Efficient Learning of Domain-invariant Image Representations
Authors: Judy Hoffman, Erik Rodner, Jeff Donahue, Kate Saenko, Trevor Darrell
ICLR 2013

Abstract: We present an algorithm that learns representations which explicitly compensate for domain mismatch and which can be efficiently realized as linear classifiers. Specifically, we form a linear transformation that maps features from the target (test) domain to the source (training) domain as part of training the classifier. We optimize both the transformation and classifier parameters jointly, and introduce an efficient cost function based on misclassification loss. Our method combines several features previously unavailable in a single algorithm: multi-class adaptation through representation learning, ability to map across heterogeneous feature spaces, and scalability to large datasets. We present experiments on several image datasets that demonstrate improved accuracy and computational advantages compared to previous approaches.

Efﬁcient Learning of Domain-invariant Image
Representations
Judy Hoffman
UCB EECS & ICSI
jhoffman@eecs.berkeley.edu
Erik Rodner
UCB EECS & ICSI
erik.rodner@gmail.com
Jeff Donahue
UCB EECS & ICSI
jdonahue@eecs.berkeley.edu
Trevor Darrell
UCB EECS & ICSI
trevor@eecs.berkeley.edu
Kate Saenko
University of Massachusetts, Lowell
saenko@cs.uml.edu
Abstract
We present an algorithm that learns representations which explicitly compensate
for domain mismatch and which can be efﬁciently realized as linear classiﬁers.
Speciﬁcally, we form a linear transformation that maps features from the target
(test) domain to the source (training) domain as part of training the classiﬁer. We
optimize both the transformation and classiﬁer parameters jointly, and introduce
an efﬁcient cost function based on misclassiﬁcation loss. Our method combines
several features previously unavailable in a single algorithm: multi-class adapta-
tion through representation learning, ability to map across heterogeneous feature
spaces, and scalability to large datasets. We present experiments on several im-
age datasets that demonstrate improved accuracy and computational advantages
compared to previous approaches.
1 Introduction
We address the problem of learning domain-invariant image representations for multi-class classi-
ﬁers. The ideal image representation often depends not just on the task but also on the domain.
Recent studies have demonstrated a signiﬁcant degradation in the performance of state-of-the-art
image classiﬁers when input feature distributions change due to different image sensors and noise
conditions [1], pose changes [2], a shift from commercial to consumer video [3, 4], and, more
generally, training datasets biased by the way in which they were collected [5]. Learning adaptive
representations for linear classiﬁers is particularly interesting as they are efﬁcient and prevalent in
vision applications, with fast linear SVMs forming the core of some of the most popular object
detection methods [6, 7].
Previous work proposed to adapt linear SVMs [8, 9, 10], learning a perturbation of the source hyper-
plane by minimizing the classiﬁcation error on labeled target examples for each binary task. These
perturbations can be thought of as new feature representations that correct for the domain change.
The recent HFA method [11] learns both the perturbed classiﬁer and a latent domain-invariant fea-
ture representation, allowing domains to have heterogeneous features with different dimensionali-
ties. However, existing SVM-based methods are limited to learning a separate representation for
each binary problem and cannot transfer a common, class-independent component of the shift (such
as global lighting change) to unlabeled categories, as illustrated in Figure 1. Additionally, the HFA
algorithm cannot be solved in linear space and therefore scales poorly to large datasets.
1
arXiv:1301.3224v5  [cs.LG]  9 Apr 2013
(a) SOURCE (b) TARGET, no adaptation (c) TARGET, existing methods (d) TARGET, our method 
unlabeled 
labeled 
Figure 1: (a) Linear classiﬁers (shown as decision boundaries) learned for a four-class problem on
a fully labeled source domain. (b) Problem: classiﬁers learned on the source domain do not ﬁt the
target domain points shown here due to a change in feature distribution. (c) Existing SVM-based
methods only adapt the features of classes with labels (crosses and triangles). (d) Our method adapts
all points, including those from classes without labels, by transforming all target features to a new
domain-invariant representation.
