Discriminant Projection Representation-based Classification for Vision
Recognition
Qingxiang Feng and Yicong Zhou*

arXiv:1712.01643v1 [] 19 Nov 2017

Computer and Information Science, University of Macau
fengqx1988@gmail.com, yicongzhou@umac.mo, *Corresponding author.

Abstract
Representation-based classification methods such as sparse
representation-based classification (SRC) and linear regression classification (LRC) have attracted a lot of attentions.
In order to obtain the better representation, a novel method
called projection representation-based classification (PRC) is
proposed for image recognition in this paper. PRC is based on
a new mathematical model. This model denotes that the ’ideal
projection’ of a sample point x on the hyper-space H may be
gained by iteratively computing the projection of x on a line
of hyper-space H with the proper strategy. Therefore, PRC
is able to iteratively approximate the ’ideal representation’
of each subject for classification. Moreover, the discriminant
PRC (DPRC) is further proposed, which obtains the discriminant information by maximizing the ratio of the betweenclass reconstruction error over the within-class reconstruction
error. Experimental results on five typical databases show that
the proposed PRC and DPRC are effective and outperform
other state-of-the-art methods on several vision recognition
tasks.

Introduction
Recently, representation-based classifiers have attracted
increasing attentions of researchers, which can be roughly
divided into two kinds: all-classes-based and singleclass-based. In the first kind, the well-known method
is sparse representation-based classification (SRC)
(Wright et al. 2009). It was developed to use the allclass-model to obtain the L1 -based sparse representation
for classification . To improve the computation efficiency,
the collaborative representation-based classification (CRC)
(Zhang, Yang, and Feng 2011) was proposed to address the
L2 minimum problem. Later, several improved methods of
SRC were proposed for image recognition (Yang et al. 2012;
Feng and Zhou 2016b; Feng and Zhou 2017), such as
manifold constraint transfer (MCT) (Zhang et al. 2015)
applies a strategy to produce new data for classification.
Different from the all-class-model in SRC, some classifiers use single class to obtain its representation. For
example, linear regression-based classification (LRC)
(Naseem, Togneri, and Bennamoun 2010) was proposed for
face identification, which was based on that samples from
Copyright c 2018, Association for the Advancement of Artificial
Intelligence (www.aaai.org). All rights reserved.

a specific object class are known to lie on a linear subspace (Basri and Jacobs 2003; Feng, Zhou, and Lan 2016;
Feng and Zhou 2016a). LRC solves the least square errors
and obtain the linear projection point as the representation
for an independent class-specific models.
The common objective of existing representation-based
methods is to find the best representation for classification.
However, they have only obtained a roughly approximated
representation. For example, In ref.(Wright et al. 2009), we
know that the ideal representation of SRC is to solve the
L0 minimum problem. In LRC, the regression projection is
obtained by a matrix’s pseudo-inverse. Therefore, we know
that they only obtain the approximated representation. In
order to find a better representation of an image, this paper proposes a projection representation-based classification
(PRC) for image recognition. To approximate the ’ideal representation’ of a sample point, PRC utilizes a new mathematical model to iteratively compute the projection point of
the test sample towards a line linking a paired of specific
points. This mathematical model has been proved by a theorem. According to the theorem, we know that the generated
projection will be almost equal to the ’ideal representation’
after sufficient iterations. Moreover, the discriminant PRC
(DPRC) is further proposed, which obtains the discriminant
information by maximizing the ratio of the between-class
reconstruction error over the within-class re-construction error. The main contributions of this paper are as follows:
⊙ Firstly, we propose a new mathematical model to obtain
the projection of a point on a hyper-space, and we prove this
model mathematically.
⊙ Secondly, with the mathematical model, we propose the
projection representation-based classification (PRC) for image recognition tasks. The generated projection by PRC will
be almost equal to the ’ideal representation’ after sufficient
iterations.
⊙ In order to obtain an effective discriminant subspace
for PRC, we propose the discriminant PRC (DPRC). DPRC
utilizes the labeled training samples set to constitute a more
reliable subspace such that the effective discriminant information can be used for classification.
⊙ Experiments have been carried out on several challenging databases. The results show that the proposed PRC
and DPRC outperform several state-of-the-art methods.

