# Algorithms - A real world example: QRS-Detection#

In this example we will implement a custom algorithm and discuss, when you might want to use an algorithm class over just pipelines.

Specifically we will implement a simple algorithm, designed to identify individual QRS complexes from a continuous ECG signal. If you have no idea what this all means, don’t worry about it. Simply we want to find peaks in a continuous signal that has some artifacts.

Warning

The algorithm we design is not a good algorithms! There are way better and properly evaluated algorithms to do this job! Don’t use this algorithms for anything :)

## When should you use custom algorithms?#

Algorithms are a completely optional feature of tpcp and in many cases not required. However, algorithm subclasses provide a structured way to implement new algorithms when you don’t have any better structure to follow. Further they allow the setting of nested parameters (e.g. when used as parameters to pipelines) and can benefit from other tooling in tpcp (e.g. cloning). For more general information have a look at the general documentation page The fundamental components: Datasets, Algorithms, and Pipelines.

## Implementing QRS-Detection#

In general our QRS-Detection will have two steps:

1. High-pass filter the data to remove baseline drift. We will use a Butterworth filter for that.

2. Apply a peak finding strategy to find the (hopefully dominant) R-peaks. We will use `find_peaks` with a couple of parameters for that.

As all algorithms, our algorithm needs to inherit from `tpcp.Algorithm` and implement an action method. In our case we will call the action method `detect`, as it makes sense based on what the algorithm does. This `detect` method will first do the filtering and then the peak search, which we will split into two methods to keep things easier to understand.

If you just want the final implementation, without all the explanation, check The final QRS detection algorithms.

Ok that is still a bunch of code… But let’s focus on the aspects that are important in general:

1. We inherit from `Algorithm`

2. We get and define all parameters in the init without modification

3. We define the name of out action method using `_action_method = "detect"`

4. After we do the computations, we set the results on the instance

5. We return self

6. (Optionally) we applied the `make_action_safe` decorator to our action method, which makes some runtimes checks to ensure our implementation follows the tpcp spec.

```import numpy as np
import pandas as pd
from scipy import signal

from tpcp import Algorithm, Parameter, make_action_safe

class QRSDetector(Algorithm):
_action_methods = "detect"

# Input Parameters
high_pass_filter_cutoff_hz: Parameter[float]
max_heart_rate_bpm: Parameter[float]
min_r_peak_height_over_baseline: Parameter[float]

# Results
r_peak_positions_: pd.Series

# Some internal constants
_HIGH_PASS_FILTER_ORDER: int = 4

def __init__(
self,
max_heart_rate_bpm: float = 200.0,
min_r_peak_height_over_baseline: float = 1.0,
high_pass_filter_cutoff_hz: float = 0.5,
):
self.max_heart_rate_bpm = max_heart_rate_bpm
self.min_r_peak_height_over_baseline = min_r_peak_height_over_baseline
self.high_pass_filter_cutoff_hz = high_pass_filter_cutoff_hz

@make_action_safe
def detect(self, single_channel_ecg: pd.Series, sampling_rate_hz: float):
ecg = single_channel_ecg.to_numpy().flatten()

filtered_signal = self._filter(ecg, sampling_rate_hz)
peak_positions = self._search_strategy(filtered_signal, sampling_rate_hz)

self.r_peak_positions_ = pd.Series(peak_positions)
return self

def _search_strategy(
self, filtered_signal: np.ndarray, sampling_rate_hz: float, use_height: bool = True
) -> np.ndarray:
# Calculate the minimal distance based on the expected heart rate
min_distance_between_peaks = 1 / (self.max_heart_rate_bpm / 60) * sampling_rate_hz

height = None
if use_height:
height = self.min_r_peak_height_over_baseline
peaks, _ = signal.find_peaks(filtered_signal, distance=min_distance_between_peaks, height=height)
return peaks

def _filter(self, ecg_signal: np.ndarray, sampling_rate_hz: float) -> np.ndarray:
sos = signal.butter(
btype="high",
N=self._HIGH_PASS_FILTER_ORDER,
Wn=self.high_pass_filter_cutoff_hz,
output="sos",
fs=sampling_rate_hz,
)
return signal.sosfiltfilt(sos, ecg_signal)
```

## Testing the implementation#

To test the implementation, we load our example ECG data using the dataset created in a previous example.

Based on the simple test we can see that our algorithm works (at least for this piece of data).

```from pathlib import Path

from examples.datasets.datasets_final_ecg import ECGExampleData

try:
HERE = Path(__file__).parent
except NameError:
HERE = Path().resolve()
data_path = HERE.parent.parent / "example_data/ecg_mit_bih_arrhythmia/data"
example_data = ECGExampleData(data_path)
ecg_data = example_data.data["ecg"]

# Initialize the algorithm
algorithm = QRSDetector()
algorithm = algorithm.detect(ecg_data, example_data.sampling_rate_hz)

# Visualize the results
import matplotlib.pyplot as plt

plt.figure()
plt.plot(ecg_data[:5000])
subset_peaks = algorithm.r_peak_positions_[algorithm.r_peak_positions_ < 5000.0]
plt.plot(subset_peaks, ecg_data[subset_peaks], "s")
plt.show()
``` ## Making the algorithm trainable#

The implementation so far heavily depends on the value of the `min_r_peak_height_over_baseline` parameter. If this is set incorrectly, everything will go wrong. This parameter describes the minimal expected value of the filtered signal at the position of an R-peak. Without looking at the filtered data, this value is hard to guess. The value will depend on potential preprocessing applied to the data and the measurement conditions. But we should be able to calculate a suitable value based on some training data (with R-peak annotations) recorded under similar conditions.

