()
+ total_deposits = np.sum(deposits == 1)
+ total_no_deposits = deposits.size - total_deposits
+
+ # Class 99 (gen class)
+ class_99_count = 0
+ class_99_point_count = 0
+
+ for i in range(0, len(gen_df.index)):
+ if gen_df.loc[i, GENERALIZED_CLASS_COLUMN] == 99:
+ # class_99_count = max(gen_df.loc[i, PIXEL_COUNT_COLUMN], class_99_count)
+ # class_99_point_count = max(gen_df.loc[i, DEPOSIT_COUNT_COLUMN], class_99_point_count)
+ class_99_count += gen_df.loc[i, PIXEL_COUNT_COLUMN]
+ class_99_point_count += gen_df.loc[i, DEPOSIT_COUNT_COLUMN]
+
+ class_99_w_gen = np.log(class_99_point_count / total_deposits) - np.log(
+ (class_99_count - class_99_point_count) / total_no_deposits
+ )
+ clas_99_s_wpls_gen = np.sqrt((1 / class_99_point_count) + (1 / (class_99_count - class_99_point_count)))
+
+ gen_df[GENERALIZED_WEIGHT_PLUS_COLUMN] = gen_df[WEIGHT_PLUS_COLUMN]
+ gen_df[GENERALIZED_S_WEIGHT_PLUS_COLUMN] = gen_df[WEIGHT_S_PLUS_COLUMN]
+
+ gen_df.loc[gen_df[GENERALIZED_CLASS_COLUMN] == 99, GENERALIZED_WEIGHT_PLUS_COLUMN] = round(class_99_w_gen, 4)
+ gen_df.loc[gen_df[GENERALIZED_CLASS_COLUMN] == 99, GENERALIZED_S_WEIGHT_PLUS_COLUMN] = round(clas_99_s_wpls_gen, 4)
+
+ return gen_df
+
+
+def _generalized_classes_cumulative(df: pd.DataFrame, studentized_contrast_threshold: Number) -> pd.DataFrame:
+ """Create generalized classes based on contrast and studentized contrast threhsold value."""
+ gen_df = df.copy()
+ index = gen_df.idxmax()[CONTRAST_COLUMN]
+
+ if (
+ gen_df.loc[index, STUDENTIZED_CONTRAST_COLUMN] < studentized_contrast_threshold
+ or index == len(gen_df.index) - 1
+ ):
+ raise exceptions.ClassificationFailedException(
+ "Failed to create generalized classes with given studentized contrast treshold ({} < {})".format(
+ gen_df.loc[index, STUDENTIZED_CONTRAST_COLUMN], studentized_contrast_threshold
+ )
+ )
+
+ gen_df[GENERALIZED_CLASS_COLUMN] = 1
+ for i in range(0, index + 1):
+ gen_df.loc[i, GENERALIZED_CLASS_COLUMN] = 2
+
+ return gen_df
+
+
+def _generalized_weights_cumulative(df: pd.DataFrame, deposits: np.ndarray) -> pd.DataFrame:
+ """
+ Calculate generalized weights for cumulative methods.
+
+ Assumes there are classes 1 and 2 as the general classes.
+ """
+ gen_df = df.copy()
+ total_deposits = np.sum(deposits == 1)
+ total_no_deposits = deposits.size - total_deposits
+
+ # Class 2
+ class_2_max_index = gen_df.idxmax()[CONTRAST_COLUMN]
+ class_2_count = gen_df.loc[class_2_max_index, PIXEL_COUNT_COLUMN]
+ class_2_point_count = gen_df.loc[class_2_max_index, DEPOSIT_COUNT_COLUMN]
+
+ class_2_w_gen = np.log(class_2_point_count / total_deposits) - np.log(
+ (class_2_count - class_2_point_count) / total_no_deposits
+ )
+ clas_2_s_wpls_gen = np.sqrt((1 / class_2_point_count) + (1 / (class_2_count - class_2_point_count)))
+
+ gen_df[GENERALIZED_WEIGHT_PLUS_COLUMN] = round(class_2_w_gen, 4)
+ gen_df[GENERALIZED_S_WEIGHT_PLUS_COLUMN] = round(clas_2_s_wpls_gen, 4)
+
+ # Class 1
+ class_1_count = gen_df.loc[len(gen_df.index) - 1, PIXEL_COUNT_COLUMN] - class_2_count
+ class_1_point_count = gen_df.loc[len(gen_df.index) - 1, DEPOSIT_COUNT_COLUMN] - class_2_point_count
+
+ class_1_w_gen = np.log(class_1_point_count / total_deposits) - np.log(
+ (class_1_count - class_1_point_count) / total_no_deposits
+ )
+ clas_1_s_wpls_gen = np.sqrt((1 / class_1_point_count) + (1 / (class_1_count - class_1_point_count)))
+ gen_df.loc[gen_df[GENERALIZED_CLASS_COLUMN] == 1, GENERALIZED_WEIGHT_PLUS_COLUMN] = round(class_1_w_gen, 4)
+ gen_df.loc[gen_df[GENERALIZED_CLASS_COLUMN] == 1, GENERALIZED_S_WEIGHT_PLUS_COLUMN] = round(clas_1_s_wpls_gen, 4)
+
+ return gen_df
+
+
+def _generate_arrays_from_metrics(
+ evidence: np.ndarray, df: pd.DataFrame, metrics_to_include: List[str]
+) -> Dict[str, np.ndarray]:
+ """Generate arrays for defined metrics."""