Notation Summary
Let X = {xci ∈ Rq×1 , i = 1, 2, · · · , Nc , c = 1, 2, · · · , M }
denote the prototype data set, where xci is the ith sample of the cth class, M is the number of classes, Nc
is the number of samples of the cth class and q is the
sample’s dimension. The number of all the samples is
M
P
L=
Nc . The prototype data set can be also described as
c=1

X = {xi ∈ Rq×1 , i = 1, 2, · · · , L}.

Proposed Math Model

and new projection point closely approximates to a fixed
constant, which is the smallest distance between the test
sample x and the space of the cth class.
Proof: Because xc,0
is the projection of the test samp
c,0
ple x to the line xc,0
n xi , then
c,0
kx − xc,0
p k ≤ kx − xn k.

c,0
After the first projection procedure, xc,0
p replaces xn as the
new nearest sample and will be used to form the new line.
Following this manner, in the k th projection procedure, we
have

Before introducing the math model, we describe the ’ideal
projection’ in Definition 1.
Definition 1: Suppose that there exists a test sample x
and a specific class c. If a point in the hyper-space of the
cth class is the nearest to test sample x, it is treated as
the ’ideal representation’ or ’ideal projection’ of the test
sample x on the hyper-space.

c,k−1
kx − xc,k
k
p k ≤ kx − xp

Given a point x and a hyper-space H, the ’ideal projection’
of x on the hyper-space H may be gained by iteratively computing the projection point of x on a line of hyper-space H
with the proper strategy. It can be describe as
c,k
p{x, H} ≈ repreat p{x, xc,k
i xi∗ }

(3)

Because the distance between the test sample x and the projection point is equal or greater than 0, the projection points
satisfy the following conditions.
c,k−1
k, k = 1, 2, · · · , +∞
0 ≤ kx − xc,k
p k ≤ kx − xp

(4)

That is,
lim kx − xc,k
p k= d

Math Model

(2)

k→+∞

(5)

where d is a constant that is the smallest distance between
the test sample x and the subspace of the cth class.

Proposed Math Model vs Linear Regression
(1)

k→+∞

N
N
c,k
where p{∗, } denotes the projection of ∗ on , xc,k
i , xi∗
c,k
are two points of the hyper-space H. xi∗ is the nearest point
among all known-distance points of H.

Correctness of the Math Model
Now, we know that the proposed model is quite useful for
finding the better representation of each class for classification. Therefore, the correctness of the proposed math model
will be an important problem. The Theorem 1 is provided to
prove the proposed math model. According to the Theorem
1, a projection point with the minimum distance can be
obtained by iteratively computing the projection point of
x on hyper-space’s a line. Considering Definition 1, we
know that the obtained projection point can be treated as the
projection of x on the hyper-space. Therefore, the proposed
math model is correct.
Theorem 1: Given a test sample x, and a specific
class c with Nc training samples. Suppose the cth class in
c,0
the first round of projection is Xc0 = [xc,0
· · · xc,0
1 x1
Nc ].
c,0
Select the nearest training sample xn and another training
c,0 c,0
sample xc,0
i , i 6= n to form a line xn xi ; Compute the
c,0 c,0
projection point xc,0
p of the test sample x to the line xn xi ;
c,0
and use xc,0
p to replace xi , i 6= n as the new training set
th
of the c class. If this projection operation was performed
in sufficient times, the distance between the test sample

For a specific class subspace,the real projection point
cannot be computed using the existing math knowledge because the class subspace is a hyper-space. Ref.
(Naseem, Togneri, and Bennamoun 2010) proposed LRC to
solve the least square errors and obtain the linear projection point. LRC has the good performance. However, LRC
obtains the linear projection point by a pseudo-inverse operation such that this point is only a roughly approximated
projection point (exist the closer point than the linear projection point), not the ideal projection point according to Definition 1. Therefore, we intend to obtain a better projection
point that is the nearest one to the ’ideal projection’ point by
using the proposed math model.