Recently proposed feature adaptation methods [1, 2, 12, 13, 14, 15] offer a solution by learning a
category-independent feature transform that maps target features into the source, pooling all train-
ing labels across categories. This enables multi-class adaptation, i.e. transferring the category-
independent component of the domain-invariant representation to unlabeled categories. For exam-
ple, a map learned on the labeled “triangle” class in Figure 1 can also be used to map the unlabeled
“star” class to the source domain. An additional advantage of the asymmetric transform method
ARC-t [12] over metric learning [1] or the recently proposed Geodesic Flow Kernel (GFK) [15],
is that, like HFA [11], ARC-t can map between heterogeneous feature spaces. However, ARC-t
has two major limitations: First, the feature learning does not optimize the objective function of a
strong, discriminative classiﬁer directly; rather, it maximizes some notion of similarity between the
transformed target points and points in the source. Second, it does not scale well to domains with
large numbers of points due to the high number of constraints, which is proportional to the product
of the number of labeled data points in the source and target.
In this paper, we present a novel technique that combines the desirable aspects of recent methods in
a single algorithm, which we call Max-Margin Domain Transforms, or MMDT for short. MMDT
uses an asymmetric (non-square) transform W to map target features x to a new representation
Wx maximally aligned with the source, learning the transform jointly on all categories for which
target labels are available (Figure 1(d)). MMDT provides a way to adapt max-margin classiﬁers
in a multi-class manner, by learning a shared component of the domain shift as captured by the
feature transformation W. Additionally, MMDT can be optimized quickly in linear space, making
it a feasible solution for problem settings with a large amount of training data.
The key idea behind our approach is to simultaneously learn both the projection of the target features
into the source domain and the classiﬁer parameters themselves, using the same classiﬁcation loss
to jointly optimize both.
Thus our method learns a feature representation that combines the strengths of max-margin learning
with the ﬂexibility of the feature transform. Because it operates over the input features, it can
generalize the learned shift in a way that parameter-based methods cannot. On the other hand, it
overcomes the two ﬂaws of the ARC-t method: by optimizing the classiﬁcation loss directly in
the transform learning framework, it can achieve higher accuracy; furthermore, replacing similarity
constraints with more efﬁcient hyperplane constraints signiﬁcantly reduces the training time of the
algorithm and learning a transformation directly from target to source allows optimization in linear
space.
The main contributions of our paper can be summarized as follows (also see Table 1):
• Experiments show that MMDT in linear feature space outperforms competing methods in
terms of multi-class accuracy even compared to previous kernelized methods.
• MMDT learns a representation via an asymmetric category independent transform. There-
fore, it can adapt features even when the target domain does not have any labeled examples
for some categories and when the target and source features are not equivalent.
2
ARC-t [12] HFA [11] GFK [15] MMDT (ours)
multi-class yes no yes yes
large datasets no no yes yes
heterogeneous features yes yes no yes
optimize max-margin objective no yes no yes
Table 1: Unlike previous methods, our approach is able to simultaneously learn muti-class represen-
tations that can transfer to novel classes, scale to large training datasets, and handle different feature
dimensionalities.
• The optimization of MMDT is scalable to large datasets because the number of constraints
to optimize is linear in the number of training data points and because it can be optimized
in linear feature space.
• Our ﬁnal iterative solution can be solved using standard QP packages, making MMDT easy
to implement.
2 Related Work
Domain adaptation, or covariate shift, is a fundamental problem in machine learning, and has at-
tracted a lot of attention in the machine learning and natural language community, e.g. [16, 17, 18,
19] (see [20] for a comprehensive overview). It is related to multi-task learning but differs from it
in the following way: in domain adaptation problems, the distribution over the features p(X) varies
across domains while the output labels Y remain the same; in multi-task learning or knowledge
transfer, p(X) stays the same (single domain) while the output labels vary (see [20] for more de-
tails). In this paper, we perform multi-task learning across domains, i.e. both p(X) and the output
labels Y can change between domains.
