You can perform outlier detection with the 'autoencoder' architecture. Usually you hear this term in the context of neural networks but actually applies for any method which performs dimensionality reduction and which also has an inverse transform defined.
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1) Reduce the dimensionality of your data, then perform the inverse transform. This will project your data onto a subset of the original space.
2) Measure the distance between the original data and this 'autoencoded' data. This measures the distance from the data to that particular subspace. Data which is 'described better' by the transform will be closer to the subspace and is more 'typical' of the data and its associated underlying generative process. Conversely, the data which is far away is atypical and can be considered an outlier or anomalous.
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Precisely which dimensionality reduction technique (PCA, neural networks, etc.) is chosen depends on which assumptions you wish to encode into the model. The vanilla technique for anomaly/outlier detection using neural networks relies on this idea, but encodes almost zero assumptions beyond smoothness in the reduction operation and its inverse.
---
1) Reduce the dimensionality of your data, then perform the inverse transform. This will project your data onto a subset of the original space.
2) Measure the distance between the original data and this 'autoencoded' data. This measures the distance from the data to that particular subspace. Data which is 'described better' by the transform will be closer to the subspace and is more 'typical' of the data and its associated underlying generative process. Conversely, the data which is far away is atypical and can be considered an outlier or anomalous.
---
Precisely which dimensionality reduction technique (PCA, neural networks, etc.) is chosen depends on which assumptions you wish to encode into the model. The vanilla technique for anomaly/outlier detection using neural networks relies on this idea, but encodes almost zero assumptions beyond smoothness in the reduction operation and its inverse.