Therefore, we will create a second implementation of our algorithm that is trainable. Meaning, we will implement a method (`self_optimize`) that is able to estimate a suitable value for our cutoff based on some training data. Note, that we do not provide a generic base class for optimizable algorithms. If you need one, create your own class with a call signature for `self_optimize` that makes sense for the group of algorithms you are trying to implement.

From an implementation perspective, this means that we need to do the following things:

1. Implement a `self_optimize` method that takes the data of multiple recordings including the reference labels to calculate a suitable threshold. This method should modify only parameters marked as `OptimizableParameter` and then return `self`.

2. We need to mark the parameters that we want to optimize as `OptimizableParameter` using the type annotations on the class level.

3. We introduce a new parameter called `r_peak_match_tolerance_s` that is used by our `self_optimize` method. Changing it, changes the output of our optimization. Therefore, it is a Hyper-Parameter of our method. We mark it as such using the type-hints on class level.

4. (Optional) Wrap the `self_optimize` method with the `make_optimize_safe` decorator. It will perform some runtime checks and inform us, if we did not implement `self_optimize` as expected.

Note

The process required to implement an optimizable algorithm will always be very similar to what we did here. It doesn’t matter, if the optimization only optimizes a threshold or trains a neuronal network. The structure will be very similar.

From a scientific perspective, we optimize our parameter by trying to find all R-peaks without a height restriction first. Based on the detected R-peaks, we determine, which of them are actually correctly detected, by checking if they are within the threshold `r_peak_match_tolerance_s` of a reference R-peak. Then we find the best height threshold to maximise our predictive power within these preliminary detected peaks.

Again, there are probably better ways to do it… But this is just an example, and we already have way too much code that is not relevant for you to understand the basics of Algorithms.

```from sklearn.metrics import roc_curve

from examples.algorithms.algorithms_qrs_detection_final import match_events_with_reference
from tpcp import HyperParameter, OptimizableParameter, make_optimize_safe

class OptimizableQrsDetector(QRSDetector):
min_r_peak_height_over_baseline: OptimizableParameter[float]
r_peak_match_tolerance_s: HyperParameter[float]

def __init__(
self,
max_heart_rate_bpm: float = 200.0,
min_r_peak_height_over_baseline: float = 1.0,
r_peak_match_tolerance_s: float = 0.01,
high_pass_filter_cutoff_hz: float = 1,
):
self.r_peak_match_tolerance_s = r_peak_match_tolerance_s
super().__init__(
max_heart_rate_bpm=max_heart_rate_bpm,
min_r_peak_height_over_baseline=min_r_peak_height_over_baseline,
high_pass_filter_cutoff_hz=high_pass_filter_cutoff_hz,
)

@make_optimize_safe
def self_optimize(self, ecg_data: list[pd.Series], r_peaks: list[pd.Series], sampling_rate_hz: float):
all_labels = []
all_peak_heights = []
for d, p in zip(ecg_data, r_peaks):
filtered = self._filter(d.to_numpy().flatten(), sampling_rate_hz)
# Find all potential peaks without the height threshold
potential_peaks = self._search_strategy(filtered, sampling_rate_hz, use_height=False)
# Determine the label for each peak, by matching them with our ground truth
labels = np.zeros(potential_peaks.shape)
matches = match_events_with_reference(
events=potential_peaks,
reference=p.to_numpy().astype(int),
tolerance=self.r_peak_match_tolerance_s * sampling_rate_hz,
)
tp_matches = matches[(~np.isnan(matches)).all(axis=1), 0].astype(int)
labels[tp_matches] = 1
labels = labels.astype(bool)
all_labels.append(labels)
all_peak_heights.append(filtered[potential_peaks])
all_labels = np.hstack(all_labels)
all_peak_heights = np.hstack(all_peak_heights)
# We "brute-force" a good cutoff by testing a bunch of thresholds and then calculating the Youden Index for
# each.
fpr, tpr, thresholds = roc_curve(all_labels, all_peak_heights)
youden_index = tpr - fpr
# The best Youden index gives us a balance between sensitivity and specificity.
self.min_r_peak_height_over_baseline = thresholds[np.argmax(youden_index)]
return self
```

## Testing the implementation#

To test the trainable implementation, we need a train and a test set. In this case we simply use the first two recordings as train set and a third recording as test set.

Then we first call `self_optimize` with the train data.

```train_data = example_data[:2]
train_ecg_data = [d.data["ecg"] for d in train_data]
train_r_peaks = [d.r_peak_positions_["r_peak_position"] for d in train_data]

algorithm = OptimizableQrsDetector()
algorithm = algorithm.self_optimize(train_ecg_data, train_r_peaks, train_data.sampling_rate_hz)
```

After the optimization, we can access the modified parameters.

```print(
"The optimized value of the threshold `min_r_peak_height_over_baseline` is:",
algorithm.min_r_peak_height_over_baseline,
)
```
```The optimized value of the threshold `min_r_peak_height_over_baseline` is: 0.5434583752370183
```

Then we can apply the algorithm to our test set. And again, we can see that the algorithm works fine on the piece of data we are inspecting here.

```test_data = example_data
test_ecg_data = test_data.data["ecg"]

algorithm = algorithm.detect(test_ecg_data, test_data.sampling_rate_hz)

# Visualize the results
plt.figure()
plt.plot(test_ecg_data[:5000])
subset_peaks = algorithm.r_peak_positions_[algorithm.r_peak_positions_ < 5000.0]
plt.plot(subset_peaks, test_ecg_data[subset_peaks], "s")
plt.show()
``` Total running time of the script: (0 minutes 6.257 seconds)

Estimated memory usage: 196 MB

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