Domain adaptation has been gaining considerable attention in the vision community. Several SVM-
based approaches have been proposed for image domain adaptation, including: weighted combi-
nation of source and target SVMs and transductive SVMs applied to adaptation in [21]; the feature
replication method of [17]; Adaptive SVM [8, 9], where the source model parameters are adapted by
adding a perturbation function, and its successor PMT-SVM [10]; Domain Transfer SVM [3], which
learns a target decision function while reducing the mismatch in the domain distributions; and a re-
lated method [4] based on multiple kernel learning. In the linear case, feature replication [17] can be
shown to decompose the learned parameter into θ = ˆθ+ θ′, where ˆθis shared by all domains [22],
in a similar fashion to adaptive SVMs.
Several authors considered learning feature representations for unsupervised and transfer learn-
ing [23], and for domain adaptation [18, 24]. For visual domain adaptation, transform-based adap-
tation methods [1, 12, 13, 2, 14, 11] have recently been proposed. These methods attempt to learn a
perturbation over the feature space rather than a class-speciﬁc perturbation over the model parame-
ters, typically in the form of a transformation matrix/kernel. The most closely related are the ARC-t
method [12], which learns a transformation that maximizes similarity constraints between points
in the source and those projected from the target domain, and the recent HFA method [11], which
learns a transformation both from the source and target into a common latent space, as well as the
classiﬁer parameters. Another related method is the recently proposed GFK [15], which computes a
symmetric kernel between source and target points based on geodesic ﬂow along a latent manifold.
We will present a detailed comparison to these three methods in the next section.
3 Max-Margin Domain Transforms
We propose a novel method for multi-task domain adaptation of linear SVMs by learning a target
feature representation. Denote the normal to the afﬁne hyperplane associated with the k’th binary
SVM as θk, k = 1,...,K , and the offset of that hyperplane from the origin as bk. Intuitively, we
would like to learn a new target feature representation that is shared across multiple categories.
We propose to do so by estimating a transformation W of the input features, or, equivalently, a
transformation WT of the source hyperplane parameters θk. Let xs
1,...,x s
nS denote the training
points in the source domain ( DS), with labels ys
1,...,y s
nS . Let xt
1,...,x t
nT denote the labeled
3
points in the target domain ( DT), with labels yt
1,...,y t
nT . Thus our goal is to jointly learn 1)
afﬁne hyperplanes that separate the classes in the common domain consisting of the source domain
and target points projected to the source and 2) the new feature representation of the target domain
determined by the transformationW mapping points from the target domain into the source domain.
The transformation should have the property that it projects the target points onto the correct side of
each source hyperplane.
For simplicity of presentation, we ﬁrst show the optimization problem for a binary problem (drop-
ping k) with no slack variables. Our objective is as follows:
min
W,θ,b
1
2||W||2
F + 1
2||θ||2
2 (1)
s.t. ys
i
([
xs
i
1
]T [
θ
b
])
≥1 ∀i∈DS (2)
yt
i
([
xt
i
1
]T
WT
[
θ
b
])
≥1 ∀i∈DT (3)
Note that this can be easily extended to the multi-class case by simply adding a sum over the regu-
larizers on all θk parameters and pooling the constraints for all categories. The objective function,
written as in Equations (1)-(3), is not a convex problem and so is both hard to optimize and is not
guaranteed to have a global solution. Therefore, a standard way to solve this problem is to do alter-
nating minimization on the parameters, in our caseW and (θ,b). We can effectively do this because
when each parameter vector is ﬁxed, the resulting optimization problem is convex.
