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Title: RaPP: Novelty Detection with Reconstruction along Projection Pathway

Paper content:
We propose RaPP, a new methodology for novelty detection by utilizing hidden space activation values obtained from a deep autoencoder.
Precisely, RaPP compares input and its autoencoder reconstruction not only in the input space but also in the hidden spaces.
We show that if we feed a reconstructed input to the same autoencoder again, its activated values in a hidden space are equivalent to the corresponding reconstruction in that hidden space given the original input.
In order to aggregate the hidden space activation values, we propose two metrics, which enhance the novelty detection performance.
Through extensive experiments using diverse datasets, we validate that RaPP improves novelty detection performances of autoencoder-based approaches.
Besides, we show that RaPP outperforms recent novelty detection methods evaluated on popular benchmarks.
How can we characterize novelty when only normality information is given?
Novelty detection is the mechanism to decide whether a data sample is an outlier with respect to the training data.
This mechanism is especially useful in situations where a proportion of detection targets is inherently small.
Examples are fraudulent transaction detection (Pawar et al., 2014; Porwal & Mukund, 2018) , intrusion detection (Lee, 2017; Aoudi et al., 2018) , video surveillance (Ravanbakhsh et al., 2017; Xu et al., 2015b) , medical diagnosis (Schlegl et al., 2017; Baur et al., 2018) and equipment failure detection (Kuzin & Borovicka, 2016; Zhao et al., 2017; Beghi et al., 2014) .
Recently, deep autoencoders and their variants have shown outstanding performances in finding compact representations from complex data, and the reconstruction error has been chosen as a popular metric for detecting novelty (An & Cho, 2015; Vasilev et al., 2018) .
However, this approach has a limitation of measuring reconstruction quality only in an input space, which does not fully utilize hierarchical representations in hidden spaces identified by the deep autoencoder.
In this paper, we propose RAPP, a new method of detecting novelty samples exploiting hidden activation values in addition to the input values and their autoencoder reconstruction values.
While ordinary reconstruction-based methods carry out novelty detection by comparing differences between input data before the input layer and reconstructed data at the output layer, RAPP extends these comparisons to hidden spaces.
We first collect a set of hidden activation values by feeding the original input to the autoencoder.
Subsequently, we feed the autoencoder reconstructed input to the autoencoder to calculate another set of activation values in the hidden layers.
This procedure does not need additional training of the autoencoder.
In turn, we quantify the novelty of the input by aggregating these two sets of hidden activation values.
To this end, we devise two metrics.
The first metric measures the total amount of reconstruction errors in input and hidden spaces.
The second metric normalizes the reconstruction errors before summing up.
Note that RAPP falls back to the ordinary reconstruction-based method if we only aggregate input values before the input layer and the reconstructed values at the output layer.
Also, we explain the motivations that facilitated the development of RAPP.
We show that activation values in a hidden space obtained by feeding a reconstructed input to the autoencoder are equivalent to the corresponding reconstruction in that hidden space for the original input.
We refer the latter quantity as a hidden reconstruction of the input.
Note that this is a natural extension of the reconstruction to the hidden space.
Unfortunately, we cannot directly compute the hidden reconstruction as in the computation of the ordinary reconstruction because the autoencoder does not impose any correspondence between encoding-decoding pairs of hidden layers during the training.
Nevertheless, we show that it can be computed by feeding a reconstructed input to the autoencoder again.
Consequently, RAPP incorporates hidden reconstruction errors as well as the ordinary reconstruction error in detecting novelty.
With extensive experiments, we demonstrate using diverse datasets that our method effectively improves autoencoder-based novelty detection methods.
In addition, we show by evaluating on popular benchmark datasets that RAPP outperforms competing methods recently developed.
Our contributions are summarized as follows.
• We propose a new novelty detection method by utilizing hidden activation values of an input and its autoencoder reconstruction, and provide aggregation functions for them to quantify novelty of the input.
• We provide motivation that RAPP extends the reconstruction concept in the input space into the hidden spaces.
Precisely, we show that hidden activation values of a reconstructed input are equivalent to the corresponding hidden reconstruction of the original input.
• We demonstrate that RAPP improves autoencoder-based novelty detection methods in diverse datasets.
Moreover, we validate that RAPP outperforms recent novelty detection methods on popular benchmark datasets.
In this paper, we propose a novelty detection method which utilizes hidden reconstructions along a projection pathway of deep autoencoders.
To this end, we extend the concept of reconstruction in the input space to hidden spaces found by an autoencoder and present a tractable way to compute the hidden reconstructions, which requires neither modifying nor retraining the autoencoder.
Our experimental results show that the proposed method outperforms other competing methods in terms of AUROC for diverse datasets including popular benchmarks.
A SVD COMPUTATION TIME
We compare running times of training an autoencoder and computing SVD for NAP.
We choose two packages for the SVD computation: Pytorch SVD and fbpca provided in https://fbpca.
readthedocs.io/en/latest/.
Since the time complexity of SVD is linear in the number of data samples 1 , we mainly focus on the performance of SVD with varying the number of columns of the input matrix that SVD is applied.
To obtain variable sizes of the columns, we vary the depth and bottleneck size of autoencoders.
The result is shown below.
Notably, Pytorch SVD utilizing GPU is at least 47x faster than training neural networks.
Even, fbpca running only on CPU achieves at least 2.4x speedup.
The detailed setups to obtain the matrices for the experiment are given in the 1  20  100  20  40  20  90  2  18  100  18  40  18  90  3  16  100  16  40  16  90  4  14  100  14  40  14  90  5  12  100  12  40  12  90  6  10  100  10  40  10  90  7  8  100  8  40  8  90  8  6  100  6  40  6  90  9  4  100  4  40  4  90  10  2  100  2  40  2  90  11  2  80  2  30  2  70  12  2  60  2  20  2  50  13  2  40  2  10  2  30  14  2  20  2  10 B STANDARD DEVIATIONS OF EXPERIMENTAL RESULTS
We provide the standard deviations of the result in We investigate the performance of NAP while increasing the number of hidden layers involved in the NAP computation.
Specifically, we consider two ways for the increment:
1) adding hidden layers one by one from the input layer (forward addition), and
2) adding hidden layers one by one from the bottleneck layer (backward addition).
Experimental results on two datasets are shown below.
For most cases, more hidden layers tend to result in higher performance.
The values are obtained from one trial, not averaged over 5 trials as done in Section 5.

assistant: text: A new methodology for novelty detection by utilizing hidden space activation values obtained from a deep autoencoder.