Scene Image Clustering Based on Boosting and GMM Khiem Ngoc Doan
Toan Thanh Do
Thai Hoang Le
Academic Affairs Department Vietnam National University Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Viet Nam
Department of Computer Science University of Science HCMC 227 Nguyen Van Cu, District 5, Ho Chi Minh City,Vietnam
Department of Computer Science University of Science HCMC 227 Nguyen Van Cu, District 5, Ho Chi Minh City,Vietnam
[email protected]
[email protected]
[email protected]
multiple k-means results [4]. A different partitional clustering approach is based on probability density function (pdf) estimation using the Gaussian mixture model. The specification of the parameters of mixtures is based on the expectation minimization algorithm (EM ) in [5]. Hierarchical clustering methods can be displayed in the form of dendrogram or a tree in [7]. These methods can be classified as agglomerative or divisive. A hierarchical agglomerative method, which is also called a bottom-up clustering method, treats each sample as a singleton cluster at the outset and gradually merges the clusters into larger clusters until all samples are ultimately in a single cluster (the root node). A hierarchical divisive method, which is called a top-down clustering method, starts at the top with all samples in one cluster. The cluster is split into smaller clusters. This procedure is applied recursively until each sample is in its own singleton cluster.
ABSTRACT Gaussian M ixture M odel (GM M ) is widely used in unsupervised learning tasks. In this paper, we propose the boost-GM M algorithm which uses GM M s to cluster real world scenes. At first, images will be extracted with gist-feature to get the data set. At each boosting iteration, a new training set is constructed by using weighted sampling from the original dataset and GM M is used to provide a new data partitioning. The final clustering solution is produced by aggregating the multiple clustering results. Experiments on real-world scene sets indicate that boost-GM M has higher result than other algorithms.
Keywords Cluster, Gaussian M ixture M odel, boosting, scene feature.
1. INTRODUCTION
Grid-based clustering algorithms are mainly proposed for spatial data mining. These algorithms quantize the space into a finite number of shells and then do all operations on the quantized space. On the other hand, density -based clustering algorithms are based on density conditions.
Data clustering is one of the most important techniques in data mining. It is used to understand and analy ze the structure of unlabeled data. Image is a special data in which there is a lot of information. This problem becomes harder because when we use different metrics we obtain different results. The majority of clustering algorithms are based on the following four most popular clustering approaches: iterative square-error partitional clustering, hierarchical clustering, grid-based clustering, and density-based clustering in [1].
However, many of the above clustering methods require additional user-specified parameters, such as the optimality and shapes of clusters, similarity thresholds, and stopping criteria. M oreover, we can get different solutions due to the random initializations of many algorithms such as k-means and GM M .
The partitional clustering methods can be classified into hard clustering methods and soft clustering methods. In hard clustering methods, each sample is assigned to only one cluster. In soft clustering method , each sample can be associated with several clusters. K-means, which is the most used algorithm in partitional clustering, is based on the square-error criterion. This algorithm is computationally efficient and yields good results if the clusters are compact, hyper-spherical in shape, and well separated in feature space. Numerous attempts have been made to improve the performance of the simple k-means algorithm by using M ahalanobis distance to detect hyper-ellipsoidal shaped cluster in [3] or by incorporating a fuzzy criterion function resulting in fuzzy c-means algorithm in [2] or using boosting to aggregate the
Boosting is one of the most important developments in classification methodology, and this method is the linear combination of weak learners to create a stronger learner. It is also a multi-clustering approach. A multi-clustering approach is introduced by Fred in [8] and Frossyniotis in [4], where multiple clusterings (using k-means) are aggregated to get a better result. Another multi-clustering approach is BoGM M in [9]. In this paper, the author divided this method into two parts. The first part is Boosting GM M in which the BIC (Bayesian Information Criterion) algorithm is used to generate the sized of GM M . The second part is Boosted Clustering in which the clusters of GM M are combined into a C cluster (user-specified parameter). This method was shown to have good results in the case of small and basic dimensions database, while having bad results in the case of large and complex dimensions because of the large number of clusters generated by BIC (45 in the case of four input clusters).
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For cluster images, we suggest using the gist-feature for the feature extraction step and propose boost-GM M for the clustering step. In our clustering method, at each iteration, a GM M is used to model the dataset; therefore, each cluster is represented by Gaussian. After several iterations, some Gausses, which represent the same cluster, are aggregated. In consequence, the combination
226
of Gaussians (with the compatible weight) is the same as a GM M . We tested the on scene database of Oliva Aude (M IT). Experimental results show that our method has good results in scene image clustering.