We begin by re-writing Equations (1)-(3) for the more general problem with soft constraints and K
categories. Let us denote the hinge loss as: L(y,x,θ ) = max{0,1 −δ(y,k) ·xTθ}. We deﬁne a
cost function
J(W,θk,bk) = 1
2 ||W||2
F +
K∑
k=1
[1
2 ||θk||2
2 (4)
+CS
nS∑
i=1
L
(
ys
i ,
[
xs
i
1
]
,
[
θk
bk
])
+CT
nT∑
i=1
L
(
yt
i,W ·
[
xt
i
1
]
,
[
θk
bk
])]
where the constant CS penalizes the source classiﬁcation error and CT penalizes the target adapta-
tion error. Finally, we deﬁne our objective function with soft constraints as follows:
min
W,θk,bk
J(W,θk,bk) (5)
To solve the above optimization problem we perform coordinate descent onW and (θ,b).
1. Set iteration j = 0, W(j) = 0.
2. Solve the sub-problem (θ(j+1)
k ,b(j+1)
k ) =arg minθk,bk J(W(j),θk,bk) by solving:
min
θ,b
K∑
k=1
[1
2||θk||2
2 + CS
nS∑
i=1
L
(
ys
i,
[
xs
i
1
]
,
[
θk;
bk
])
+CT
nT∑
i=1
L
(
yt
i,W(j) ·
[
xt
i
1
]
,
[
θk
bk
])]
Notice, this corresponds to the standard SVM objective function, except that the target points
are ﬁrst projected into the source using W(j). Therefore, we can solve this intermediate problem
using a standard SVM solver package.
3. Solve the subproblem W(j+1) = arg minW J(W,θ(j+1),b(j+1)) by solving
min
W
1
2||W||2
F + CT
K∑
k=1
nT∑
i=1
L
(
yt
i,W ·
[
xt
i
1
]
,
[
θ(j+1)
k
b(j+1)
k
])
and increment j. This optimization sub-problem is convex and is in a form that a standard QP
optimization package can solve.
4
4. Iterate steps 2 & 3 until convergence.
It is straightforward to show that both stages (2) and (3) cannot increase the global cost function
J(W,θ,b ). Therefore, this algorithm is guaranteed to converge to a local optimum. A proof is
included in the supplemental material.
It is important to note that since both steps of our iterative algorithm can be solved using standard
QP solvers, the algorithm can be easily implemented. Additionally, since the constraints in our
algorithm grow linearly with the number of training points and it can be solved in linear feature
space, the optimization can be solved efﬁciently even as the number of training points grows.
Relation to existing work: We now analyze the proposed algorithm in the context of the previous
feature transform methods ARC-t [12], HFA [11] and GFK [15]. ARC-t introduced similarity-based
constraints to learn a mapping similar to that in step 3 in our algorithm. This approach creates a
constraint for each labeled point xs
i in the source and labeled point xt
i in the target, and then learns
a transformation W that satisﬁes constraints of the form (xs
i)TWxt
i > uif the labels of xs
i and xt
i
are the same, and (xs
i)TWxt
i <l if the labels are different, for some constants u,l.
The ARC-t formulation has two distinct limitations that our method overcomes. First, it must solve
nS·nT constraints, whereas our formulation only needs to solveK·nT constraints, for a Kcategory
problem. In general, our method scales to much larger source domains than with ARC-t. The second
beneﬁt of our max-margin transformation learning approach is that the transformation learned using
the max-margin constraints is learned jointly with the classiﬁer, and explicitly seeks to optimize the
ﬁnal SVM classiﬁer objective. While ARC-t’s similarity-based constraints seek to map points of the
same category arbitrarily close to one another, followed by a separate classiﬁer learning step, we
seek simply to project the target points onto the correct side of the learned hyperplane, leading to
better classiﬁcation performance.
