# ChaMTeC: CHAnnel Mixing and Temporal Convolution Network for Time-Series Anomaly Detection
## 2 Literature Review  
The field of time-series anomaly detection has seen significant advancements, with classical methods evolving to address diverse data characteristics. Traditional techniques such as time-series decomposition, clustering, and density estimation have provided robust solutions for identifying anomalies, particularly in data with distinct patterns or significant deviations from normal distributions. Notable examples include the Local Outlier Factor (LOF) [4], which identifies anomalies based on local density deviations, and the Deep Autoencoding Gaussian Mixture Model (DAGMM) [12], which leverages density estimation principles. These methods are particularly effective in scenarios where the underlying data distribution is good, allowing for the identification of deviant outliers. Clustering-based methods often use the distance to the cluster center as an anomaly score. For instance, ITAD (Integrative Tensor-based Anomaly Detection ) [13] employs tensor-based decomposition to model normal behavior patterns and utilizes clustering to group similar patterns. This approach not only enhances the detection of anomalies but also facilitates the understanding of the underlying structure of the data, which can be crucial for operational insights. Deep-SVDD [3] trains a neural network to map normal data instances close to a central point in the latent space, while IForest [14] isolates anomalies through a recursive partitioning process, randomly selecting features and split values. The iterative nature of IForest enables the efficient processing of high-dimensional data, making it suitable for complex time-series datasets. Autoregressive models, which predict future values based on past observations, have also been widely used. With the rise of deep learning, recurrent neural networks (RNNs) and their variants, such as LSTM networks, have gained prominence for their ability to capture long-term dependencies and temporal patterns. CL-MPPCA [15], an extension of ARIMA, combines LSTM-based neural networks with probabilistic PCA (Principal Component Analysis) models to detect deviations between predicted and actual values. This hybrid approach provides a more detailed understanding of the data as it combines both temporal dynamics and probabilistic modeling. Autoencoders, a class of neural networks designed for dimensionality reduction and feature learning, have also been extensively applied in anomaly detection. They consist of an encoder that maps input data to a lower-dimensional latent space and a decoder that reconstructs the data from this representation. Variational Autoencoders (VAEs) extend this framework by encoding inputs into distributions, typically Gaussian, and reconstructing data from these distributions. For example, LSTM-VAE [16] and its improved variants [17; 18] have been applied to anomaly detection. The ability of VAEs to model uncertainty in the data representation makes them particularly suitable for scenarios where anomalies may not conform to a single distribution. [PERSON] [19] presents a comprehensive examination of dimension reduction techniques in time-series data through a novel framework called the Bi-Functional Autoencoder (BFAE) in their work. The paper identifies the limitations of existing methods, such as Functional Principal Component Analysis (FPCA) and standard Autoencoders, which typically rely on linear approximations and scalar representations, thus inadequately addressing the complex and nonlinear nature of real-world time-series data. The authors propose an innovative methodology that utilizes a nonlinear function-on-function approach by integrating a functional encoder and decoder to effectively capture dynamic temporal relationships. This is achieved through the deployment of continuous neurons that facilitate the transformation of functional inputs into a lower-dimensional latent space, preserving the functional nature of the data throughout the encoding and decoding processes.