2. FEATURE EXTRACTION Haar features’s advantage is fast and known to work well in image processing tasks such as face detection. In clustering, an image has a lot of information and Haar features are so simple that an image has a large amount of Haar windows. Therefore without a labeled dataset, we would not be able to choose good features for clustering. Edges can give a rough idea of a scene. But in some cases, it seems to be not effective. For example, a tall building image would show many long vertical edges and possibly numerous horizontal edges; Similarly a forest image would show uniform distribution of dominant long vertical edges. The coast, open country and highway on the one hand would give a relatively fewer edges and more of horizontal lines as prominent ones. M ountains on the other hand can be expected to give more of diagonal edges, due to their characteristic shap e; similarly streets and highways have characteristic edges marking the outlines of the road.
Figure 2. Gabor filter at 3 scales (8-8-4) In gist feature extraction part, we apply 20 Gabor filters at 3 spatial scales (8-8-4) to the 3 color subchannels R-G-B of the prefiltered image. For each of the subchannels, average values from a predefined 4 by 4 grid (16 values) are computed for a total of 960 raw gist value (3 subchannels * 20 Gabor filters * 16 values = 960 raw gist value).
Color features were proven to have good results. However, it is not efficient when images of different scenes have similar colors. For example, images of forests and mountains in winter will be white, images of the coast and open country are yellow in sunset, or images of tall-buildings with gray walls and blue skies are similar to images of highway s, which have gray roadbeds and blue skies. Gist feature is proposed by Aude Oliva in [12], and it is effective in scene classification.
Gabor filters
Figure 3. Illustration of the application Gabor filters to an image. We suggest using the gist feature for scene image clustering. However, a 960-dimension vector is too large for clustering so we used Principal Component Analysis (PCA) to reduce it to a 30dimension vector. The gist feature has more advantages than other features because it is the combination of colors and texture. M oreover, texture is extracted by exhausting all of the directions. However, the gist feature has a weakness of having longer extraction time than other features.
3. BOOST-GMM We propose a new algorithm to clustering images based on boosting and the Gaussian M ixture M odel (GM M ) that we will call boost-GM M which iteratively recycles the training examples, providing multiple clusterings and resulting in a common partition. At each iteration, the weights of the original data set are computed, and a new training set is constructed based on this weight. GM M is then applied to the partition the new training set. The final cluster solution is produced by aggregating the obtained partitions using weighted voting, where the weight of each
Figure 1. Illustration of gist feature (a) input image (b) prefiltered image (c) 960 dimensions gist feature. This method has two parts. The first step is pre-filtering and the second step is gist feature extraction. In pre-filtered part, there are four steps: padding images to reduce boundary artifacts, whitening, local contrast normalization, and crop ping the output image to have the same size as the input image.
227
x
partition is a measure of its quality. The algorithm is summarized below. Algorithm boost-GMM. Given: Input sequence of N instances (ݔଵ ǡ ǥ ǡ ݔே ), ݔ ܴ אௗ ǡ ݅ ൌ ͳǡ ǥ ǡ ܰ , the number ܥof clusters to partition the data set and the maximum iterations ܶ.
x
x
x
x
o Produce the new training set by getting ܰ௧ samples whose weight are biggest. Call GM M to partition the training data, and get the partition ୲ ܪ. Get the cluster hypothesis ܪ௧ ൌ ൫݄௧ǡଵ ǡ ݄ ௧ǡଶǡ ǥ ǡ ݄௧ǡ ൯ for all ݅, ݅ ൌ ͳ ǥ ǡ ܰ, where ݄ǡ is the membership degree of instance ݅ to cluster ݆. If ݐ ͳ, renumber the cluster indexes of ܪ௧ according to the highest matching score, given by the fraction of shared instances with the clusters provided by the boost௧ିଵ . clustering until now, using ܪ Calculate pseudoloss ே
௧ୀଵ
ܳܥ௧
where is a measurement index which is used to evaluate the clustering quality of an instance ݔ for the partition ୲ : (3)
where ݄௧ǡௗ is the maximum membership degree of ݔ to a cluster and ݄௧ǡௗ is the minimum membership degree of ݔ to a cluster. x
Stopping criteria: o If Ԗ୲ ͲǤͷ then
ݐൌ ݐ ͳ
Another issue in the above methodology is how to renumber the cluster indexes at the iteration ݐ. Because the initialization of GM M is random, difference times may have difference partitions. We need to renumber the cluster indexes of ܪ௧ according to the highest matching score with cluster indexes of ܪ௧ିଵ. To solve this problem we use Hungarian algorithm. We assume that ܲଵ and ܲଶ is two data partitions. At first, from two difference partitions ܲଵ and ܲଶ we produce a matrix ܯ:
ଵିఢ ఢ
Set ߚ௧ ൌ
ܶൌ ݐെ ͳ go to step 3
ܯሺ݇ ሻ ൌ ቊ
o If Ԗ୲ ൏ Ԗ୫ୟ୶ then
ൌ
ͳ
ͳ݂݅ݔ ܥ א Ͳ݂݅ݔ ܥ ב
ǡ ݇ ൌ ͳǡ ǥ ǡ ܰ
where ݅ is the index of the partition ݅ ൌ ͳܥ ;ʹݎ is the list of samples in the ݆th cluster of partition ݅.