The HFA formulation also takes advantage of the max-margin framework to directly optimize the
classiﬁcation objective while learning transformations. HFA learns the classiﬁer and transforma-
tions to a common latent feature representation between the source and target. However, HFA is
formulated to solve a binary problem so a new feature transformation must be learned for each cat-
egory. Therefore, unlike MMDT, HFA cannot learn a representation that generalizes to novel target
categories. Additionally, due to the difﬁculty of deﬁning the dimension of the latent feature repre-
sentation directly, the authors optimize with respect to a larger combined transformation matrix and
a relaxed constraint. This transformation matrix becomes too large when the feature dimensions in
source and target are large so the HFA must usually be solved in kernel space. This can make the
method slow and cause it to scale poorly with the number of training examples. In contrast, our
method can be efﬁciently solved in linear feature space which makes it fast and potentially more
scalable.
Finally, GFK [15] formulates a kernelized representation of the data that is equivalent to computing
the dot product in inﬁnitely many subspaces along the geodesic ﬂow between the source and target
domain subspaces. The kernel is deﬁned by the authors to be symmetric and so can not handle source
and target domains of different initial dimension. Additionally, GFK does not directly optimize a
classiﬁcation objective. In contrast, our method, MMDT, can handle source and target domains of
different feature dimensions via an asymmetric W, as well as directly optimizes the classiﬁcation
objective.
4 Experiments on Image Datasets
We now present experiments using theOfﬁce [1], Caltech256 [25] and Bing [21] datasets to evaluate
our algorithm according to the following four criteria. 1) Using a subset of theOfﬁce and Caltech256
datasets we evaluate multi-class accuracy performance in a standard supervised domain adaptation
setting, where all categories have a small number of labeled examples in the target. 2) Using the full
Ofﬁce dataset we evaluate multi-class accuracy for the supervised domain adaptation setting where
the source and target have different feature dimensions. 3) Using the full Ofﬁce dataset we evaluate
multi-class accuracy in the multi-task domain adaptation setting with novel target categories at test
time. 4) Using the Bing dataset we assess the ability to scale to larger datasets by analyzing timing
performance.
5
svms svmt arct [12] hfa [11] gfk[15] mmdt (ours)
a →w 33.9 ±0.7 62.4 ±0.9 55.7 ±0.9 61.8 ±1.1 58.6 ±1.0 64.6 ±1.2
a →d 35.0 ±0.8 55.9 ±0.8 50.2 ±0.7 52.7 ±0.9 50.7 ±0.8 56.7 ±1.3
w →a 35.7 ±0.4 45.6 ±0.7 43.4 ±0.5 45.9 ±0.7 44.1 ±0.4 47.7 ±0.9
w →d 66.6 ±0.7 55.1 ±0.8 71.3 ±0.8 51.7 ±1.0 70.5 ±0.7 67.0 ±1.1
d →a 34.0 ±0.3 45.7 ±0.9 42.5 ±0.5 45.8 ±0.9 45.7 ±0.6 46.9 ±1.0
d →w 74.3 ±0.5 62.1 ±0.8 78.3 ±0.5 62.1 ±0.7 76.5 ±0.5 74.1 ±0.8
a →c 35.1 ±0.3 32.0 ±0.8 37.0 ±0.4 31.1 ±0.6 36.0 ±0.5 36.4 ±0.8
w →c 31.3 ±0.4 30.4 ±0.7 31.9 ±0.5 29.4 ±0.6 31.1 ±0.6 32.2 ±0.8
d →c 31.4 ±0.3 31.7 ±0.6 33.5 ±0.4 31.0 ±0.5 32.9 ±0.5 34.1 ±0.8
c →a 35.9 ±0.4 45.3 ±0.9 44.1 ±0.6 45.5 ±0.9 44.7 ±0.8 49.4 ±0.8
c →w 30.8 ±1.1 60.3 ±1.0 55.9 ±1.0 60.5 ±0.9 63.7 ±0.8 63.8 ±1.1
c →d 35.6 ±0.7 55.8 ±0.9 50.6 ±0.8 51.9 ±1.1 57.7 ±1.1 56.5 ±0.9
mean 40.0 ±0.6 48.5 ±0.8 49.5 ±0.6 47.4 ±0.8 51.0 ±0.7 52.5 ±1.0
Table 2: Multi-class accuracy for the standard supervised domain adaptation setting: All results are
from our implementation. When averaged across all domain shifts the reported average value forgfk
was 51.65 while our implementation had an average of 51.0 ±0.7. Therefore, the result difference
is within the standard deviation over data splits. Red indicates the best result for each domain split.
