Signal Processing - November 2017 - 79

n

ed
ct
lly ne
Fu o n
C

io
ut

l
vo

io
ut

g

l
vo

in

pl

on

C

am
bs

on

Su

C

coming testing samples can also be used
Input
Layer 1
Layer 2
Layer 3
Output
with the learned metric; and 4) the mappings generated by the function is smooth
and coherent in the output space.
Cai et al. [20] introduced a deep
nonlinear metric learning (DNLML)
method by using a deep independent
subspace analysis (ISA) network, called
DNLML-ISA for face verification. ISA
is an unsupervised learning algorithm
and a two-layer neural network, where
different active functions in the first and FIGURE 3. An illustration of a CNN architecture. This CNN comprises two convolutional layers C1 and
second layers were used, respectively. C3, a subsampling layer S2, and a fully connected layer F3.
Specifically, DNLML-ISA employed the
ISA network to transform features from
the original space to another feature subspace. To identify -discriminative features,
Loss Function
Loss Function
DNLML-ISA combined the side information constraints for metric learning
df (xi, xj)
df (xi, x+i )
df (xi, xi- )
with ISA, and stacked the ISA networks
||f (xi+) - f (xi)||2
||f (xi-) - f (xi)||2
||f (xi) - f (xj)||2
into a deep architecture. Since DNLMLISA is trained layer by layer, it cannot use
-
+
f (xi )
f (xi )
the backpropagation algorithm to update
f (xj)
f (xi )
f (xi)
the model and also cannot fully exploit
f
f
f
f
f
the discriminative information.
Hu et al. [6] introduced a discrimixj
xi+
xi
xi-
xi
native DML (DDML) method for face
verification. Unlike the stacked model
Triplet Networks
Siamese Networks
used in DNLML-ISA, DDML employed
a fully connected deep neural network to FIGURE 4. Diagrams of Siamese networks and triplet networks for DML. Siamese networks are comlearn multiple nonlinear transformations posed of two same neural networks f  with shared parameters, where (xi, xj) is a similar/dissimilar pair.
same neural networks f  with shared parameters, where ^x i , x +i , x -i h is
to map face samples into a discrimina- Triplet networks consist of three
+
a
triplet,
x
is
a
reference,
x
i and x i are similar and dissimilar examples to xi.
i
tive distance space, where the similarity
of each positive pair is enlarged and that of
each negative pair is reduced, respectively. The denoising autoencoder was used as the initialization of the parameters of each layer
and then the backpropagation was used to update the model. The key
advantage of DDML is that it can be trained on a small size of training data set and without using the extensive outside labeled data.
Taigman et al. [21] introduced a DeepFace method by employτ1
ing an end-to-end metric learning method with the Siamese netSame
τ2
work for face recognition. Unlike DDML, where only the metrics
Different
Before
After
were learned at the fully connected layers, DeepFace performed
discriminative learning with the convolutional, pooling, and fully
FIGURE 5. The basic idea of DML methods via Siamese -network using (4)
connected layers so that more labeled training samples were used
[6]. At the top layer of the network, the distance d f (x i , x j ) for a positive
to train the model. Finally, the parameters of the Siamese netpair is less than a smaller parameter x 1 and that of a negative pair is
larger than a larger parameter x 2, respectively.
work were trained by the standard cross-entropy loss and backpropagation method.
Sun et al. [7] used carefully designed deep convolutional netother one is the verification signal, which enforced that DeepID2
works (deep ConvNets) by making use of both the verification and
features extracted from the same class are as similar as possible.
identification information to learn the deep identification-verifiTheir method showed that both the identification and verification
cation features (DeepID2) [7] for face verification. Specifically,
signal contributed to the final discriminative feature learning.
their method extracted deep features with two signals: the first is
Yi et al. [12] proposed a DML method with a Siamese deep
the identification signal, which was achieved by following the
neural network to learn a similarity metric from image pixels
DeepID2 layer with an n-way softmax layer. The network was
directly for person reidentification. Their -method jointly learned
trained by minimizing the cross-entropy identification loss. The
discriminative features and similarity measures under a unified
n

IEEE SIGNAL PROCESSING MAGAZINE

|

November 2017

|

79
Table of Contents for the Digital Edition of Signal Processing - November 2017