+ array_dict = {}
+ for metric in metrics_to_include:
+ metric_array = np.full(evidence.shape, np.nan)
+ for _, row in df.iterrows():
+ mask = np.isin(evidence, row[CLASS_COLUMN])
+ metric_array[mask] = row[metric]
+ array_dict[metric] = metric_array
+ return array_dict
+
+
+@beartype
+def weights_of_evidence_calculate_weights(
+ evidential_raster: rasterio.io.DatasetReader,
+ deposits: gpd.GeoDataFrame,
+ raster_nodata: Optional[Number] = None,
+ weights_type: Literal["unique", "categorical", "ascending", "descending"] = "unique",
+ studentized_contrast_threshold: Number = 1,
+ arrays_to_generate: Optional[Sequence[str]] = None,
+) -> Tuple[pd.DataFrame, dict, dict, int, int]:
+ """
+ Calculate weights of spatial associations.
+
+ Args:
+ evidential_raster: The evidential raster.
+ deposits: Vector data representing the mineral deposits or occurences point data.
+ raster_nodata: If nodata value of raster is wanted to specify manually. Optional parameter, defaults to None
+ (nodata from raster metadata is used).
+ weights_type: Accepted values are 'unique', 'categorical', 'ascending' and 'descending'.
+ Unique weights does not create generalized classes and does not use a studentized contrast threshold value
+ while categorical, cumulative ascending and cumulative descending do. Categorical weights are calculated so
+ that all classes with studentized contrast below the defined threshold are grouped into one generalized
+ class. Cumulative ascending and descending weights find the class with max contrast and group classes
+ above/below into generalized classes. Generalized weights are also calculated for generalized classes.
+ studentized_contrast_threshold: Studentized contrast threshold value used with 'categorical', 'ascending' and
+ 'descending' weight types. Used either as reclassification threshold directly (categorical) or to check
+ that class with max contrast has studentized contrast value at least the defined value (cumulative).
+ Defaults to 1.
+ arrays_to_generate: Arrays to generate from the computed weight metrics. All column names
+ in the produced weights_df are valid choices. Defaults to ["Class", "W+", "S_W+]
+ for "unique" weights_type and ["Class", "W+", "S_W+", "Generalized W+", "Generalized S_W+"]
+ for the cumulative weight types.
+
+ Returns:
+ Dataframe with weights of spatial association between the input data.
+ Dictionary of arrays for specified metrics.
+ Raster metadata.
+ Number of deposit pixels.
+ Number of all evidence pixels.
+ """
+
+ if arrays_to_generate is None:
+ if weights_type == "unique":
+ metrics_to_arrays = DEFAULT_METRICS_UNIQUE
+ else:
+ metrics_to_arrays = DEFAULT_METRICS_CUMULATIVE
+ else:
+ for col_name in arrays_to_generate:
+ if col_name not in VALID_DF_COLUMNS:
+ raise exceptions.InvalidColumnException(
+ f"Arrays to generate contains invalid metric / column name: {col_name}."