Proposed PRC
Based on the concept of finding the best representation of
each class, this section proposes a new classifier, called projection representation-based classification (PRC). According to the proposed math model, PRC may obtain the approximated projection point by computing the projection
point of the test sample to a line linking with a pair of training samples iteratively. The flowchart of PRC is shown in
Figure 1.

Projection Representation
To find a point extremely close to the ideal representation
of a sample point, PRC iteratively computes the projection
point of the test sample on a line. The final result will be
treated as the projection representation for classification.

Figure 1: The flowchart of the proposed PRC. ′ e = 0′ means
that PRC satisfies the stop condition. The detailed information of e can be found in the stop condition.
Start the iteration For the first iteration, suppose that a
class model Xc0 is described as follows
q×Nc
Xc0 = [xc,0
xc,0
· · · xc,0
,
1
2
Nc ] ∈ R
c
where xc,0
i = xi , i
c,0
est point xi∗ from

(6)

= 1, 2, · · · , Nc . We then select the nearthe class model Xc0 as follow.

i∗ = arg min(kx − xc,0
i k), i = 1, 2, · · · , Nc

(7)

c,0
∗
Use the nearest point xc,0
i∗ and a training sample xi , i 6= i
c,0 c,0
to form a line xi∗ xi . Next, the projection point of the test
c,0
sample x on the line xc,0
i∗ xi can be computed by:
c,0
c,0
0 c,0
pc,0
i∗ = xi∗ + t (xi − xi∗ )

(8)

where t ∈ R is the position parameter. The vector xpc,0
i∗ is
c,0
c,0
c,0
orthogonal to xc,0
− xc,0
i∗ xi , that is, (x − pi∗ )(xi
i∗ ) =
0 where • denotes the dot product. Therefore, the position
parameter can be computed as

t0 =

c,0
c,0
T
(x − xc,0
i∗ ) (xi − xi∗ )
c,0 T
c,0
c,0
(xc,0
i − xi∗ ) (xi − xi∗ )

(9)

For the (k + 1)th (k ≥ 1) iteration, it is easy to know
that the projection point pic,k−1
in the k th iteration is nearest
∗
c,k
c,k−1
point. That is, xi∗ = pi∗ . The projection point pc,k
i∗ in
the (k + 1)th iteration will be computed by x and a line constituted by pic,k−1
and another train sample. The procedure
∗
of computing the projection point of x on a line is similar to
the first iteration.
Rule: All the projection procedure is similar. However, they
need to satisfy the following rule. The number of samples
from the class subspace is fixed. The new projection points

Figure 2: An example of convergence analysis: The distances variations between the test sample and approximation
projection point in the iteration procedure.
will replace the farther point of the line because they are
closer to the test sample. All the samples of class subspace
will be sequentially used to constitute the line (as farther
point of the line) so that the projection point may contain
the information of all the training samples.
Convergence Analysis and Stop Condition Because the
number of iterations is unlimited, we need to determine the
condition for stopping the iteration processes. In order to
obtain a good parameter for ending of the process, an example is given as follows. The training set and test sample are produced randomly, the dimension of each sample
is 5000, and the number of training samples is 20. Fig. 2
shows that the distance between the test sample and the projection point changes with the number of iterations. As can
be seen, the difference between two adjacent distances tends
to zeros. Thus, the stop conditions of the iteration process
are described as follows.
Condition 1: Suppose that pic,k−1
and pc,k
∗
i∗ are two nearest
projection points in the kth and (k + 1)th iterations. If δ <
δ0 , the iteration process stops, where δ0 is given before the
iteration and the threshold value δ can be computed as
!
kx − pic,k−1
k − kx − pc,k
∗
i∗ k
δ = abs
.
(10)
kx − pic,k−1
k + kx − pc,k
∗
i∗ k
Besides, in order to avoid the unpredicted situation, another
condition is described as follows.
Condition 2: Set the maximum iterative times J. Based on
the Figure 2, we suggest that J is set no more than 100.
Notice that this condition is rarely used. It can be treated as
an insurance.
Set a stop parameter e = 1, if one of the two stop conditions
is satisfied, e = 0, the iteration stops. Then the projection
representation pc can be described as
c,k
c,k
k c,k
pc = pc,k
i∗ = xi∗ + t (xi − xi∗ )

