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Univariate Anomaly Detection
To detect anomalies in a univariate dataset, we often rely on statistical methods to identify data points that are significantly different from the rest of the dataset. Here's a step-by-step approach:
Understand the Distribution:
Calculate Statistical Metrics:
Apply the 3-Sigma Rule:
Calculate the Z-score for each data point using the formula:
Z=standard deviation(X−mean)
Flag data points as anomalies if their Z-score is greater than +3 or less than -3, indicating they are more than three standard deviations away from the mean.
Visualize:
Function Implementation:
def detect_anomalies_univariate(data, threshold=3):
mean = np.mean(data)
std_dev = np.std(data)
anomalies = []
for i in data:
z = (i - mean) / std_dev
if np.abs(z) > threshold:
anomalies.append(i)
return anomalies
Bivariate Anomaly Detection
When dealing with a bivariate dataset, anomaly detection becomes more complex as it involves understanding the relationship between two variables.
Visual Exploration:
Statistical Approach:
Correlation Analysis:
Advanced Techniques:
Function Implementation:
def detect_anomalies_bivariate(data, threshold=3):
mean1, std_dev1 = np.mean(data[:,0]), np.std(data[:,0])
mean2, std_dev2 = np.mean(data[:,1]), np.std(data[:,1])
anomalies = []
for x, y in data:
z1 = (x - mean1) / std_dev1
z2 = (y - mean2) / std_dev2
if np.abs(z1) > threshold or np.abs(z2) > threshold:
anomalies.append((x, y))
return anomalies
Conclusion:
Detecting anomalies in datasets is crucial for maintaining data integrity and making informed decisions. While univariate anomaly detection can often rely on simple statistical methods, bivariate anomaly detection may require more sophisticated techniques to account for the relationship between variables. Visualization and exploratory data analysis are essential steps in both cases to understand the data before applying automated methods.