+ )
+ metrics_to_arrays = arrays_to_generate.copy()
+
+ # 1. Preprocess data
+ evidence_array = _read_and_preprocess_evidence(evidential_raster, raster_nodata)
+ raster_meta = evidential_raster.meta
+
+ # Rasterize deposits
+ deposit_array, _ = rasterize_vector(
+ geodataframe=deposits, default_value=1.0, base_raster_profile=raster_meta, fill_value=0.0
+ )
+
+ # Mask NaN out of the array
+ nodata_mask = np.isnan(evidence_array)
+ masked_evidence_array = evidence_array[~nodata_mask]
+ masked_deposit_array = deposit_array[~nodata_mask]
+
+ # 2. WofE calculations
+ if weights_type == "unique" or weights_type == "categorical":
+ wofe_weights = _unique_weights(masked_deposit_array, masked_evidence_array)
+ elif weights_type == "ascending":
+ wofe_weights = _cumulative_weights(masked_deposit_array, masked_evidence_array, ascending=True)
+ elif weights_type == "descending":
+ wofe_weights = _cumulative_weights(masked_deposit_array, masked_evidence_array, ascending=False)
+ else:
+ raise exceptions.InvalidParameterValueException(
+ "Expected weights_type to be one of unique, categorical, ascending or descending."
+ )
+
+ # 3. Create DataFrame based on calculated metrics
+ df_entries = []
+ for cls, metrics in wofe_weights.items():
+ metrics = [round(metric, 4) if isinstance(metric, np.floating) else metric for metric in metrics]
+ A, _, C, _, w_plus, s_w_plus, w_minus, s_w_minus, contrast, s_contrast, studentized_contrast = metrics
+ df_entries.append(
+ {
+ CLASS_COLUMN: cls,
+ PIXEL_COUNT_COLUMN: A + C,
+ DEPOSIT_COUNT_COLUMN: A,
+ WEIGHT_PLUS_COLUMN: w_plus,
+ WEIGHT_S_PLUS_COLUMN: s_w_plus,
+ WEIGHT_MINUS_COLUMN: w_minus,
+ WEIGHT_S_MINUS_COLUMN: s_w_minus,
+ CONTRAST_COLUMN: contrast,
+ S_CONTRAST_COLUMN: s_contrast,
+ STUDENTIZED_CONTRAST_COLUMN: studentized_contrast,
+ }
+ )
+ weights_df = pd.DataFrame(df_entries)
+
+ # 4. If we use cumulative weights type, calculate generalized classes and weights
+ if weights_type == "categorical":
+ weights_df = _generalized_classes_categorical(weights_df, studentized_contrast_threshold)
+ weights_df = _generalized_weights_categorical(weights_df, masked_deposit_array)
+ elif weights_type == "ascending" or weights_type == "descending":
+ weights_df = _generalized_classes_cumulative(weights_df, studentized_contrast_threshold)
+ weights_df = _generalized_weights_cumulative(weights_df, masked_deposit_array)
+
+ # 5. Generate arrays for desired metrics
+ arrays_dict = _generate_arrays_from_metrics(evidence_array, weights_df, metrics_to_arrays)
+
+ # Return nr. of deposit pixels and nr. of all evidence pixels for to be used in calculate responses
+ nr_of_deposits = int(np.sum(masked_deposit_array == 1))
+ nr_of_pixels = int(np.size(masked_evidence_array))
+
+ return weights_df, arrays_dict, raster_meta, nr_of_deposits, nr_of_pixels
+
+
+@beartype
+def weights_of_evidence_calculate_responses(
+ output_arrays: Sequence[Dict[str, np.ndarray]], nr_of_deposits: int, nr_of_pixels: int
+) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+ """Calculate the posterior probabilities for the given generalized weight arrays.
+
+ Args:
+ output_arrays: List of output array dictionaries returned by weights of evidence calculations.
+ For each dictionary, generalized weight and generalized standard deviation arrays are used and summed
+ together pixel-wise to calculate the posterior probabilities. If generalized arrays are not found,
+ the W+ and S_W+ arrays are used (so if outputs from unique weight calculations are used for this function).
+ nr_of_deposits: Number of deposit pixels in the input data for weights of evidence calculations.
+ nr_of_pixels: Number of evidence pixels in the input data for weights of evidence calculations.
+
+ Returns:
+ Array of posterior probabilites.
+ Array of standard deviations in the posterior probability calculations.
+ Array of confidence of the prospectivity values obtained in the posterior probability array.