Blue indicates the group of results that are close to the best performing result. The domain names
are shortened for space: a: amazon, w: webcam, d: dslr, c: Caltech256
Ofﬁce Dataset The Ofﬁce dataset is a collection of images that provides three distinct domains:
amazon, webcam, and dslr. The dataset has 31 categories consisting of common ofﬁce objects
such as chairs, backpacks and keyboards. Theamazon domain contains product images (from ama-
zon.com) containing a single object, centered, and usually on a white background. Thewebcam and
dslr domains contain images taken in“the wild” using a webcam or a dslr camera, respectively.
They are taken in an ofﬁce setting and so have different lighting variation and background changes
(see Figure 1 for some examples.) We use the SURF-BoW image features provided by the au-
thors [1]. More details on how these features were computed can be found in [1]. The available
features are vector quantized to 800 dimensions for all domains and additionally for the dslr do-
main there are 600 dimensional features available (we denote this as dslr-600).
Ofﬁce + Caltech256 Dataset This dataset consists of the 10 common categories shared by the
Ofﬁce and Caltech256 datasets. To better compare to previously reported performance, we use the
features provided by [15], which are also SURF-BoW 800 dimensional features.
Bing Dataset To demonstrate the effect that constraint set size has on run-time performance, we
use the Bing dataset from [21], which has a larger number of images in each domain thanOfﬁce. The
source domain has images from the Bing search engine and the target domain is from theCaltech256
benchmark. We run experiments using the ﬁrst 20 categories and set the number of source examples
per category to be 50. We use the train/test split from [21] and then vary the number of labeled target
examples available from 5 to 25.
Baselines We use the following baselines as a comparison in the experiments where applicable.1
•svms: A support vector machine using source training data.
•svmt: A support vector machine using target training data.
• arc-t: A category general feature transform method proposed by [12]. We implement the
transform learning and then apply both a KNN classiﬁer (as originally proposed) and an
SVM classiﬁer.
• hfa: A max-margin transform approach that learns a latent common space between source
and target as well as a classiﬁer that can be applied to points in that common space [11].
• gfk: The geodesic ﬂow kernel [15] applied to all source and target data (including test data).
Following [15], we use a 1-nearest neighbor classiﬁer with the kernel.
1We used the LIBSVM package [26] for kernelized methods and Liblinear [27] package for linear methods.
6
source target svmt arc-t hfa mmdt
amazon dslr-600 52.9 ±0.7 58.2 ±0.6 57.8 ±0.6 62.3 ±0.8
webcam dslr-600 51.8 ±0.6 58.2 ±0.7 60.0 ±0.6 63.3 ±0.5
Table 3: Multiclass accuracy results on the standard supervised domain adaptation task with different
feature dimensions in the source and target. The target domain is dslr for both cases.
source svms arc-t gfk mmdt
amazon 10.3 ±0.6 41.4 ±0.3 38.9 ±0.4 44.6 ±0.3
webcam 51.6 ±0.5 59.4 ±0.4 62.9 ±0.5 58.3 ±0.5
Table 4: Multiclass accuracy results on the Ofﬁce dataset for the domain shift of webcam→dslr
for target test categories not seen in at training time. Following the experimental setup of [12]. We
compare against pmt-svm [10] and ARC-t [12] using both knn and svm classiﬁcation.
Standard Domain Adaptation Experiment For our ﬁrst experiment, we use the Of-
ﬁce+Caltech256 domain adaptation benchmark dataset to evaluate multi-class accuracy in the stan-
dard domain adaptation setting where a few labeled examples are available for all categories in the
target domain. We follow the setup of [1] and [15]: 20 training examples for amazon source (8 for
all other domains as source) and 3 labeled examples per category for the target domain. We created
20 random train/test splits and averaged results across them.