(11)

Algorithm 1: Projection Representation

Proposed DPRC

Inputs The entire training samples xci , c = 1, 2, · · · , M , i =
1, 2, · · · , Nc and a test image vector x ∈ Rq×1 . The stop parameter δ0 and J.

PRC obtains the ’ideal projection’ while it doesn’t use discriminant analysis for classification. Thus, this section pay
attention to utilize the labeled training samples set to constitute a more reliable subspace such that the effective discriminant information can be used for classification. In order to obtain an effective discriminant subspace for PRC, we
propose a novel method, called discriminant PRC (DPRC),
which obtains the discriminant information by maximizing
the ratio of the between-class reconstruction error over the
within-class reconstruction error by the PRC.

Output The projection representation pc .
1. Set e = 1; J = 100; δ0 = 0.01
Repeat
k
2. Find the nearest point xc,k
n from the class-models Xc

3. Compute the projection point pc,k
i∗ of the test sample x on the
c,k
(i = 1, 2, · · · , Nc and i 6= i∗ ) as
line xc,k
i∗ xi
 c,k
c,k
k
 pi∗ = xc,k
− xc,k
i∗ + t (xi
i∗ )



t=

Optimization of DPRC
The proposed DPRC approach is formulated as the optimization problem to maximize the objective function as,

c,k T
c,k
c,k
(x−xi∗ ) (xi −xi∗ )
c,k
c,k T
c,k
c,k
(xi −xi∗ ) (xi −xi∗ )

4. Update the class-models Xck using the pc,k
i∗ to replace the farther

max J(P ) = max

c,k
point xc,k
of line xc,k
as Xck+1
i
i∗ xi

P

in
5. Update the parameters δ by using the projection point pic,k−1
∗
in
this
iteration
as
the last iteration and pc,k
∗
i
!
k − kx − pc,k
kx − pic,k−1
∗
i∗ k
δ = abs
k + kx − pc,k
kx − pic,k−1
∗
i∗ k
6. Update the parameter J = J − 1.
7. Update the e as
If (δ < δ0 kJ < 0)
e = 0; break;
end if
Until the e = 0 and output the pc = pc,k
i∗

Jb
Jw
1
L(M−1)

k

t =

c,k
c,k
T
(x − xc,k
i∗ ) (xi − xi∗ )

(xc,k
i

−

c,k
T
xc,k
i∗ ) (xi

−

xc,k
i∗ )

=

Classification Using the Algorithm 1, the approximation
projection pc is obtained for the cth class subspace. The distance between the test sample and the cth class subspace can
be computed as
dc (x) = kx − pc k.

(13)

PRC selects the class with the minimum distance
min
dc (x), c = 1, 2, · · · , M.
∗
c

(14)

1
L(M−1)

=

M
P

i=1 j=1,j6=l(xi )
L
P

i=1

L
P

L
P

i=1

b
||wi − wij
||

||wi − wiw ||
M
P

i=1 j=1,j6=l(xi )
1
L

(16)

||P T xi − P T xbij ||

||P T xi − P T xw
i ||

w
b
w
b
= P T xw
where wij
= P T xbij , wij
i , xij and xi are the
between-class and within-class projection vectors. That is,
they are projection representation of xi on Xjb and Xiw , respectively. They can be calculated by Algorithm 1 with the
xi , Xiw and Xjb . Xiw denotes the l(xi )-th class-model in (1)
(don’t include the sample xi ), l(xi ) denotes the class label
of xi , Xjb denotes the j-th (j 6= l(xi ) ) class-model, With
some algebraic derivations in matrices, we have
1
L

Computational Complex
Suppose the dimensional of each sample is q, it is easy to
know that the computational cost of each projection operation is O(q). Therefore, the computational complex of PRC
is O(Kq) , K is the number of projection operations. From
the Figure 2, we know that the iteration number is not large,
that is to say, the computational cost of PRC is small.

