Hierarchical Feature Construction for ImageClassification Using Genetic Programming
Masanori Suganuma, Daiki Tsuchiya, Shinichi Shirakawa and Tomoharu Nagao
Graduate School of Environment and Information Sciences, Yokohama National University
Yokohama, Japan
Email: suganuma-masanori-hf@ynu.jp

Abstract—In this paper, we design a hierarchical feature
construction method for image classification. Our method has
two feature construction stages: (1) feature construction by a
combination of primitive image processing filters, and (2) feature
construction by evolved filters. We verify the image classification
performance of the proposed method on the MIT urban andnature scene dataset. The experimental results show that the twostage feature construction improves the classification accuracy
compared to single stage feature construction. In addition, theproposed method outperforms several existing feature construction methods.

I. I NTRODUCTION
Image understanding is an important task in computer visionbecause of its broad range of applications, such as image classification [1] [2] and object recognition [3] [4]. Many state-ofthe-art hand-crafted feature descriptors such as the local binary
pattern (LBP) [5], histogram of oriented gradients (HOG) [6],scale-invariant feature transform (SIFT) [7], and Gabor bank[8] have shown good classification performance. Althoughthese hand-crafted descriptors can show good performance on
certain image types, they may show poor performance on othertypes. For instance, LBP works well for texture classification
tasks but may not be a good descriptor for scene classification
tasks. Hence, a domain adaptive feature construction method
is needed.
Deep learning [9] has been used to extract domain adaptive features for image classification. The greedy layer-wisetraining technique [10], which learns the feature extraction
process in a hierarchical way, has been developed in the
deep learning community. This method has demonstrated thatlayer-wise stacking of feature extractors achieves better performance compared to the single layer architecture. Recently,
the multiple-layered architecture (i.e., the deep architecture)
is setting the winning records in image classification competitions [11] [12].
Evolutionary algorithms, especially genetic programming(GP) [13], have been successfully used to generate domain
adaptive features for image classification. To the best of ourknowledge, there are two major types of studies: studies thatuse predefined features as inputs of GP [14] [15], and studies
that use raw pixel values as inputs of GP [16] [17]. In the first
type, the inputs of GP are domain specific or domain independent statistical features such as the average intensity of thec
978-1-5090-1897-0/16/$31.00 ⃝2016
IEEE

central local region and the standard deviation of all pixels of
the image. The second type uses the raw pixel intensity values
as the inputs of GP. In [16], the image transformation programis evolved by Cartesian Genetic Programming (CGP) [18] [19],and several statistical moments extracted from the transformed
image are used for inputs to the classifier. Al-Sahaf et al.
[17] have proposed a two-tier approach that uses GP to selectregions of an image and to extract pixel statistics featuresfrom the regions. This approach used simple pixel statistics
from selected regions, which also produced easily interpretable
solutions; a region encloses the eye of a face dataset, whichsuggests that the eye pixels are descriptive regions for facerecognition. Shirakawa et al. [20] have proposed a genetic
image network for image classification (GIN-IC). GIN-IC
transforms original images using simple image processing
filters and extracts statistical features from the transformed
images. The GIN-IC evolves the combination of the image
processing filters, the statistical features, and the classifier.
Hirano et al. [21] have also proposed a feature extraction
method using image transformation. These approaches showthat the image transformation based on the combination ofimage processing filters is effective for image classification
tasks.
Most GP-based works for evolving feature descriptors selectand combine a predefined set of features based on statistical
moments. In addition, they construct the feature descriptor
by a single evolutionary computation process. Similarly to a
deep learning methodology, a hierarchical architecture must
perform better than a single stage architecture in the GP-based
feature construction methods. In fact, Agapitos et al. [22] haveproposed a way to evolve a hierarchical feature construction
method with GP and shown that the hierarchical architecture
improves the classification accuracy compared to the single
stage architecture. The method has four layers: (1) filter banklayer; (2) transformation layer; (3) average pooling layer; (4)classification layer. The filter bank layer is a collection of
random-value filters that are used as kernels in convolution
operations. The transformation layer has one or two feature
extraction stages, which transforms input images into featuremaps with evolved programs by GP. In the pooling layer, anaverage operation is performed over local neighborhoods ofa feature map with a window, and the classification layer
is a regularized logistic regression classifier. In this method,
the image transformation is first performed with random-First stage of evolution
Transformation
using image
processing filters
Input image