The multi-class accuracy for each domain pair is shown in Table 2. Our method produced the
highest multi-class accuracy for 9 out of 12 of the domain shifts and competitively on the other 3
shifts. This experiment demonstrates that our method achieves a high recognition performance and
is able to outperform the most recent domain adaptation algorithms. Our method especially stands
out in the settings where the domains are initially very different. The most similar domains in this
dataset are webcam and dslr and we see that our algorithm does not perform as well on those two
shifts as gfk. This ﬁts with our intuition since gfk is a 1-nearest neighbor approach and so is more
suitable when the domains are initially similar.
Additionally, an important observation is that our linear method on average outperforms all the
baselines, even though they each learn a non-linear transformation.
Asymmetric Transform Experiment Next, we analyze the effectiveness of our asymmetric trans-
form learning by experimenting with the source and target having different feature dimensions. We
use the same experimental setup as previously, but use the Ofﬁce dataset and the alternate represen-
tation for the dslr domain that is 600-dimensional (denoted as dslr-600). We compare against
svmt, arc-t and hfa, the baselines that can handle this scenario. The results are shown in Table 3.
Again, we ﬁnd that our method can effectively learn a feature representation for the target domain
that optimizes the ﬁnal classiﬁcation objective.
Generalizing to Novel Categories Experiment We next consider the setting of practical impor-
tance where labeled target examples are not available for all objects. Recall that this is a setting that
many category speciﬁc adaptation methods cannot generalize to, including hfa [11]. Therefore, we
compare our results for this setting to the arc-t [12] method which learns a category independent
feature transform and the gfk [15] method which learns a category independent kernel to compare
the domains. Following the experimental setup of [12], we use the full Ofﬁce dataset and allow 20
labeled examples per category in the source for amazon and 10 labeled examples for the ﬁrst 15
object categories in the target ( dslr). For the webcam→dslr shift, we use 8 labeled examples
per category in the source for webcam and 4 labeled examples for the ﬁrst 15 object categories in
the target dslr.
The experimental results for the domain shift of webcam→dslr are evaluated and shown in Ta-
ble 4; MMDT outperforms the baselines for the amazon→dslr shift and offers adaptive beneﬁt
over svms for the shift from webcam to dslr. As in the ﬁrst experiment, both arc-t and gfk use
nearest neighbor classiﬁers on a learned kernel are more suitable to the shift between webcam and
dslr, which are initially very similar.
Scaling to Larger Datasets Experiment With our last experiment we show that our method not
only offers high accuracy performance it also scales well with an increasing dataset size. Speciﬁ-
7
5 10 15 2030
40
50
60
70
Number of Labeled Target Examples
Multiclass accuracy (%)
Multiclass Accuracy vs #Target Example
 
 
5 10 15 200
20
40
60
Number of Labeled Target Examples
Time (min)
Time vs #Target Examples
 
 
5 10 15 2030
35
40
45
50
55
60
65
Number of Labeled Target Examples
Multiclass accuracy (%) 
 
svms svmt arct hfa gfk mmdt (ours)
Figure 2: Left: multiclass accuracy on the Bing dataset using 50 training examples in the source and
varying the number of available labeled examples in the target. Right: training time comparison.
cally, the number of constraints our algorithm optimizes scales linearly with the number of training
points. Conversely, the number of constraints that need to be optimized for the arc-t baseline is
quadratic in the number of training points.
To demonstrate the effect that constraint set size has on run-time performance, we use theBing [21]
dataset, which has a larger number of images in each domain than Ofﬁce. The source domain has
images from the Bing search engine and the target domain is from the Caltech256 benchmark. We
run experiments using the ﬁrst 20 categories and set the number of source examples per category
to be 50. We use the train/test split from [21] and then vary the number of labeled target examples
available from 5 to 20. The left-hand plot in Figure 2 presents multi-class accuracy for this setup.