L
P
1
L

(12)

Notice: For the example of convergence analysis in Figure 2,
we repeat the experiment more than one hundred times. The
tendency of the distance variations is similar. Select only
some valuable samples that is helpful for classification.

(15)

where P is the optimal projection matrix that we want to estimate, Jb and Jw denote the between-class and within-class
reconstruction representative metrics, respectively. Then, the
goal of the DPRC approach becomes to find an optimal mapping matrix, P = [p1 , ..., pk , ..., pd ] which could project the
original sample xi to a new data sample as wi = P T xi for
i = 1, 2...L. The proposed projection reduces the dimension and is effective for classification. The above objective
function can be also expressed as
J(P ) =

where

P

Jb
Jw

J(P ) =

L
P

M
P

i=1 j=1,j6=l(xi )

=tr(

1
L

L
P

i=1

T

tr[P T (xi − xbij )(xi − xbij ) P ]
T

w
tr[P T (xi − xw
i )(xi − xi ) P ]

P T Jb P
)
P T Jw P
(17)

where
Jb =

1
L

L
X

M
X

T

(xi − xbij )(xi − xbij )

i=1 j=1,j6=l(xi )

and

L

Jw =

1X
w T
(xi − xw
i )(xi − xi )
L i=1

Afterwards, the objective function can be expressed as
T

arg max PPT JJwb PP
P

s.t. P T P = I

• Difference: In ULDA, Jb = Sb + Ub , Jw = Sw + Uw ,
where Sb , Sw are the within-class and between-class scat(18) ters in LDA. ULDA proposes the uncertain within-class
and between-class scatters Ub , Uw . In DPRC, the Jb , Jw
can be treated as new projection-based within-class and
between-class scatters, which has significantly difference
(19) to Sb , Sw and Ub , Uw .

Experimental Results
This section evaluate the proposed PRC and DPRC on sev(20)eral vision recognition databases.

In order to address the typical small sample size problem, theFace recognition
term εI is increased without affecting the subspace. Thus,LFW-a database (Zhu et al. 2012) is used in this experiment. Following (Zhang et al. 2015), we apply 158
the objective function can be rewritten as
subjects that have no less than ten samples for evalT
bP
arg max P T P(JwJ+εI)P
uation. The experiment set: 5 samples are randomly
(21)
P
T
selected to form the training set, while other 2 samples are
s.t. P P = I
exploited for testing. The SRC (Wright et al. 2009),
where ε is a small number and I is an identity matrix.SVM
(Schüldt, Laptev, and Caputo 2004),
FDDL
By using Lagrange multiplier, the projection matrix P =(Yang et al. 2014),
MCT
(Zhang et al. 2015),
[p1 , ..., pk , ..., pd ] that maximizes the objective function,RCR
(Yang et al. 2012),
ULDA
which can be gained by solving the eigen decomposition(Saeidi, Astudillo, and Kolossa 2016),
ProCRC
b
problem of JwJ+εI
as
(Cai et al. 2016) and CRC (Zhang, Yang, and Feng 2011)
Jb pk = λk (Jw + εI)pk , k = 1, 2, ..., d
(22)algorithms are chosen for comparison. Table 1 illustrates
the comparison results of all methods. DPRC obtains better
where λ1 ≥ ... ≥ λk ≥ ... ≥ λd is d largest eigenvalues andperformance than PRC. Compared to the exsiting methods,
their corresponding eigenvectors, p1 , ..., pk , ..., pd of JJwb . ItDPRC has more than 3% improvement..
is noted that P = [p1 , ..., pk , ..., pd ] is a q × d projection
matrix, which can project the original q-element data vector
Classifier Accuracy Classifier Accuracy (%)
to the new d-element data vector as wi = P T xi for i =
SRC
44.10
CRC
44.30
1, 2...L.
SVM
43.30
ULDA
44.30
FDDL
42.00
ProCRC
44.90
Classification
MCT
44.90
PRC
46.84
In the above Section, DPRC obtains the effective discrimiRCR
36.70
DPRC
47.90
nant space W = {wi ∈ Rd×1 , i = 1, 2, · · · , L}. Using the
discriminant space W and Algorithm 1, the approximation
Table 1: The recognition rate (RR) of several classifiers on
projection pc is obtained for the cth class subspace. The disLFW face database
th
tance between the test sample and the c class subspace can
be computed as
dc (w) = kw − pc k.
DPRC selects the class with the minimum distance

