A2CNN datasheet(5/19 Pages) ETC1

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It’s obvious that if two domains perfectly overlap with each other, (hd) ≈ 0.5, and ˆ

dH∆H(S, T ) ≈

0. On the contrary, if two domains are completely distinct from each other, (hd) ≈ 0, and

dH∆H(S, T ) ≈ 1. Therefore, ˆ

dH∆H(S, T ) ∈ [0, 1]. The lower the value is, the smaller two domains

divergence.

2.3. Generative Adversarial Networks

In 2014, Goodfellow et al. proposed a novel method named Generative Adversarial Networks

(GAN). A GAN consists of two part: a generator G that synthesizes data whose distribution

closely matches that of the real data, and a discriminator D that estimates the probability that a

sample came from the real data rather than G [36].

Similar to Section 2.2, real data are labeled with 0 and data generated by G are labeled with

1. The discriminator is trained to maximize the probability of assigning the correct label to both

real samples and samples from G [36]. While, the training procedure for G is to maximize the

probability of D making mistake. Therefore, the two models G and D formulated as a two-

player minimax game, are trained simultaneously. A unique solution exists with G recovering

the real data and D is unable to distinguish between real and generated samples, i.e. D(x)

= 0.5

everywhere [36].

By comparing DA, domain divergence measure dH∆H and GAN, we observe that they have

a similar objective, that is, ﬁnding a feature representation that the data drawn from di

ﬀerent

distributions or di

ﬀerent domains have the same distribution and perfectly overlap with each

other after mapping to the learned feature space. As a result, a domain discriminator (resp.

classiﬁer) cant distinguish between the real (resp. the source domain) data and the generated

(resp. the target domain) data.

3. Proposed adversarial adaptive 1-D CNN

3.1. Problem Formalization

Let the labeled source domain data as DS

= {(xi

S , y

S )

=1, where x

∈ Rm×1 is the data

instance and yi

∈ {1, ..., K} is the corresponding class label. While, DT

= {(xi

T )

=1 is the

unlabeled target domain data. Here, NS and NT are the numbers of instances in DS and DT . In

addition, each data instance is pseudo-labeled with a domain label d ∈ {0, 1} respectively, which

indicates whether the instance comes from the source domain (d

= 0) or from the target domain

= 1).

The overall framework of the proposed Adversarial Adaptive 1-D CNN (A2CNN) is shown in

Figure 1. It includes a source feature extractor MS , a target feature extractor MT , a label classiﬁer

and a domain discriminator D, which together form a deep feed-forward architecture that maps

each input sample xi

S (resp. x

T ) to a K-dimensional feature vector MS (x

S ) (resp. MT (x

T )) (K

equals to the number of class label) and predicts its class label y ∈ {1, ..., K} and its domain label

d ∈ {

0, 1}.

Compared with the traditional deep domain adaptation models, the proposed framework is

more like an adversarial learning framework similar to GAN. The parameters of C and D should

be optimized to minimizes the label prediction loss S (C) (for the labeled source domain) and

the domain classiﬁcation loss (D) (for all domains). And the parameters of the feature extractor

MS and MT should be discriminative to minimize S (C) and domain-invariant to maximize (D).

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