Additionally, the training time of our method (run to convergence) and that of the baselines is shown
on the right-hand plot.
Our mmdt method provides a considerable improvement over all the baselines in terms of multi-
class accuracy. It is also considerably faster than all but the gfk method. An important point to note
is that both our method and arc-t scale approximately linearly with the number of target training
points which is empirical veriﬁcation for our claims. Note that hfa and gfk do not vary signiﬁcantly
as the number of target training points increases. However, for hfa the main bottleneck time is
consumed by a distance computation between each pair of training points. Therefore, since there are
many more source training points than target, adding a few more target points does not signiﬁcantly
increase the overall time spent for this experiment, but would present a problem as the size of the
dataset grew in general.
5 Conclusion
In this paper, we presented a feature learning technique for domain adaptation that combines the
ability of feature transform-based methods to perform multi-task adaptation with the performance
beneﬁts of directly adapting classiﬁer parameters.
We validated the computational efﬁciency and effectiveness of our method using two standard
benchmarks used for image domain adaptation. Our experiments show that 1) our method is a
competitive domain adaptation algorithm able to outperform previous methods, 2) is successfully
able to generalize to novel target categories at test time, and 3) can learn asymmetric transforma-
tions. In addition, these beneﬁts are offered through a framework that is scalable to larger datasets
and achieves higher classiﬁcation accuracy than previous approaches.
So far we have focused on linear transforms because of its speed and scalability; however, our
method can also be kernelized to include nonlinear transforms. In future work, we would like to
explore the kernelized version of our algorithm and especially experiment with the geodesic ﬂow
kernel as input to our algorithm.
Acknowledgements: This work was supported by NSF grants IIS-1116411 and IIS-1212798,
DARPA, and the Toyota Corporation.
8
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9


Peer review:
[Review]:
This paper focuses on multi-task learning across domains, where both the data generating distribution and the output labels can change between source and target domains. It presents a SVM-based model which jointly learns 1) affine hyperplanes that separate the classes in a common domain consisting of the source and the target projected to the source; and 2) a linear transformation mapping points from the target domain into the source domain.

Positive points

1) The method is dead simple and seems technically sound. To the best of my knowledge it's novel, but I'm not as familiar with the SVM literature - I am hoping that another reviewer comes from the SVM community and can better assess its novelty.
2) The paper is well written and understandable
3) The experiments seem thorough: several datasets and tasks are considered, the model is compared to various baselines. The model is shown to outperform contemporary domain adaption methods, generalize to novel test categories at test time (which many other methods cannot do) and can scale to large datasets.

Negative points

I have one major criticism: the paper doesn't seem really focused on representation learning - it's more a paper about a method for multi-task learning across domains which learns a (shallow, linear) mapping from source to target. I agree - it's a representation but there's no real analysis or focus on the representation itself - e.g. what is being captured by the representation. The method is totally valid, but I just get the sense that it's a paper that could fit well with CVPR or ICCV (i.e. a good vision paper) where the title says 'represention learning', and a few sentences highlight the 'representation' that's being learned, however the method nor the paper's focus is really on learning interesting representations. On one hand I question its suitability for ICLR and it's appeal to the community (compared to CVPR/ICCV, etc.) but on the other hand, I think it's great to encourage diversity in the papers/authors at the conference and having a more 'visiony'-feeling paper is not a bad thing.

Comments
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Can you state up front what is meant by the asymmetry of the transform (e.g. when it's first mentioned)? Later on in the paper it becomes clear that it has to do with the source and target having different feature dimensions but it wasn't obvious to me at the beginning of the paper. 

Just before Eq (4) and (5) it says that 'we begin by rewriting Eq 1-3 with soft constraints (slack)'. But where are the slack variables in Eq 4?