+ """
+ gen_weights_sum = sum(
+ [
+ item[GENERALIZED_WEIGHT_PLUS_COLUMN]
+ if GENERALIZED_WEIGHT_PLUS_COLUMN in item.keys()
+ else item[WEIGHT_PLUS_COLUMN]
+ for item in output_arrays
+ ]
+ )
+ gen_weights_variance_sum = sum(
+ [
+ np.square(item[GENERALIZED_S_WEIGHT_PLUS_COLUMN])
+ if GENERALIZED_S_WEIGHT_PLUS_COLUMN in item.keys()
+ else np.square(item[WEIGHT_S_PLUS_COLUMN])
+ for item in output_arrays
+ ]
+ )
+
+ prior_probabilities = nr_of_deposits / nr_of_pixels
+ prior_odds = np.log(prior_probabilities / (1 - prior_probabilities))
+ posterior_probabilities = np.exp(gen_weights_sum + prior_odds) / (1 + np.exp(gen_weights_sum + prior_odds))
+
+ posterior_probabilities_squared = np.square(posterior_probabilities)
+ posterior_probabilities_std = np.sqrt(
+ (1 / nr_of_deposits + gen_weights_variance_sum) * posterior_probabilities_squared
+ )
+
+ confidence_array = posterior_probabilities / posterior_probabilities_std
+ return posterior_probabilities, posterior_probabilities_std, confidence_array
diff --git a/notebooks/weights_of_evidence.ipynb b/notebooks/weights_of_evidence.ipynb
new file mode 100644
index 00000000..62bddc71
--- /dev/null
+++ b/notebooks/weights_of_evidence.ipynb
@@ -0,0 +1,1213 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rasterio\n",
+ "from matplotlib import pyplot as plt\n",
+ "from rasterio.plot import show\n",
+ "import geopandas as gpd\n",
+ "\n",
+ "import sys\n",
+ "sys.path.insert(0, \"..\")\n",
+ "\n",
+ "from eis_toolkit.prediction.weights_of_evidence import weights_of_evidence_calculate_weights, weights_of_evidence_calculate_responses"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "108 1\n"
+ ]
+ }
+ ],
+ "source": [
+ "with rasterio.open(\"../tests/data/remote/wofe/wofe_evidence_raster.tif\") as evidence_raster:\n",
+ " deposits = gpd.read_file(\"../tests/data/remote/wofe/wofe_deposits.shp\")\n",
+ "\n",
+ " weights_unique, arrays_unique, raster_meta, nr_of_deposits, nr_of_pixels = weights_of_evidence_calculate_weights(evidence_raster, deposits, weights_type='unique')\n",
+ " weights_categorical, arrays_categorical, _, _, _= weights_of_evidence_calculate_weights(evidence_raster, deposits, weights_type='categorical', studentized_contrast_threshold=1)\n",
+ " weights_ascending, arrays_ascending, _, _, _= weights_of_evidence_calculate_weights(evidence_raster, deposits, weights_type='ascending', studentized_contrast_threshold=1)\n",
+ " weights_descending, arrays_descending, _, _, _ = weights_of_evidence_calculate_weights(evidence_raster, deposits, weights_type='descending', studentized_contrast_threshold=1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Class | \n",
+ " Pixel count | \n",
+ " Deposit count | \n",
+ " W+ | \n",
+ " S_W+ | \n",
+ " W- | \n",
+ " S_W- | \n",
+ " Contrast | \n",
+ " S_Contrast | \n",
+ " Studentized contrast | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 1.0 | \n",
+ " 275 | \n",
+ " 9 | \n",
+ " 0.4810 | \n",
+ " 0.3389 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ " 0.8804 | \n",
+ " 0.5096 | \n",
+ " 1.7275 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 2.0 | \n",
+ " 11 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 3.0 | \n",
+ " 396 | \n",
+ " 5 | \n",
+ " -0.4920 | \n",
+ " 0.4501 | \n",
+ " 0.3409 | \n",
+ " 0.3059 | \n",
+ " -0.8329 | \n",
+ " 0.5442 | \n",
+ " -1.5306 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 5.0 | \n",
+ " 43 | \n",
+ " 1 | \n",
+ " 0.1296 | \n",
+ " 1.0118 | \n",
