# Source code for etna.analysis.outliers.density_outliers

```
from typing import TYPE_CHECKING
from typing import Callable
from typing import Dict
from typing import List
import numpy as np
import pandas as pd
if TYPE_CHECKING:
from etna.datasets import TSDataset
[docs]def absolute_difference_distance(x: float, y: float) -> float:
"""Calculate distance for :py:func:`get_anomalies_density` function by taking absolute value of difference.
Parameters
----------
x:
first value
y:
second value
Returns
-------
result: float
absolute difference between values
"""
return abs(x - y)
[docs]def get_segment_density_outliers_indices(
series: np.ndarray,
window_size: int = 7,
distance_threshold: float = 10,
n_neighbors: int = 3,
distance_func: Callable[[float, float], float] = absolute_difference_distance,
) -> List[int]:
"""Get indices of outliers for one series.
Parameters
----------
series:
array to find outliers in
window_size:
size of window
distance_threshold:
if distance between two items in the window is less than threshold those items are supposed to be close to each other
n_neighbors:
min number of close items that item should have not to be outlier
distance_func:
distance function
Returns
-------
:
list of outliers' indices
"""
def is_close(item1: float, item2: float) -> int:
"""Return 1 if item1 is closer to item2 than distance_threshold according to distance_func, 0 otherwise."""
return int(distance_func(item1, item2) < distance_threshold)
outliers_indices = []
for idx, item in enumerate(series):
is_outlier = True
left_start = max(0, idx - window_size)
left_stop = max(0, min(idx, len(series) - window_size))
closeness = None
n = 0
for i in range(left_start, left_stop + 1):
if closeness is None:
closeness = [is_close(item, series[j]) for j in range(i, min(i + window_size, len(series)))]
n = sum(closeness) - 1
else:
n -= closeness.pop(0)
new_element_is_close = is_close(item, series[i + window_size - 1])
closeness.append(new_element_is_close)
n += new_element_is_close
if n >= n_neighbors:
is_outlier = False
break
if is_outlier:
outliers_indices.append(idx)
return list(outliers_indices)
[docs]def get_anomalies_density(
ts: "TSDataset",
in_column: str = "target",
window_size: int = 15,
distance_coef: float = 3,
n_neighbors: int = 3,
distance_func: Callable[[float, float], float] = absolute_difference_distance,
) -> Dict[str, List[pd.Timestamp]]:
"""Compute outliers according to density rule.
For each element in the series build all the windows of size ``window_size`` containing this point.
If any of the windows contains at least ``n_neighbors`` that are closer than ``distance_coef * std(series)``
to target point according to ``distance_func`` target point is not an outlier.
Parameters
----------
ts:
TSDataset with timeseries data
in_column:
name of the column in which the anomaly is searching
window_size:
size of windows to build
distance_coef:
factor for standard deviation that forms distance threshold to determine points are close to each other
n_neighbors:
min number of close neighbors of point not to be outlier
distance_func:
distance function
Returns
-------
:
dict of outliers in format {segment: [outliers_timestamps]}
Notes
-----
It is a variation of distance-based (index) outlier detection method adopted for timeseries.
"""
segments = ts.segments
outliers_per_segment = {}
for seg in segments:
# TODO: dropna() now is responsible for removing nan-s at the end of the sequence and in the middle of it
# May be error or warning should be raised in this case
segment_df = ts[:, seg, :][seg].dropna().reset_index()
series = segment_df[in_column].values
timestamps = segment_df["timestamp"].values
series_std = np.std(series)
if series_std:
outliers_idxs = get_segment_density_outliers_indices(
series=series,
window_size=window_size,
distance_threshold=distance_coef * series_std,
n_neighbors=n_neighbors,
distance_func=distance_func,
)
outliers = [timestamps[i] for i in outliers_idxs]
outliers_per_segment[seg] = outliers
else:
outliers_per_segment[seg] = []
return outliers_per_segment
__all__ = ["get_anomalies_density", "absolute_difference_distance"]
```