AveragepoolingFeature maps

Best individual of thefirst stage of evolution

Second stage of evolution

Transformation
using best individual
and average pooling
Input image

Best individual

Classifier

Transformation
using evolved
programs

AveragepoolingFeature maps

Classifier

Feature maps

Fig. 1. Outline of the proposed method.

value filters. However, the image transformation based on the
combination of image processing filters must perform better
than the image transformation based on random-value filters,
as was reported in [20] [21].
In this paper, we propose a hierarchical feature construction
method based on GP and aim to improve the classification
performance by incorporation of the filter bank in the evolution. The architecture of the proposed method has two
feature construction stages: (1) a transformation of original
images into feature maps based on the combination of image
processing filters, and (2) a transformation of the feature maps
into final feature maps using evolved programs. By converting
2-D final feature maps to 1-D vectors, we obtain the final
feature descriptor. By incorporating the filter bank in theevolution, we aim to improve the classification performance.
To evaluate the classification performance of the proposed
method, we apply the proposed method on the MIT urban
and nature scene dataset.
The rest of this paper is organized as follows. Section
II describes the proposed method. Section III presents theexperimental setup and results. Section IV concludes andproposes future works.
II. H IERARCHICAL FEATURE CONSTRUCTION
The outline of the proposed method is shown in Fig. 1. The
multilayer architecture is defined as follows:
1) Filtering layer.
2) Average pooling layer.
3) Transformation layer.
4) Classification layer.
A. Filtering layer
The filtering layer extracts the discriminative features fromthe input images using image processing filters. Fig. 2 shows
the structure of the filtering layer and an example of thephenotype and the genotype. The structure of the layer is

in0

out0

0

in1

F2

F9

F3

4

6

8

1

out1

in2
2

in3

F4

F7

F2

5

7

9

out2

3
Input node
(nodeNo.)

Genotype

Transformation node
4

5

F2 0

Filter ID

2

F4 3

Input1 nodeNo.

6

1

F9 4

Output node

73

Input2 nodeNo.

F7 5

8

0

F3 5

9

6

F2 4

out0 out1 out2

7

8

7

9

: not expressed in the phenotype

Fig. 2. Example of the filtering layer and its phenotype and genotype.

a feed-forward network structure that is similar to CGP and
GIN-IC. Each node in the network has one or two connections
to previous nodes or input nodes. The types and connections ofnodes are optimized by the evolutionary algorithm. The nodes
are categorized into input nodes, transformation nodes, andoutput nodes. Four input nodes correspond to the red, green,
and blue components of the input RGB image and a grayscaled image. The transformation nodes execute the imagetransformation using the predefined image processing filters
shown in Table I, which transform one or two 2-D images toa single 2-D image of the same size. The output nodes havefeature maps from the original images through the transformation nodes. The output nodes pick up the transformed imagesby the image filters. We call the transformed output images
feature maps.
B. Average pooling layer
The average pooling layer receives n feature maps fromthe previous filtering layer. The layer is the w × w × n

TABLE I
I MAGE PROCESSING FILTERS USED IN THE FILTERING LAYER
Function name
Ave
Max
Min
Sob
Lap
Gau
LoG
Exp
Con
Gab0
Gab45
Gab90
Gab135Function
+
−
×
÷
Max
Min
Ave
log
Sqrt
×2.0
×0.5
×0.1