+ " -0.0081 | \n",
+ " 0.2609 | \n",
+ " 0.1377 | \n",
+ " 1.0449 | \n",
+ " 0.1318 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 6.0 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 8.0 | \n",
+ " 43 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 10.0 | \n",
+ " 2 | \n",
+ " 1 | \n",
+ " 3.8673 | \n",
+ " 1.4142 | \n",
+ " -0.0632 | \n",
+ " 0.2607 | \n",
+ " 3.9305 | \n",
+ " 1.4380 | \n",
+ " 2.7332 | \n",
+ "
\n",
+ " \n",
+ " | 7 | \n",
+ " 13.0 | \n",
+ " 10 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Class | \n",
+ " Pixel count | \n",
+ " Deposit count | \n",
+ " W+ | \n",
+ " S_W+ | \n",
+ " W- | \n",
+ " S_W- | \n",
+ " Contrast | \n",
+ " S_Contrast | \n",
+ " Studentized contrast | \n",
+ " Generalized class | \n",
+ " Generalized W+ | \n",
+ " Generalized S_W+ | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 1.0 | \n",
+ " 275 | \n",
+ " 9 | \n",
+ " 0.4810 | \n",
+ " 0.3389 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ " 0.8804 | \n",
+ " 0.5096 | \n",
+ " 1.7275 | \n",
+ " 1.0 | \n",
+ " 0.4810 | \n",
+ " 0.3389 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 3.0 | \n",
+ " 396 | \n",
+ " 5 | \n",
+ " -0.4920 | \n",
+ " 0.4501 | \n",
+ " 0.3409 | \n",
+ " 0.3059 | \n",
+ " -0.8329 | \n",
+ " 0.5442 | \n",
+ " -1.5306 | \n",
+ " 3.0 | \n",
+ " -0.4920 | \n",
+ " 0.4501 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 10.0 | \n",
+ " 2 | \n",
+ " 1 | \n",
+ " 3.8673 | \n",
+ " 1.4142 | \n",
+ " -0.0632 | \n",
+ " 0.2607 | \n",
+ " 3.9305 | \n",
+ " 1.4380 | \n",
+ " 2.7332 | \n",
+ " 10.0 | \n",
+ " 3.8673 | \n",
+ " 1.4142 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 2.0 | \n",
+ " 11 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 99.0 | \n",
+ " -0.8055 | \n",
+ " 1.0047 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 5.0 | \n",
+ " 43 | \n",
+ " 1 | \n",
+ " 0.1296 | \n",
+ " 1.0118 | \n",
+ " -0.0081 | \n",
+ " 0.2609 | \n",
+ " 0.1377 | \n",
+ " 1.0449 | \n",
+ " 0.1318 | \n",
+ " 99.0 | \n",
+ " -0.8055 | \n",
+ " 1.0047 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 6.0 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 99.0 | \n",
+ " -0.8055 | \n",
+ " 1.0047 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 8.0 | \n",
+ " 43 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 99.0 | \n",
+ " -0.8055 | \n",
+ " 1.0047 | \n",
+ "
\n",
+ " \n",
+ " | 7 | \n",
+ " 13.0 | \n",
+ " 10 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 99.0 | \n",
+ " -0.8055 | \n",
+ " 1.0047 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Class | \n",
+ " Pixel count | \n",
+ " Deposit count | \n",
+ " W+ | \n",
+ " S_W+ | \n",
+ " W- | \n",
+ " S_W- | \n",
+ " Contrast | \n",
+ " S_Contrast | \n",
+ " Studentized contrast | \n",
+ " Generalized class | \n",
+ " Generalized W+ | \n",
+ " Generalized S_W+ | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 1.0 | \n",
+ " 275 | \n",
+ " 9 | \n",
+ " 0.4810 | \n",
+ " 0.3389 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ " 0.8804 | \n",
+ " 0.5096 | \n",
+ " 1.7275 | \n",
+ " 2 | \n",
+ " 0.4810 | \n",
+ " 0.3389 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 2.0 | \n",
+ " 286 | \n",
+ " 9 | \n",
+ " 0.4405 | \n",
+ " 0.3387 | \n",
+ " -0.3771 | \n",
+ " 0.3807 | \n",
+ " 0.8176 | \n",
+ " 0.5095 | \n",
+ " 1.6046 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 3.0 | \n",
+ " 682 | \n",
+ " 14 | \n",
+ " 0.0021 | \n",
+ " 0.2700 | \n",
