Limitations of Double MAD and Comparison with Z-Score
As powerful as Double MAD is in anomaly detection, it's important to acknowledge its limitations. One key limitation is its inability to account for the shape of seasonal data. Time series data often exhibit cyclical patterns based on the time of day, week, or year. For instance, web traffic to an e-commerce site might spike during holidays and dip on off-peak days.
While Double MAD can capture shifts in the median of these data, it does not consider the shape or pattern of the data within these cycles. As such, it might fail to detect anomalies that occur within a specific season, or it might flag normal seasonal variations as anomalies.
Another potential limitation of Double MAD is that it doesn't account for trends over time. In other words, if your time series data exhibits a consistent increase or decrease over time, Double MAD might misinterpret this trend as a series of anomalies.
Double MAD vs. Z-Score
When discussing anomaly detection, it's worth comparing Double MAD to the more traditional Z-score method. A Z-score measures how many standard deviations a data point is from the mean. It assumes that the data follows a Gaussian (or normal) distribution, which often doesn't hold true for real-world data.
Double MAD, on the other hand, is a non-parametric method that doesn't make any assumptions about the distribution of data. This makes it more robust to outliers and skewed distributions.
However, Z-score holds an advantage when it comes to data that follows a Gaussian distribution or when the data size is large enough for the Central Limit Theorem to take effect. It also accounts for the mean and standard deviation, giving it an edge in datasets where these measures are informative.
In contrast, Double MAD is more robust for datasets with outliers or skewed distributions, as it uses the median and absolute deviations from the median, which are less sensitive to extreme values.
In summary, while both Double MAD and Z-score have their strengths, the choice between them should be guided by the nature of your data. Understanding these nuances can help you make an informed decision and apply the most effective method for your specific use case.
