(Oral) Visual Domain Adaptation with Manifold
Embedded Distribution Alignment
Jindong Wang*, Wenjie Feng, Yiqiang Chen , Han Yu, Meiyu Huang, and Philip S. Yu
Inst. of Computing Tech., Chinese Academy of Sciences · NTU · China Academy of Space Tech. · UIC
jindongwang@outlook.com; Paper online: https://arxiv.org/abs/1807.07258; Code: http://transferlearning.xyz

1. Introduction

2. Our Method: MEDA

Visual domain adaptation aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Existing methods are facing two significant challenges:

Manifold Embedded Distribution Alignment• Degenerated feature transformation: feature distortion often happens; subspace learning is not
sufficient to reduce the distribution divergence.
• Unevaluated distribution alignment: existing methods fail to evaluate the different importanceof marginal and conditional distributions.

Source12

TargetOur method: Manifold Embedded Distribution Alignment (MEDA)
f=arg
Pnminf∈i=1`(f (g(xi )), yi ) + η||f ||2K + λDf (Ds , Dt ) + ρRf (Ds , Dt )HKMEDA learns a domain-invariant classifier in Grassmann manifold with structural risk minimization, while performing dynamic distribution alignment to quantitatively account for the relative
importance of marginal and conditional distributions.

2.1 Manifold Feature Learning
We adopted Geodesic Flow Kernel (GFK) [1]as the basic manifold learning method. GFKtries to model the domains with d-dimensional
subspaces and then embed them into G. Eachoriginal subspace can be seen as a point in G.
Therefore, the geodesic flow {Φ(t) : 0 ≤ t ≤ 1}
between two points can draw a path for the two
subspaces. If we let Ss = Φ(0) and St = Φ(1),then finding a geodesic flow from Φ(0) to Φ(1)equals to transforming the original features into
an infinite-dimensional feature space.
The new features can be represented as z =g(x) = Φ(t)T x. The inner product of transformed features zi and zj gives rise to a positive
semidefinite geodesic flow kernel:
Z 1TTTThzi , zj i =(Φ(t) xi ) (Φ(t) xj ) dt = xi Gxj• G: Manifold feature learning• µ: Dynamic distribution alignment• f : Prediction function• Rf : Manifold regularization
MEDA works in both traditional and deepframeworks.

2.2 Dynamic Distribution Alignment
The Dynamic Distribution Alignment (DDA)
is to tackle with the unevaluated distribution alignment challenge. The core is an adaptive factor to
dynamically leverage the importance of marginal andconditional distributions. The DDA Df is formed bylinear combination of two distributions:
Df (Ds , Dt ) = (1 − µ)Df (Ps , Pt ) + µ

CX(c)Df (Qs , Qt )c=1

where µ ∈ [0, 1] is the adaptive factor and c ∈ {1, · · · , C} is the class indicator. Df (Ps , Pt ) denotes(c)the marginal distribution alignment, and Df (Qs , Qt ) denotes the conditional distribution alignment
for class c.
Taking the projected MMD, dynamic distribution alignment can be expressed as2
Df (Ds , Dt ) = (1 − µ)kE[f (zs ) − E[f (zt )]kHK + µ

CX(c)
(c)
2
kE[f (zs )] − E[f (zt )]kHK

c=10

The first quantitative calculation of µ:

2.3 Learning
Using the representer theorem [2], f becomesf (z) =n+mX

βi K(zi , z)dMµ̂ ≈ 1 −, dM : marginal A-distance,dc : conditional A-distance [3]PC
dM + c=1 dc

3. Experiments

i=1T(n+m)×1

where β = (β1 , β2 , · · · ) ∈ R
efficients vector and K is a kernel.
f can be reformulated as
f = arg min ||(Y − βf ∈HK

Tis the co-On Office31, Office-Caltech10, USPS, MNIST, ImageNet, and VOC2007 datasets, MEDA shows:• Over 3.5% improvement in classification accuracy• Over 11.6% of error reduction• Over 50.0% drop of standard deviation2TK)A||F + η tr(β Kβ)T+ tr β K(λM + ρL)KβSetting ∂f /∂β = 0, we obtain the solution−1?

β = ((A + λM + ρL)K + ηI)

AYTIt shows that MEDA can directly learn the labels of the target domain, rather than train another classifier.

References[1] B. Gong, et al. Geodesic flow kernel for unsupervised domain adaptation. CVPR 2012.
[2] M. Belkin, et al. Manifold Regularization:
A Geometric Framework for Learning from Labeled and Unlabeled Examples. JMLR 2006.
[3] S. Ben-David, et al. Analysis of Representations for Domain Adaptation. NIPS 2007.

With regards to the different importance of marginal and conditional distributions:• There does exist different importance between these two distributions (µ)• MEDA can provide an accurate, even better calculation of µ compared to gridsearch• DDA can also be included in the deep transfer learning frameworks