# Inputs
2
2
2
2
4
4
4
1
1
1
1
1

in0

C. Transformation layer
The transformation layer receives n feature maps from theaverage pooling layer and the down-sampled four original
images (red, green, and blue component of an RGB-image anda gray scale image), which is the (w/2) × (w/2) × (n + 4)
representation. The original images are used to avoid the lossof important information through the previous filtering layer
processing. In this layer, the output pixels are calculated byonly using the local pixels in the input feature maps. The
calculation process is defined by the feed-forward network
structure like CGP and optimized by the evolutionary algorithm. In other words, the inputs of the evolved program are
the pixel values of the s×s local patches in a given pixel. The
d output images, the 1 × 1 × d representation, are obtained by
the processing in this layer, i.e., the n + 4 feature maps aretransformed into d feature maps, which is a (w/2)×(w/2)×d
representation. The mathematical functions displayed in Table
II are used as the function set for the evolved programs. Fig.
3 shows an example of the transformation layer.
D. Classifier layer
The classifier layer receives d feature maps, which is a h ×
h × d representation. By converting 2-D feature maps to 1D vectors, we obtain the final feature descriptor, which has
h × h × d features for classification. We use a linear support
vector machine (SVM) as the classifier. The cost parameter c
is set to 1. For the SVM solver, we use the implementation ofmulti-core LIBLINEAR (version 2.1-4) [23].

F2

F9

F4

F7

F3

F5

F1

F5

in1
in2

out0

in3

in25

out1

in26

Input feature maps

representation, which means that the w × w-sized n featuremaps are used. In the average pooling layer, an average
operation is performed over the local neighborhoods of the
w×w feature map with 2×2 window. As a result, the w×w×n
feature maps are reduced into (w/2)×(w/2)×n feature maps.

Description
Add two inputs
Subtract two inputs
Multiply two inputs
Divide two inputs
The largest value of inputs
The smallest value of inputs
The average value of inputs
Take the natural logarithm for a input
Extract a square root of a input
Multiply a input by 2.0
Multiply a input by 0.5
Multiply a input by 0.1

…

Add
Sub
Mul
Div
Abs

Description
Averaging filter with 3 × 3, 5 × 5 window
Maximum filter with 3 × 3, 5 × 5 window
Minimum filter with 3 × 3, 5 × 5 window
Sobel filter with 3 × 3, 5 × 5 window
Laplacian filter with 3 × 3, 5 × 5 window
Gaussian smooth filter with 3 × 3, 5 × 5 window
Laplacian of gaussian filter with 3 × 3, 5 × 5 window
Expansion processing
Contraction processing
Gabor filter with 7 × 7, 11 × 11 window
with orientation of 0 degree
Gabor filter with 7 × 7, 11 × 11 window
with orientation of 45 degree
Gabor filter with 7 × 7, 11 × 11 window
with orientation of 90 degree
Gabor filter with 7 × 7, 11 × 11 window
with orientation of 135 degree
Add input two images pixel by pixel
Subtract input two images pixel by pixel
Multiply input two images pixel by pixel
Divide input two images pixel by pixel
Absolute subtraction of input two images pixel by pixel

TABLE IIF UNCTION SET USED IN THE TRANSFORMATION LAYER

Transformed feature maps

Fig. 3. Example of the transformation layer that transforms 8 × 8 × 3 featuremaps into 8 × 8 × 2 feature maps using the evolved program. The inputs are
the 3 × 3 × 3 pixel intensity values surrounding a target pixel.

E. Training protocol
The training procedure in the proposed method consistsof two-stage evolutionary optimization. In the first stage ofevolution, we evolve the filtering layer F using the architectureof I → F → P → C, where I is the input image, F
is the filtering layer, P is the average pooling layer, and C
is the classification layer. The filtering layer generates thew × w-sized n feature maps, where w is the size of theoriginal image. The average layer reduces the resolution of
the representation to (w/2) × (w/2)-sized n feature maps,
and the feature maps are used for classification. We employ
the classification accuracy for validation images as the fitnessof each individual in the first stage of evolution. At the end of
the first evolution stage, we obtain the best filter combination
Fbest that generates the w × w-sized n feature maps.
In the second stage of evolution, we evolve the transformation layer T using the architecture of Fbest → P →T → P → C, where Fbest is the feature map generated in
the first evolution stage, T is the transformation layer, P is
the average pooling layer, and C is the classification layer.
The transformation layer receives the down-sampled evolved
feature maps Fbest (consisting of n feature maps) and thedown-sampled four original images. The transformation layer
generates the (w/2) × (w/2)-sized d feature maps, and theaverage layer reduces the resolution of the representation to(w/4) × (w/4)-sized d feature maps, which are used forclassification. We also employ the classification accuracy forvalidation images as the fitness similar to the first stage

the same genetic operators, the uniform crossover and themutation for each gene. We implemented the filtering layer,
the transformation layer, and the average pooling layer of our
proposed method on the graphic processing unit (GPU) using
the compute unified device architecture (CUDA) 2 , and hence,each pixel is independently processed. We run our experiments
on a machine with 3GHz CPU, 32GB RAM, and NVIDIA
GeForce GTX TITAN X GPU.
For comparison, we tested the five following methods:
Fig. 4. Sample images from the MIT urban and nature scene dataset.
TABLE III
PARAMETER SETTINGS FOR THE PROPOSED METHODParameter
Num. of generations (Filtering layer)
Num. of generations (Transformation layer)
Generation alternation model
Population size
Children size
Crossover rate
Ratio for uniform crossover
Mutation rate

Value
3000
4000
MGG [24]
50
10
1.0
0.8
0.1

TABLE IVPARAMETER SETTING FOR GPIP
Parameter
Num. of generations
Generation alternation model
Population size
Children size (genotype 1)
Children size (genotype 2)
Crossover rate
Mutation rate

Value
500
MGG [24]
50
50
10
1.0
0.05

of evolution. In this way, we obtain the best program thatgenerates the (w/2) × (w/2)-sized d feature maps.
III. E XPERIMENT AND RESULTS
A. Data sets
We test the proposed method with the MIT urban and naturescene dataset1 . This dataset has eight categories (coast &beach, forest, highway, city center, mountain, open country,
street, and tall building), and all of the images are 256 × 256
pixels. In this paper, each image in the dataset is resized fromits original size to 128 × 128 pixels by linear interpolation,and then, we randomly choose 50 images from each category
as the learning set for training SVM, 50 images from eachcategory as the evaluation set for evaluating the individuals in
the evolutionary optimization, and 1, 488 images as the test
set. Some image examples of this dataset are shown in Fig. 4.
B. Experiment setup
Parameter setting for the proposed method is shown in Table
III. Both the filtering layer and the transformation layer use
1 http://cvcl.mit.edu/database.htm, Urban and Natural Scene Categories.

1) Single transformation (Proposal 1). This architecture is
I → F → P → C. In the filter layer, we adopt the
CGP-based method with 40 filtering nodes and 8 output
nodes for evolving the filtering network, i.e., the filtering
layer generates 8 feature maps. The average poolinglayer performs an average operation with 2 × 2 window.
2) Double transformation (Proposal 2). This architecture
is Fbest → P → T → P → C. The filtering layer
Fbest is the one obtained by the method of 1) single
transformation. The transformation layer uses 3 × 3 × 12
patches as the input and generates 16 feature maps as theoutputs. The number 12 indicates that the transformation
layer receives 8 feature maps obtained by the filtering
layer and down-sampled 4 original images. The numberof the function nodes is 50. The average pooling layer
performs the average operation with 2 × 2 window.
3) A GP method that transforms feature maps generated
by random-valued filter bank into the final feature maps
using an evolved program (SST) [22]. This architectureis I → Frand → P → T → P → C. The random
filter bank Frand is composed of 50 filters with 3 × 3
receptive fields. We generated 10 filters from each of
U (−1.0, 1.0), U (−5.0, 5.0), D(1, 5), N (1.0), N (5.0),
where U (a, b) denotes the uniform sampling of real valued numbers within the [a, b] interval, D(a, b) denotes
uniform sampling of integer numbers [a, b] interval, andN (a) denotes sampling from a normal distribution withzero mean and the standard deviation a. As a result,
Frand generates 50 feature maps. The transformation
layer uses 3 × 3 × 50 pixels as the input and generates
16 outputs, i.e., the transformation layer generates 16
feature maps. The architecture of the transformation
layer is identical to that in the proposed method. The
number of the function nodes is 200.
4) A method that transforms an original image using thefilter bank and then extracts the statistical moments fromthe transformed images [21] (we call this method GPIP
in this paper) . The filter bank consists of 14 well-known
image processing filters, such as the laplacian filter, andthe statistical moments consist of simple 17 statisticalvalues, such as standard deviation and mean value, see[21] for details. The parameter setting for this method
is shown in Table IV. We set the number of generations
to 500 since the fitness transition was converged ade2 https://developer.nvidia.com/cuda-zone, CUDA Zone

TABLE V
C OMPARISON OF CLASSIFICATION ACCURACY.

Proposal 1
Proposal 2
SST [22]
GPIP [21]Gabor bank [8]

Best
0.786
0.831
0.681
0.771
0.764

Average
0.759
0.810
0.667
0.718
0.764

Original image(Tall building)

TABLE VI
C ONFUSION MATRIX OF THE PROPOSED DOUBLE TRANSFORMATIONMETHOD ON THE MIT URBAN AND NATURE SCENE DATASET.

(c) Coast(f) Forest(h) Highway(cc)City center(m) Mountain(o) Open country(s) Street(f) Tall building

(c)
177
0
7
0
15
13
0
0

(f)
1
154
0
2
6
17
0
0

(h)
9
0
73
1
7
7
1
0

(cc)
0
0
13
152
3
2
0
0

(m)
10
9
6
1
156
23
0
1

(o)
13
14
11
2
37
197
0
0

(s)
0
0
0
0
0
1
125
2

(f)
0
1
0
0
0
0
16
203

quately. In this method, we used a gaussian kernel withparameter γ = 0.6 as the kernel function of SVM.
5) Gabor filtering with 8 orientation at 4 different scales,
and the output of each filter is averaged on a 4 × 4 grid
to form a feature vector [8].
In order to compare the classification errors by the eachmethod on the test set, we employ 10-fold cross-validation.
The averaged 10 SVM test-fold accuracies are computed forthe comparison of each method.
C. Results
Table V shows the classification accuracies of each method
in five evolutionary runs. The results suggest that the proposed
method, i.e., double transformation (Proposal 2), outperforms
the rest of the methods. Comparing the double transformation(Proposal 2) and the SST, we observe that the classification
accuracy of the double transformation is significantly better
than that of the SST (from 0.681 to 0.831). This means thatincorporating the evolved filter bank can be beneficial for
improving the classification performance as compared to therandom-value filters. Fig. 5 shows examples of a tall building
image and its transformed images by the filtering layer ofthe proposed method. From these transformed images, thedistinctive features such as vertical edges seen in the tallbuilding are extracted by the filtering layer, which seems tobe beneficial for the classification. The double transformation
method shows better classification accuracy than that of thesingle transformation method and the GPIP, which indicatesthat two-stage transformation can contribute to constructing
the discriminative descriptors. In addition, the descriptor constructed by the proposed method outperforms the hand-craftedfeatures (the Gabor bank).
We tested a Wilcoxon rank sum test for comparison of
Proposal 2 and other methods. We set the significance level
at 5%. The p-value for Proposal 2 and Proposal 1 is 0.024,

Transformed image 1

Transformed image 2

Fig. 5. Examples of an original image and its transformed images by thefiltering layer.

which means that Proposal 2 is statistically better regarding
accuracy than Proposal 1. The p-value for Proposal 2 and the
SST is 0.0079 and the p-value for Proposal 2 and the GPIP is
0.036, which means that Proposal 2 outperforms the SST and
the GPIP.
Table VI shows the confusion matrix of the classification
result by the proposed double transformation method for thetest images. From this confusion matrix, we can see that theevolved descriptor can successfully classify City center, Street
and Tall building, whereas it can not classify Highway andMountain well.
The time costs of Proposal 1 and Proposal 2 are around11.9 hrs and 10.8 hrs, respectively.
IV. C ONCLUSION
In this paper, we have presented a hierarchical feature
construction method for image classification. The proposed
method has two-stage feature construction: (1) feature construction by a combination of primitive image processing
filters, and (2) feature construction by evolved filters. We
have evaluated our method on the MIT urban and naturescene dataset, and outperformed several GP methods and handcrafted descriptor. Experimental results showed that incorporating the filter bank in the evolution and the two-stage
evolution can be beneficial to the classification performance.
In our future work, we will evaluate our method with a morechallenging dataset.
ACKNOWLEDGMENT
This work was supported by JSPS Grant-in-Aid for Scientific Research (B) Grant Number 26280056.
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