Time Series Anomaly Detection 📉🚨📈

Group:

• Isaac Gonzales Vizcarra
• Ibrahim Sobh
• Anthony Siampiringue

Dataset::potable_water:

Water pump data predictions Data
https://www.kaggle.com/datasets/nphantawee/pump-sensor-data

Description:

• Data driven prediction models of water pump sensor.

Anomalies Detection Approaches 🧑‍🔬

1. Heuristics based approaches 👨‍🍳

   • Cutoff method using Mean and Standard deviation
     cutoff = mean + upper_cutoff_threshold * std
   • Global Z-score:
     Z_score = (x - mean) / std
   • Inter quartile range IQR:
     [ – 1.5 * IQR , + 1.5 * IQR ]
   • Special Z-score with Sliding Window:
     ( Local_Z_score + Lambda * Global_Z-score ) / 2

2. Gaussian Hidden Markov Model 🧑‍💻

The Gaussian hidden Markov model (Gaussian HMM) is a type of finite-state-space and homogeneous HMM where the observation probability distribution is the normal distribution (Gaussian).

Y_t | S_t ~ N(mu_St, sigma_St)

where x_t is the observation at time t, x_1 ... x_t−1 are the observations at time t−1, ..., t−k, and mu_St and sigma_St are the mean and standard deviation of the normal distribution.

3. Local Outlier Factor LOF: 🥷

4. LSTM 🤖

LSTM is a recurrent neural network (RNN) that is designed to process sequences of data. with LSTM, you can process sequences of data in a way that is similar to how you process data in a language. the architecture used is the autoencoder.