(23)Scene classification

The well-known 15 scene database contains 4,485 images of
(24)15 scene categories (Lazebnik, Schmid, and Ponce 2006).
c
Each image is transformed to spatial pyramid feature
T
provided by (Jiang, Lin, and Davis 2013). The followwhere w = P x.
ing experimental protocol is used (Liu and Liu 2015):
100 images per class are randomly chosen for trainDPRC vs ULDA
This section compares DPRC with a discriminant-ing and the rest images are used for testing. The Dbased
method:
Uncertain
LDA
(ULDA)KSVD (Zhang and Li 2010), LLC (Wang et al. 2010),
(Jiang, Lin, and Davis 2013),
ULDA
(Saeidi, Astudillo, and Kolossa 2016). To better explain it,LC-KSVD
(Saeidi, Astudillo, and Kolossa 2016),
LLNMC
their similarity and difference are given as follows.
(Liu and Liu 2015),
LLKNNC
(Liu and Liu 2015),
• Similarity: They both maximize the following objecLRC
(Naseem,
Togneri,
and
Bennamoun
2010), CRC
tive function max J(P ) = max JJwb , where Jb , Jw (Zhang, Yang, and Feng 2011), SRC (Wright et al. 2009),
P
P
are the within-class and between-class scatters. ThisProCRC (Cai et al. 2016), DADL (Guo et al. 2016) methods
objective function is the same to that in LDAare chosen for comparison. The average classification rate
of 10 runs is used to evaluate all methods. From the results
(Haeb-Umbach and Ney 1992).
min
dc (w), c = 1, 2, · · · , M.
∗

in Table 2, our proposed PRC and DPRC obtain the best
performance compared with other methods.
Classifier
LRC
LLC
D-KSVD
LC-KSVD
ULDA
LLKNNC
LLNMC

Accuracy
95.51
80.57
89.10
90.40
97.70
93.54
97.45

Classifier
CRC
SSRC
SRC
ProCRC
DADL
PRC
DPRC

Accuracy (%)
95.95
96.45
96.53
96.54
98.30
98.47
98.70

Table 2: The recognition rate (RR) of several classifiers on
the 15 scenes database.

ProCRC (Cai et al. 2016) and DADL (Guo et al. 2016)
methods are chosen for comparison. The experiment results
are shown in Table 4. DPRC has the better performance
than PRC and gains the best performance compared with
several popular methods.
Classifier
CRC
SSRC
SRC
DLSI
FDDL
LC-KSVD

Accuracy
75.60
76.40
75.00
75.40
76.50
70.10

Classifier
DPL
ULDA
ProCRC
DADL
PRC
DPRC

Accuracy(%)
77.40
77.60
77.40
78.00
78.50
79.10

Table 4: The recognition rate (RR) of several classifiers on
the Ucf50 action database.