+ " -0.0143 | \n",
+ " 0.7144 | \n",
+ " 0.0163 | \n",
+ " 0.7637 | \n",
+ " 0.0214 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 5.0 | \n",
+ " 725 | \n",
+ " 15 | \n",
+ " 0.0101 | \n",
+ " 0.2609 | \n",
+ " -0.1400 | \n",
+ " 1.0090 | \n",
+ " 0.1501 | \n",
+ " 1.0422 | \n",
+ " 0.1440 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 6.0 | \n",
+ " 726 | \n",
+ " 15 | \n",
+ " 0.0087 | \n",
+ " 0.2609 | \n",
+ " -0.1217 | \n",
+ " 1.0092 | \n",
+ " 0.1304 | \n",
+ " 1.0424 | \n",
+ " 0.1251 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 8.0 | \n",
+ " 769 | \n",
+ " 15 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ " 1.4694 | \n",
+ " 1.0445 | \n",
+ " -1.5194 | \n",
+ " 1.0765 | \n",
+ " -1.4114 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 10.0 | \n",
+ " 771 | \n",
+ " 16 | \n",
+ " -0.0507 | \n",
+ " 0.2607 | \n",
+ " 1.5547 | \n",
+ " 1.0536 | \n",
+ " -1.6054 | \n",
+ " 1.0854 | \n",
+ " -1.4791 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ " | 7 | \n",
+ " 13.0 | \n",
+ " 781 | \n",
+ " 16 | \n",
+ " -0.0626 | \n",
+ " 0.2606 | \n",
+ " 3.8673 | \n",
+ " 1.4213 | \n",
+ " -3.9299 | \n",
+ " 1.4450 | \n",
+ " -2.7196 | \n",
+ " 1 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Class | \n",
+ " Pixel count | \n",
+ " Deposit count | \n",
+ " W+ | \n",
+ " S_W+ | \n",
+ " W- | \n",
+ " S_W- | \n",
+ " Contrast | \n",
+ " S_Contrast | \n",
+ " Studentized contrast | \n",
+ " Generalized class | \n",
+ " Generalized W+ | \n",
+ " Generalized S_W+ | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 13.0 | \n",
+ " 10 | \n",
+ " 0 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 0.0000 | \n",
+ " 2 | \n",
+ " 1.4694 | \n",
+ " 1.0445 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 10.0 | \n",
+ " 12 | \n",
+ " 1 | \n",
+ " 1.4694 | \n",
+ " 1.0445 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ " 1.5194 | \n",
+ " 1.0765 | \n",
+ " 1.4114 | \n",
+ " 2 | \n",
+ " 1.4694 | \n",
+ " 1.0445 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 8.0 | \n",
+ " 55 | \n",
+ " 1 | \n",
+ " -0.1217 | \n",
+ " 1.0092 | \n",
+ " 0.0087 | \n",
+ " 0.2609 | \n",
+ " -0.1304 | \n",
+ " 1.0424 | \n",
+ " -0.1251 | \n",
+ " 1 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 6.0 | \n",
+ " 56 | \n",
+ " 1 | \n",
+ " -0.1400 | \n",
+ " 1.0090 | \n",
+ " 0.0101 | \n",
+ " 0.2609 | \n",
+ " -0.1501 | \n",
+ " 1.0422 | \n",
+ " -0.1440 | \n",
+ " 1 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 5.0 | \n",
+ " 99 | \n",
+ " 2 | \n",
+ " -0.0143 | \n",
+ " 0.7144 | \n",
+ " 0.0021 | \n",
+ " 0.2700 | \n",
+ " -0.0163 | \n",
+ " 0.7637 | \n",
+ " -0.0214 | \n",
+ " 1 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 3.0 | \n",
+ " 495 | \n",
+ " 7 | \n",
+ " -0.3771 | \n",
+ " 0.3807 | \n",
+ " 0.4405 | \n",
+ " 0.3387 | \n",
+ " -0.8176 | \n",
+ " 0.5095 | \n",
+ " -1.6046 | \n",
+ " 1 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 2.0 | \n",
+ " 506 | \n",
+ " 7 | \n",
+ " -0.3994 | \n",
+ " 0.3806 | \n",
+ " 0.4810 | \n",
+ " 0.3389 | \n",
+ " -0.8804 | \n",
+ " 0.5096 | \n",
+ " -1.7275 | \n",
+ " 1 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ "
\n",
+ " \n",
+ " | 7 | \n",
+ " 1.0 | \n",
+ " 781 | \n",
+ " 16 | \n",
+ " -0.0626 | \n",
+ " 0.2606 | \n",
+ " 3.8673 | \n",
+ " 1.4213 | \n",
+ " -3.9299 | \n",
+ " 1.4450 | \n",
+ " -2.7196 | \n",
+ " 1 | \n",
+ " -0.0501 | \n",
+ " 0.2608 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "