Information Ranking Using Optimum-Path Forest
Nathalia Q. Ascenção, Luis C. S. Afonso, Danilo Colombo, Luciano Oliveira, João P. Papa
IInformation Ranking Using Optimum-Path Forest
Nathalia Q. Ascenc¸ ˜ao ∗ Luis C. S. Afonso † , Danilo Colombo ‡ , Luciano Oliveira § and Jo˜ao P. Papa ∗∗ UNESP - Univ. Estadual Paulista, School of Sciences, Bauru, BrazilEmail: { nathalia.ascencao,joao.papa } @unesp.br † UFSCar - Federal University of S˜ao Carlos, Department of Computing, S˜ao Carlos, BrazilEmail: [email protected] ‡ Cenpes, Petr´oleo Brasileiro S.A.,Email: [email protected] § UFBA - Federal University of Bahia, Salvador, BrazilEmail: [email protected]
Abstract —The task of learning to rank has been widely studiedby the machine learning community, mainly due to its use andgreat importance in information retrieval, data mining, andnatural language processing. Therefore, ranking accurately andlearning to rank are crucial tasks. Context-Based InformationRetrieval systems have been of great importance to reduce theeffort of finding relevant data. Such systems have evolved by usingmachine learning techniques to improve their results, but theyare mainly dependent on user feedback. Although informationretrieval has been addressed in different works along withclassifiers based on Optimum-Path Forest (OPF), these have sofar not been applied to the learning to rank task. Therefore, themain contribution of this work is to evaluate classifiers basedon Optimum-Path Forest, in such a context. Experiments wereperformed considering the image retrieval and ranking scenarios,and the performance of OPF-based approaches was comparedto the well-known SVM-Rank pairwise technique and a baselinebased on distance calculation. The experiments showed compet-itive results concerning precision and outperformed traditionaltechniques in terms of computational load.
I. I
NTRODUCTION
Information Retrieval stands for a field of knowledge thataims to return relevant data given an input query, which canbe a multimedia content such as an image, audio, video,or a text-based information [1]. Nowadays, the amount ofdata that has been generated has increased considerably. E-mails and multimedia data are interchanged among millionsof users daily, thus contributing to spreading communicationand increasing the workload in Internet traffic. Therefore, it ishighly desired to handle such amount of data efficiently, i.e.,to store and further retrieve the relevant information only.Images have a crucial role in several fields of research, suchas medicine, advertising, education, and entertainment, amongothers [2]. Content-based Image Retrieval (CBIR) systemscome to reduce the costs of manually retrieving relevant datasince it is a laborious and very much time-consuming task.CBIR-driven systems aim at retrieving relevant images from adataset based on features such as color, shape, and texture, andhave been assisting in a broad range of applications [3]–[7].
The authors are grateful to Petrobras grant
However, CBIR systems face the problem of being prettymuch user-dependent, which means that it is not straight-forward to learn models that can generalize well for everykind of input query. Such techniques make use of relevancefeedback from the user to overcome such dependence. Theuser indicates the images that are relevant (and non-relevant) totheir needs, and the process is repeated until the retrieved datais satisfactory [8]–[11]. Hence, ranking accurately is crucialfor CBIR systems.In this sense, machine learning techniques have been ap-plied in the context of learning to rank. Younus et al. [12]used image features such as color histogram, color moment,co-occurrence matrices, and wavelet moment for measuringthe similarity among samples. Then, they applied k -meanswith the Particle Swarm Optimization algorithm for retrievingimages. Irtaza et al. [13] proposed a method that uses anin-depth texture analysis, a learning scheme based on k -nearest neighbors and a neural network to the retrieval task. ABayesian network based on feedback relevance was appliedin [14] on medical image retrieval using feature analysissuch as color, texture, and shape jointly with some visualdescriptors.In [15], an artificial neural network along with SupportVector Machine (SVM) was employed on face image retrievaland recognition. Support Vector Machine also has been appliedin content-based image retrieving [16]–[24] to reduce thesemantic gap problem by enhancing the image classificationprocess; as an active classifier combining classification withactive learning based on feedback relevance; together withvisual descriptors to improve retrieval performance, and also indeep learning as proposed in [25], where a framework basedon Convolutional Neural Networks and SVM was used onfeature extraction, classification, and image retrieval.A few years ago, the Optimum-Path Forest (OPF) frame-work was proposed to handle the problem of pattern classifi-cation as a graph partitioning task. The framework comprisessupervised [26]–[28], semi-supervised [29], and unsupervisedversions [30]. Such approaches work by mapping the classifi-cation problem as a graph partition task, where the nodes standfor the samples that are represented by their correspondingfeature vectors and are connected through some adjacency a r X i v : . [ c s . A I] F e b elation that has been defined previously. In a nutshell, nodesare classified based on a competitive process among keysamples that try to conquer others offering them optimum-path costs. The key samples, also called prototypes, are theones that best represent different classes and are chosen basedon a specific heuristic.Although OPF has been used in several areas, only afew works have applied such a technique to the context ofimage retrieval. Tavares et al. [8] proposed two approaches forcontent-based image retrieval based on OPF, where the mainidea is to ask the user to mark some relevant images whichare further used as prototypes for a new training step. Lateron, the remaining data is classified and sorted in such a waythat contains only the relevant images, which are presented tothe user once more. This process is repeated until the user issatisfied.Dhawale and Joglekar [31] compared OPF against otherclassifiers for image retrieval purposes, and concluded thatit could be much faster than widely used techniques suchas Artificial Neural Networks, Support Vector Machines, andthe k -Nearest Neighbours ( k -NN) classifier. However, thoseworks are based on user feedback only. Therefore, the maincontribution of our work is to introduce the OPF-Ranking(OPF-R), which is an OPF-based approach that can rankimages automatically, i.e., without user intervention. The OPF-R was evaluated under three well-known image datasets wherethere were considered two relevance metrics. The performancewas compared against a baseline technique and the SVM-Rank, in which OPF-R showed competitive results and lowerranking computing times.The remainder of this paper is organized as follows. Sec-tion II reviews the theoretical background concerning OPF-based classifiers. The proposed approach and methodologyare presented in Sections III and IV, respectively. Section Vdiscusses the experiments and results. Finally, Section VIstates conclusions and future works.II. O PTIMUM -P ATH F OREST
The Optimum-Path Forest is a framework for the designof graph-based classifiers. Let Z be a labeled dataset, suchthat Z = Z ∪ Z , in which Z and Z are training andtesting sets, respectively. OPF encodes each sample u ∈ Z asa graph node, and the graph is initially designed based on apredefined adjacency relation A with edges weighted by thedistance between the feature vectors of their connecting nodes.The general OPF training algorithm is divided into twoparts: (i) to find a set of samples called prototypes, and(ii) to compute optimum-path trees (OPTs) rooted at them.The prototypes are the most representative samples from eachclass. The definition of most representative sample , as wellas the method for computing prototypes, are different foreach variant of OPF, and they are explained in the followingsections.Let P be the set of prototypes such that P ⊂ Z . The OPTsare built through a competitive process in which samples try to“conquer” each other by offering costs. The competition starts at the prototypes that offer their best cost to the remainingtraining samples (i.e., non-prototype samples). The costs aredefined by a path-cost function, which is also different foreach OPF variant.Let p ∈ P and s ∈ Z \P be some prototype and non-prototype samples, respectively. Suppose that sample s isconquered by a sample p that offers to it the best cost. Uponsuch an assumption, p assigns its label to s , and s is added totree rooted at p . Notice that prototypes cannot be conquered,and a class is represented by at least one tree. The outcome ofthe training step is a set of optimum-path trees (i.e., optimum-path forest) G tr = ( Z , A ) .Concerning the classification step, a node v ∈ Z isconnected to G tr according to A (i.e., if A is a k -NN adjacencyrelation, then v is first connected to the k -nearest samples from G tr ). Besides, the sample u ∈ Z that offers the best cost to v assigns its label to it. This work makes use of two variants ofthe supervised version whose working mechanisms are furtherexplained. A. OPF with Complete Graph (CG-OPF)
This supervised variant was introduced by Papa et al. [26]and implements the complete graph as the adjacency relation(i.e., all nodes are connected). As aforementioned, the first stepin the training phase is to find the set of prototypes P , whichis computed through the minimum spanning tree (MST) over G tr . The prototype nodes are the samples belonging to theintersection region among classes since they are more likelyto be misclassified.The following step is the competition process, which is car-ried out using Equations 1 and 2 that stand for the initializationand propagation of costs, respectively: f max ( (cid:104) p (cid:105) ) = (cid:26) if p ∈ P, + ∞ otherwise (1)and f max ( π p · (cid:104) p , v (cid:105) ) = max { f max ( π p ) , d ( p , v ) } , (2)in which f is a real-valued path-cost function, π p ·(cid:104) p, v (cid:105) standsfor the concatenation of path π p (i.e., a sequence of adjacentnodes starting from any node and with terminus at node p )with an edge (cid:104) p, v (cid:105) , and d denotes a distance function.The conquering of samples happens during the propagationof costs where prototypes offer their optimum-path costs toother samples. The sample v is conquered by sample p thatminimizes (2). The classification is based on the connectingforce between samples from Z and testing samples from Z ,and works similarly to the training phase. Each t ∈ Z isconnected to G tr obbeying A . Then, it is evaluated the sample v ∗ ∈ Z that satisfies Equation 3: C ( t ) = arg min max v ∈Z { C ( v ) , d ( v , t ) } , (3)where C is the cost of the sample. Figure 1 depicts the trainingand classification processes. .21.0 0.80.8 0.30.60.90.7 0.50.71.00.70.8 0.50.4 0.2 0.30.50.50.4 0.0 0.50.50.4(0.0, 2)(0.4, 1) (0.5, 1)(0.0, 1) (0.3, 2)(0.5, 2)0.9 0.8 0.40.50.30.6 (?, ?) (0.0, 2)(0.4, 1) (0.5, 1)(0.0, 1) (0.3, 2)(0.5, 2)(0.4, 2) (a) (b) (c)(d) (e) Fig. 1. OPF with complete graph. Training phase: (a) a two-class traininggraph with weighted arcs, (b) an MST with prototypes highlighted, and (c)optimum-path forest generated during the training phase with costs over thenodes (notice the prototypes have zero cost). Classification phase: (d) samplepenthagon is connected to all training nodes, and (e) penthagon is conqueredby a sample from the class “square”, and it receives the “square” label.
B. OPF with k-nearest neighbors Graph ( k -NN-OPF) The OPF with k-nearest neighbors Graph was proposedby Papa et al. [32]–[34], whose main differences to CG-OPF are the adjancency relation, the weighting of nodes, andhow prototypes are computed. The k -NN-OPF employs the k -nearest neighbors as the adjacency relation, and the nodes arenow weighted by a probability density function. The methodfor building the set of prototypes must be changed sincea k -NN adjacency relation does not guarantee a connectedgraph. Instead, the set P is computed based on region den-sity values where samples of higher density are selected asprototypes. Such approach is similar to selecting the centroidsof clusters [35]. Hence, k -NN-OPF is understood as a “dualversion” of CG-OPF (minimization problem) since it aims atmaximizing the cost of each sample according to Equation 4: max f ( π u ) , ∀ u ∈ Z . (4)Besides, samples u ∈ Z are weighted by a function ρ ( u ) that computes the probability density value as follows: ρ ( u ) = 1 √ πσ k (cid:88) ∀ v ∈A k ( u ) exp (cid:18) − d ( u , v )2 σ (cid:19) , (5)where A k ( u ) stands for the k -nearest neighbors of sample u , d max = max { d ( u, v ) ∈ G tr } , and σ = d max / . Aftercomputing the density values for all training samples, k -NN-OPF starts the competition process through the path-costfunction f min defined as follows: f min ( (cid:104) v (cid:105) ) = (cid:26) ρ ( v ) if v ∈ P ρ ( v ) − otherwise f min ( π u · ( u , v )) = min { f min ( π u ) , ρ ( v ) } . (6) The upper formulation stands for the proper initialization ofthe training nodes. The term ρ ( v ) − must be used to avoidover clustering since a plateau of densities may occur.The competition itself stands for the propagation of costsamong samples. Since the prototype holds the higher cost ofits optimum-path tree, the idea is to conquer samples withlower costs. Finally, the sample that maximizes f min for agiven sample v will be the one to conquer it.The classification of samples in Z is performed similarly tothe conquering process. The first step computes the k -nearestneighbors from Z to a testing sample t ∈ Z . Finally, it isverified which node s ∗ ∈ Z satisfies the equation below: C ( t ) = arg max v ∈Z min { C ( v ) , ρ ( t ) } . (7)Figure 2 depicts the classification process. (a) (b) (2, 1)(3, 1)(2, 1) (1, 1) (2, 2) (2, 2)(3, 2) (1, 2)(5, 2) 0.2 0.40.3 (4, ?)(2, 1)(3, 1)(2, 1) (1, 1) (2, 2) (2, 2)(3, 2) (1, 2)(5, 2) (c) Fig. 2. OPF with k -NN graph classification: (a) optimum-path forestgenerated during the training phase with the pair (cost, label) over the nodes,(b) sample penthagon is connected to its k -nearest training nodes, and (c)penthagon is conquered by a sample from the class “circle”, and it receivesthe “circle” label. III. P
ROPOSED A PPROACH
The idea of ranking in CBIR is to retrieve the most similarimages for a given query. However, OPF does not rely onany similarity metric solely. Instead, the ranking problem isdesigned as a connectivity problem, where a testing sample isassigned to a class based on the strength of its connection toeach sample in G tr , where the path cost defines the strengthlevel (i.e., the better the path-cost, the stronger is the strength).Therefore, (OPF-R) maps the similarity as the strength of thequery to the samples from the trained model (i.e., the strongeris the connection between a query and a model sample, thehigher is their similarity).After training OPF-R, a given query q is further connectedto G tr according to the adjacency relation A , i.e., if A is thecomplete graph type, then q is connected to all samples in A ; if A is the k -NN graph type, then q is connected to the k -nearest samples in A . Notice that the training is perfomedas described in Section II.he next step is to perform the competition process, simi-larly to the classification process. The difference is that bothCG-OPF and k -NN-OPF store all path-costs offered to q . Inthe end, the path-costs are sorted, and the r best costs comprisethe ranking list. Figure 3 depicts the ranking approach throughOPF-R with a complete graph (CG-OPF-R) considering theTop-5 results. One interesting point is that OPF ranks samplesnatively, i.e., there is no need to perform complex changes inthe original classifier to support both ranking and retrieval. (0.0, 2)(0.4, 1) (0.5, 1)(0.0, 1) (0.3, 2)(0.5, 2)0.9 0.8 0.40.50.30.6 (?, ?)queryAB C D EF Top-5Sample Relevance ClassE 0.4C 0.5F 0.5B 0.6D 0.8 Fig. 3. Ranking by OPF. The query sample is connected to the training setaccording and costs are further computed. Samples of lower cost are the moststrongly connected ones.
IV. M
ETHODOLOGY
This section presents the data and techniques employed tovalidate the proposed approach.
A. Datasets
The proposed approach was evaluated in three datasets withdetailed information presented in Table I. Notice that Brodatzdataset has originally a total of images, and was laterexpanded to , images by dividing the original ones into parts. This strategy was applied to increase the number ofsamples per class. TABLE ID
ATASET INFORMATION . dataset type Brodatz texture ,
792 112 16
Caltech101 objects/scenes ,
677 101 40 − MPEG-7 shape ,
500 70 20
B. Features
The experiments considered a total of seven features. How-ever, they are not applied to all datasets since their nature isnot suitable for all cases. For instance, Brodatz is a datasetcharacterized by texture images. Therefore, only Local BinaryPattern (LBP) [36] and Statistical Analysis of Structural Infor-mation (SASI) [37] features are computed. Table II presentsthe seven extracted features.
C. Experimental Setup
The experiments were carried out using three configurationsof training and testing set (querying set) sizes: (i) samples for training and samples for classification, (ii) samples for training and samples for classification,and (iii) samples for training and samples for
TABLE IIF
EATURE INFORMATION . feature type dataset Auto-color correlation (ACC) [38] color Caltech101Border/Interior Pixel Classification (BIC) [39] color Caltech101Color Coherence Vectors (CCV) [40] color Caltech101Local Color Histogram (LCH) [41] color Caltech101Local Binary Pattern (LBP) [36] texture BrodatzStatistical Analysis of Structural Information (SASI) [37] texture BrodatzSpherical Pyramid-Technique (SPYTEC) [42] shape MPEG-7 classification. The sets were randomly generated. Table IIIpresents the parameter values used in this work . TABLE IIIP
ARAMETERS . technique parameters CG-OPF – k -NN-OPF k max = 20 SVM-Rank c = 0 . , l = 0 , e = 0 . The remaining parameters of SVM-Rank were set in theirdefault values as defined in [43].
D. Relevance Metric
The accuracy is measured by two metrics as described: • Normalized Discounted Cumulative Gain (NDCG): TheNDCG computes the cumulative gain (i.e., the sum ofthe relevance score of the candidate samples) consideringthe ordering in the ranking. The metric is based onthe Discounted Cumulative Gain (DCG) that reduces thescore of relevant data in a logarithmical proportional totheir position in the ranking, Equation 8. The lower theposition, the higher is the penalization:
DCG r = r (cid:88) i =1 rel i − ( i + 1) , (8)where rel i is the graded relevance of the result at position i . Thus, NDCG is defined as follows: N DCG r = DCG r DCG r ideal , (9)where DCG r ideal stands for the case where the data issorted by their relevance score. • Mean Average Precision (MAP): The MAP is commonlyused to evaluate ranking methods applied to binary scoreproblems and computes the mean average precision foreach query as follows:
M AP = 1 n n (cid:88) q =1 AP q , (10)where n is the number of queries and AP is the averageprecision of a single query and defined as: AP = (cid:80) nr =1 ( P @ r × I ( rel r == 1)) (cid:80) nr =1 I ( rel r == 1) , (11) These parameters were obtained empirically. eing P@r the precision: P @ r = 1 r r (cid:88) i =1 ( rel r == 1) , (12)which is the normalized number of relevant candidates inthe first r positions.Both metrics use the absolute relevance (i.e., a label of or is assigned to the candidate based on its relevance). Therelevance of a candidate is defined by comparing its label to thequery after the ranking. The candidate is assigned a relevance if it does not have the same label as the query, or if thecandidate and query share the same label.V. E XPERIMENTAL R ESULTS
The experimental results are organized by datasets withtables presenting the NDGC and MAP values for each scenario(i.e., dataset × training/testing sets configuration × descrip-tor). Besides evaluating OPF-Rank in a great variety of cases,we also compared its performance against a distance-basedtechnique (Distance) and the well-known SVM-Rank consid-ering the top- , top- , and top- rankings. Notice that theDistance technique computes the ranking based on the distancefunction suggested by the author of the descriptor (i.e., eachdescriptor has its most appropriate distance function). The bestresults (i.e., for each configuration, descriptor and top-r) areshown in bold, according to the Wilcoxon signed-rank test withthe significance of . . Besides, a hold-out approach with runs with randomly generated training and testing sets wasapplied for validation purposes. A. Brodatz
The experimental results are presented in Table IV. Onecan observe that the best results achieved by CG-OPF and k -NN-OPF were using the SASI descriptor regardless of thetraining/testing sets configuration. Concerning the comparisonbetween the OPF-based approaches, CG-OPF obtained a betterperformance over k -NN-OPF in the × configuration,whereas the performance was very close in the remainingconfigurations. Among all techniques, SVM-Rank presentedthe best overall results. B. Caltech101
The results are presented in Table V, in which LCH andBIC provided the best results. CG-OPF showed better rele-vance values over k -NN-OPF in all considered configurations.Except for Distance, all techniques are benefited by increasingthe number of training samples. The best overall results wereachieved by SVM-Rank. C. MPEG-7
The results are presented in Table VI. Once again, CG-OPFoutperformed k -NN-OPF in all configurations. An interestingbehavior is that changing the configuration × to × provided a very small increase in the results,whereas the configuration × caused a drop in theresults. In this dataset, CG-OPF showed competitive resultswhen compared to SVM-Rank. TABLE IVR
ESULTS CONCERNING B RODATZ DATASET . × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance LBP
SASI 0.392 0.260 0.393 0.170 0.396 0.140CG-OPF LBP k -NN-OPF LBP 0.328 0.135 0.345 0.106 0.349 0.087SASI 0.378 0.189 0.381 0.146 0.383 0.120SVM-Rank LBP 0.362 0.145 × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance LBP 0.368 0.202 0.378 0.164 0.386 0.140SASI 0.406 0.289 0.411 0.236 0.411 0.201CG-OPF LBP 0.391 0.214 0.402 0.174 0.410 0.148SASI 0.428 0.222 0.431 0.176 0.432 0.148 k -NN-OPF LBP 0.361 0.197 0.370 0.160 0.378 0.137SASI 0.432 0.308 0.435 0.251 0.437 0.212SVM-Rank LBP SASI × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance LBP 0.341 0.145 0.359 0.118 0.364 0.099SASI 0.406 0.289 0.411 0.236 0.411 0.201CG-OPF LBP 0.410 0.255 0.418 0.210 0.423 0.179SASI 0.402 0.209 0.405 0.166 0.407 0.139 k -NN-OPF LBP 0.378 0.235 0.385 0.194 0.389 0.165SASI 0.403 0.334 0.403 0.274 0.406 0.236SVM-Rank LBP SASI
D. Discussion
In this section, we present a discussion concerning theresults obtained in the experiments. Besides, we also providedan additional study concerning the computational load aswell. Tables VII, VIII, and IX present the results concerningBrodatz, Caltech101, and MPEG-7 datasets, respectively. Theresults stand for the average (seconds) ranking time over runs. As one can observe, OPF-based approaches are prettymuch faster than Distance and SVM-Rank techniques (e.g., . to . times faster). However, SVM-Rank achieved thebest results in most cases but with up of superiority overOPF-based techniques.If one takes into account the trade-off between rankingrelevance and retrieving time, OPF-based approaches figureas the most prominent ones, since they achieved results closeto the SVM-Rank, but faster. Another point that should behighlighted is that the proposed approach was little modifiedto handle ranking problems; meanwhile, SVM-Rank neededa considerable adaptation in its working mechanism. In otherothers, we expect to achieve better results with a more in-depthchange in OPF-based competition process to better adapt toranking-driven applications.Also, we are not taking into account the training time,which is supposed to be even faster concerning OPF-basedapproaches. Particular attention is given to CG-OPF, which ABLE VR
ESULTS CONCERNING C ALTECH
DATASET . × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance ACC 0.252
BIC 0.264
CCV 0.242
LCH 0.269 0.162 0.289 0.151 0.302 0.142CG-OPF ACC 0.250 0.141 0.274 0.132 0.286 0.125BIC 0.259 0.151 k -NN-OPF ACC 0.232 0.132 0.254 0.124 0.266 0.116BIC 0.241 0.142 0.259 0.133 0.273 0.126CCV 0.222 0.118 0.242 0.111 0.257 0.105LCH 0.246 0.146 0.262 0.136 0.277 0.128SVM-Rank ACC × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance ACC 0.283 0.182 0.301 0.174 0.314
BIC 0.295
CCV 0.273 0.171 0.294 0.163 0.309
LCH 0.300 0.193 0.320 0.182 0.333 0.173CG-OPF ACC 0.281 0.172 0.305 0.163 0.317 0.157BIC 0.290 0.182 0.310 0.173 0.325
CCV 0.269 0.156 0.291 0.149 0.307 0.143LCH 0.295 0.187 0.313 0.175 0.330 0.172 k -NN-OPF ACC 0.263 0.163 0.285 0.155 0.297 0.147BIC 0.272 0.173 0.290 0.164 0.304 0.157CCV 0.253 0.149 0.273 0.142 0.287 0.137LCH 0.277 0.177 0.293 0.167 0.310 0.159SVM-Rank ACC BIC
CCV
LCH × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance ACC 0.340 0.239 0.358 0.231 0.371 0.224BIC 0.352 0.241 0.369 0.243 0.382 0.237CCV 0.330 0.228 0.351 0.221 0.366 0.214LCH 0.357 0.250 0.377 0.239 0.390 0.230CG-OPF ACC 0.338 0.229 0.362 0.220 0.374 0.213BIC 0.347 0.239 0.367 0.230 0.382 0.223CCV 0.326 0.213 0.348 0.206 0.364 0.201LCH 0.352 k -NN-OPF ACC 0.321 0.220 0.342 0.212 0.354 0.204BIC 0.329 0.230 0.347 0.221 0.361 0.216CCV 0.310 0.206 0.330 0.199 0.338 0.193LCH 0.336 0.235 0.351 0.224 0.367 0.216SVM-Rank ACC BIC
CCV
LCH does not comprise any parameter beforehand, thus turning outto be easier to be set up and with no need for a fine-tuningstep. Additionally, although k -NN-OPF figures one parameter,its training time is faster than SVM-Rank, in which the numberof parameters depends on the kernel function used.Based on the above assumptions, we conclude that OPF-based classifiers are suitable for ranking purposes, even withits native version. We expect that better results may comewith more in-depth modifications that shall affect little theefficiency of the methods. TABLE VIR
ESULTS CONCERNING
MPEG-7
DATASET . × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance SPYTEC 0.061 0.030 0.071 0.027 0.074 0.026CG-OPF k -NN-OPF 0.066 0.031 0.072 0.028 0.082 0.027 SVM-Rank × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance SPYTEC 0.087 0.051 0.093 0.051 0.108 0.052CG-OPF 0.094 0.054 0.098 0.053 0.113 0.055 k -NN-OPF 0.086 0.050 0.093 0.050 0.107 0.052 SVM-Rank × technique descriptor top-r10 15 20 NDGC MAP NDGC MAP NDGC MAPDistance SPYTEC 0.134 0.097 0.140 0.095 0.147 0.095CG-OPF 0.130 0.103 0.141 0.101 0.145 k -NN-OPF 0.126 0.099 0.136 0.098 0.138 0.098 SVM-Rank
TABLE VIIC
OMPUTATIONAL LOAD [ S ] CONCERNING B RODATZ DATASET . technique descriptor top-r10 15 20 SASI k -NN-OPF LBP VI. C
ONCLUSIONS
In this work, we introduced two OPF variants to thecontext of content-based image retrieval and ranking. Bothapproaches, i.e., CG-OPF and k -NN-OPF, achieved promisingresults when compared to SVM-Rank, but being faster forranking purposes. Although the latter one figured as the mostaccurate technique in almost all simulations, the best trade-offbetween effectiveness and efficiency was achieved by OPF.As future works, we intend to change the OPF workingmechanism and adapt some parts to handle better the problemof image ranking, as well as to consider different distancefunctions for the arc-weights.R EFERENCES[1] D. C. G. Pedronette and R. da S. Torres, “Image re-ranking and rankaggregation based on similarity of ranked lists,”
Pattern Recognition ,vol. 46, no. 8, pp. 2350 – 2360, 2013.[2] S. M. Youssef, “Ictedct-cbir: Integrating curvelet transform with en-hanced dominant colors extraction and texture analysis for efficientcontent-based image retrieval,”
Computers & Electrical Engineering ,vol. 38, no. 5, pp. 1358 – 1376, 2012, special issue on Recent Advancesin Security and Privacy in Distributed Communications and Imageprocessing.[3] M. Iliadis, S. Yoo, X. Xin, and A. K. Katsaggelos, “Virtual touring: Acontent based image retrieval application,” in , 2013, pp.1–4.ABLE VIIIC
OMPUTATIONAL LOAD [ S ] CONCERNING C ALTECH
DATASET . technique descriptor top-r10 15 20 BIC
CCV
LCH k -NN-OPF ACC 22.62 22.69 21.55 13.96 23.12 21.97 14.26 23.49 22.35BIC 23.45 24.05 22.21 23.95 24.38 22.55 24.39 TABLE IXC
OMPUTATIONAL LOAD [ S ] CONCERNING
MPEG-7
DATASET . technique descriptor top-r10 15 20 k -NN-OPF 20.11 20.34 21.32 21.24 21.24 21.95 22.00 22.50 24.17SVM-Rank 32.78 33.13 34.66 33.55 33.81 34.63 34.12 34.59 35.46 [4] M. Milovanovic, M. Minovic, and D. Starcevic, “Walking in colors:Human gait recognition using kinect and cbir,” IEEE MultiMedia ,vol. 20, pp. 28–36, 2013.[5] P. H. Bugatti, D. S. Kaster, M. Ponciano-Silva, C. Traina, P. M. A.Marques, and A. J. Traina, “Prosper: Perceptual similarity queries inmedical cbir systems through user profiles,”
Computers in Biology andMedicine , vol. 45, pp. 8 – 19, 2014.[6] M. H. Memon, J. P. Li, I. Memon, R. A. Shaikh, and F. A. Mangi,“Efficient object identification and multiple regions of interest usingcbir based on relative locations and matching regions,” in , 2015, pp. 247–250.[7] B. Demir and L. Bruzzone, “A novel active learning method in relevancefeedback for content-based remote sensing image retrieval,”
IEEE Trans-actions on Geoscience and Remote Sensing , vol. 53, pp. 2323–2334,2015.[8] A. d. S. Tavares, A. X. Falc˜ao, and L. P. Magalh˜aes, “Active learningparadigms for CBIR systems based on optimum-path forest classifica-tion,”
Pattern Recognition , vol. 44, no. 12, pp. 2971 – 2978, 2011.[9] J. Pardede and B. Sitohang, “Reduce semantic gap in content-basedimage retrieval.” American Scientific Publishers, 2017, pp. 10 664–10 671.[10] B. J. Rani, B.Prashanth, and B.Krishna, “Active learning methods for in-teractive image retrieval,”
International Journal of Innovative ComputerScience & Engineering , vol. 4, pp. 12–17, 2017.[11] A. Alzu’bi, A. Amira, and N. Ramzan, “Semantic content-based imageretrieval: A comprehensive study,”
Journal of Visual Communication andImage Representation , vol. 32, pp. 20 – 54, 2015.[12] Z. S. Younus, D. Mohamad, T. Saba, M. H. Alkawaz, A. Rehman, M. Al-Rodhaan, and A. Al-Dhelaan, “Content-based image retrieval using psoand k-means clustering algorithm,”
Arabian Journal of Geosciences ,vol. 8, pp. 6211–6224, 2015.[13] A. Irtaza, M. A. Jaffar, E. Aleisa, and T.-S. Choi, “Embedding neuralnetworks for semantic association in content based image retrieval,”
Multimedia Tools and Applications , vol. 72, pp. 1911–1931, 2014.[14] B. Satish and K. P. Supreethi, “Content based medical image retrievalusing relevance feedback bayesian network,” in , 2017, pp. 424–430.[15] N. S. Devi and K. Hemachandran, “Content based feature combinationmethod for face image retrieval using neural network and svm classifierfor face recognition,”
Indian Journal of Science and Technology , vol. 10,2017.[16] P. Pavani and T. S. Prabha, “Content based image retrieval using machinelearning approach,” in
Proceedings of the International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA)2013 . Springer International Publishing, 2014, pp. 173–179.[17] X.-Y. Wang, B.-B. Zhang, and H.-Y. Yang, “Active svm-based relevancefeedback using multiple classifiers ensemble and features reweighting,”
Engineering Applications of Artificial Intelligence , vol. 26, pp. 368 –381, 2013.[18] K. Sugamya, S. Pabboju, and A. V. Babu, “A cbir classification usingsupport vector machines,” in , 2016, pp. 1–6.[19] L. Hu, S. Lu, and X. Wang, “A new and informative active learningapproach for support vector machine,”
Information Sciences , vol. 244,pp. 142 – 160, 2013.[20] X.-Y. Wang, H.-Y. Yang, Y.-W. Li, W.-Y. Li, and J.-W. Chen, “A newsvm-based active feedback scheme for image retrieval,”
EngineeringApplications of Artificial Intelligence , vol. 37, pp. 43 – 53, 2015.[21] S. Saad, H. Kumar, and T. K. Tewari, “Efficient content based imageretrieval using svm and color histogram,” in , 2017, pp. 1–3.[22] N. Seth and S. Jindal, “Local binary pattern with support vector machineto enhance image retrieval,”
International Journal of Advanced Researchin Computer Science , vol. 8, 2017.[23] Y. M. Lohite and S. J. Pawar, “A novel method for content based imageretrieval using local features and svm classifier,”
International ResearchJournal of Engineering and Technology , vol. 4, 2017.[24] Y. Rao, W. Liu, B. Fan, J. Song, and Y. Yang, “A novel relevancefeedback method for cbir,”
World Wide Web , 2018.[25] O. Mohamed, E. A. Khalid, O. Mohammed, and A. Brahim, “Content-based image retrieval using convolutional neural networks,” in
LectureNotes in Real-Time Intelligent Systems . Springer International Publish-ing, 2018, pp. 463–476.[26] J. P. Papa, A. X. Falc˜ao, and C. T. N. Suzuki, “Supervised patternclassification based on optimum-path forest,”
International Journal ofImaging Systems and Technology , vol. 19, no. 2, pp. 120–131, 2009.[27] J. P. Papa, A. X. Falc˜ao, V. H. C. Albuquerque, and J. a. M. R. S.Tavares, “Efficient supervised optimum-path forest classification forlarge datasets,”
Pattern Recognition , vol. 45, no. 1, pp. 512–520, 2012.[28] J. P. Papa, S. E. N. Fernandes, and A. X. Falc˜ao, “Optimum-path forestbased on k-connectivity: Theory and applications,”
Pattern RecognitionLetters , vol. 87, pp. 117–126, 2017.[29] W. P. Amorim, A. X. Falc˜ao, J. P. Papa, and M. H. Carvalho, “Improvingsemi-supervised learning through optimum connectivity,”
Pattern Recog-nition , vol. 60, pp. 72–85, 2016.[30] L. M. Rocha, F. A. M. Cappabianco, and A. X. Falc˜ao, “Data clusteringas an optimum-path forest problem with applications in image analysis,”
International Journal of Imaging Systems and Technology , vol. 19, no. 2,pp. 50–68, 2009.[31] S. Dhawale and B. Joglekar, “Optimum path forest approach for imageretrieval based on context,” 2015.[32] J. P. Papa and A. X. Falc˜ao, “A learning algorithm for the optimum-pathforest classifier,” in
Graph-Based Representations in Pattern Recogni-tion, 7th IAPR-TC-15 International Workshop, GbRPR 2009, Venice,Italy, May 26-28, 2009. Proceedings , 2009, pp. 195–204.[33] ——, “A new variant of the optimum-path forest classifier,” in
Advancesin Visual Computing, 4th International Symposium, ISVC 2008, LasVegas, NV, USA, December 1-3, 2008. Proceedings, Part I , 2008, pp.935–944.[34] J. P. Papa, S. E. N. Fernandes, and A. X. Falc˜ao, “Optimum-path forestbased on k-connectivity: Theory and applications,”
Pattern RecognitionLetters , vol. 87, pp. 117–126, 2017.[35] G. H. Rosa, K. A. P. Costa, L. A. P. J´unior, J. P. Papa, A. X. Falc˜ao,and J. M. R. S. Tavares, “On the training of artificial neural networkswith radial basis function using optimum-path forest clustering,” in , 2014, pp. 1472–1477.[36] T. Ojala, M. Pietik¨ainen, and T. M¨aenp¨a¨a, “Multiresolution gray-scaleand rotation invariant texture classification with local binary patterns,”
IEEE Trans. Pattern Anal. Mach. Intell. , vol. 24, p. 971–987, Jul. 2002.[37] A. C¸ arkacioglu and F. Yarman Vural, “Sasi: A generic texture descriptorfor image retrieval,”
Pattern Recognition , vol. 36, pp. 2615–2633, 2003.[38] J. Huang, S. R. Kumar, M. Mitra, W.-J. Zhu, and R. Zabih, “Imageindexing using color correlograms,” 1997, pp. 762–768.[39] R. O. Stehling, M. A. Nascimento, and A. X. Falc˜ao, “A compactand efficient image retrieval approach based on border/interior pixelclassification.” ACM, 2002, pp. 102–109.40] G. Pass, R. Zabih, and J. Miller, “Comparing images using colorcoherence vectors,” in
Proceedings of the Fourth ACM InternationalConference on Multimedia . Association for Computing Machinery,1997, p. 65–73.[41] M. J. Swain and D. H. Ballard, “Color indexing,”
International Journalof Computer Vision , vol. 7, pp. 11–32, 1991.[42] T. Lu and C. Changs, “Color image retrieval technique based on colorfeatures and image bitmap,”
Inf. Processing and Management , vol. 43,p. 461–472, 2007.[43] T. Joachims, “Training linear svms in linear time,” in