Object Classification
The Caltech101 dataset (Fei-Fei, Fergus, and Perona 2007)
has 9,144 images with 102 classes. Following the common
experimental settings, we train on 5 samples per class
and the rest images are used as the testing set. In the
experiment, we utilize the 3000-dimension spatial pyramid
feature provided by (Jiang, Lin, and Davis 2013) to represent the object image. The DNNC (Zhang et al. 2006),
SVM
(Schüldt, Laptev, and Caputo 2004),
FDDL
(Yang et al. 2014),
D-KSVD
(Zhang and Li 2010),
LRC
(Naseem, Togneri, and Bennamoun 2010), CRC
(Zhang, Yang, and Feng 2011), SRC (Wright et al. 2009),
SSRC (Deng, Hu, and Guo 2013), ProCRC (Cai et al. 2016)
and ULDA (Saeidi, Astudillo, and Kolossa 2016) methods
are chosen for comparison. The experiment results are
shown in Table 3. As can be observed, DPRC gains the best
performance compared several popular methods.
Classifier
DNNC
SRC
FDDL
D-KSVD
CRC
LRC

Accuracy
46.60
48.80
49.80
49.60
44.68
47.54

Classifier
SVM
SSRC
ULDA
ProCRC
PRC
DPRC

Accuracy(%)
47.88
47.10
48.54
47.80
50.66
50.80

Table 3: The recognition rate (RR) of several classifiers on
the Caltech 101 database.

Compare with Deep Learning based Methods
The Caltech-256 dataset (Griffin, Holub, and Perona 2007)
has 30,608 object images of 256 object class, each
class has at least 80 object images. To access the performance of PRC and DPRC for object recognition
with the deep-learning-based feature, we follow Ref.
(Simon and Rodner 2015), randomly select 60 images
for training, the rest images are used for testing. Five
deep learning based methods are used for comparison.
They include NAC (Simon and Rodner 2015), CNNS (Chatfield et al. 2014), ZF (Zeiler and Fergus 2014),
CNN-M
(Chatfield et al. 2014)
and
VGG19
(Simonyan and Zisserman 2014). The experiment results are shown in Table 5. As we can see, the proposed
methods with deep feature obtain the better performance
than the deep learning based methods. The proposed DPRC
has the better performance compared to proposed PRC.
Classification Methods
CNN-S
ZF
CNN-M
VGG19+ SVM
NAC
VGG19+PRC
VGG19+DPRC

Accuracy (%)
77.6
74.2
75.5
83.9
84.1
84.9
85.3

Action Recognition

Table 5: Accuracy of several methods on the Caltech 256
object database.

The Ucf50 action dataset (Reddy and Shah 2013) has 6,680
action videos with 50 action categories, which was taken
from YouTube. For fair comparison, we follow the ref.
(Guo et al. 2016): Divide the database into five folds, use
four folds for training and one fold for testing. We use
PCA (Luo et al. 2016) to reduce the action bank features
(Sadanand and Corso 2012) to 5000 dimensions. The CRC
(Zhang, Yang, and Feng 2011), SRC (Wright et al. 2009),
DLSI
(Ramirez, Sprechmann, and Sapiro 2010),
ULDA
(Saeidi, Astudillo, and Kolossa 2016),
SSRC
(Deng, Hu, and Guo 2013) , FDDL (Yang et al. 2014), LCKSVD (Jiang, Lin, and Davis 2013), DPL (Gu et al. 2014),

In this paper, projection representation-based classification
(PRC) has been proposed for image recognition. The
PRC uses the iteratively projection procedures to obtain
a point to closely approximate the ’ideal representation’.
The objectives of PRC, SRC and LRC are similar but
PRC gains the better representation. Based on PRC, the
discriminant PRC (DPRC) is further proposed. DPRC
increase the discriminant information for PRC such that it
obtains the better performance. The experimental results

Conclusion

on several well-known databases have confirmed the good
performance of the proposed PRC and DPRC for face,
objection, scene and action recognitions. Moreover, PRC
and DPRC with deep-learning-based feature can obtain the
better performance than deep learning based methods

Acknowledgments
Thanks for the valuable suggestions of Editor and reviewers. This work was supported in part by the Macau
Science and Technology Development Fund under Grant
FDCT/016/2015/A1 and by the Research Committee at University of Macau under Grants MYRG2014-00003-FST and
MYRG2016-00123-FST.

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