If ݅ܿ ൌ ͵ then ܶൌݐ go to step 3
From the matrix ܯ, we produce the matching cost matrix between clusters of two partitions:
Else x
ఛୀଵ
ሺߚఛ ሻ ݄ఛ ሺͷሻ σ ௧ୀଵ ൫ߚ ൯ ǡ
At the first iteration, the training set is the original data set. It means we use all of instances for the first clustering. At each iteration ݐൌ ʹǡ ǥ ǡ ܶ, the data set ܺ ௧ is constructed from the original data set by getting ܰ௧ instances whose weight are highest. Then a GM M is constructed from the dataset ܺ ௧, and a partitioning result ܪ௧ is produced using parameter of GM M on the original data set. For each instance ݔ ǡ ݅ ൌ ͳǡ ǥ ǡ ܰ, we get a cluster hypothesis ܪ௧ ൌ ൫݄௧ǡଵǡ ݄௧ǡଶǡ ǥ ǡ ݄ ௧ǡ ൯ where ݄ ௧ǡ denotes the membership degree of instance ݅ to cluster ݆ with respect to σ ୀଵ ݄ ௧ǡ ൌ ͳ, for all ݅. It must be emphasized that, the membership degree ݄௧ǡ , at each iteration, will be used to produce the final partitioning, not through the specification of GM M parameters. This fact gives the flexibility when applying other boosting methods in this problem.
ͳ ߳ ௧ ൌ ݓ௧ ܳܥ௧ሺʹሻ ʹ
x
ୀଵǡǥǡ
In this problem, we assume a given set ܺ of ܰ dimentional instances ݔ , the required number of clusters C, and the maximum number of iterations T of boost-GM M . The clustering obtained at ௧ will denote the iteration ݐwill be denoted as ܪ௧, and ܪ aggregate partition obtained using clustering ܪ for ݅ ൌ ͳǡ ǥ ǡ ݐ. Consequently, the final solution ܪ produced by the clustering ் obtained at iteration : ܪ ൌ ܪ . The basic feature of this technique is that, at each iteration, the weight ݓ௧ is computed for each instance ݔ such that the weight is higher, it means this instance is more difficult to be clustered. At the beginning, the weights of all instances are equally initialized, ݓଵ ൌ ͳȀܰ. In accordance the boosting methodology, the weight of each instance ݔ is constructed for the iteration ݐ ͳ.
Produce the new training set from the original data set based on the weight of data set. o Compute the number of samples of new training set using this formula: ಿ ሺ ሻ ሺ ሻ ܰ௧ ൌ ܴ ݀݊ݑቀ݁ ିσసభ ௪ ௫ ௪ ௫ ቁሺͳሻ
ܳܥ௧ ൌ ͳ െ ݄ ௧ǡௗ ݄௧ǡௗ
ൌ ቈ
3. Output the number of iterations ܶ and the final cluster ௧ hypothesis ܪ
2.Iterate while ݐ ܶ
x
௧ ௧ ܪ
1.Initialize ݓଵ ൌ ͳȀܰǡ ݅ ൌ ͳǡ ǥ ǡ ܰ; ݐൌ ͳ; ߳ ௫ ൌ Ͳ; ݅ܿ ൌ Ͳ. x
Compute the aggregate cluster hypothesis:
்
݅ܿ ൌ Ͳ ߳ ௫ ൌ ߳ ௧ Update distribution W
ܥܯǡ ൌ
ܺଵ ܺଶ
ሺሻ ் ் ் ܺଵ ܺଵ ܺଶ ܺଶ െ ܺଵ ܺଶ where ݅ǡ ݆ ൌ ͳǡ ǥ ǡ ܥǤ
ொ
ݓ௧ߚ௧ Ǣ ݅ ൌ ͳǡ ǥ ǡ ܰሺͶሻ ܼ௧ where ୲ is the nomalization constant such that ܹ ௧ାଵ is ୲ a distribution: ୲ ൌ σ ୧ୀଵ ୧ ݓ௧ାଵ ൌ
We apply the Hungarian algorithm for matrix ܥܯto determine C best matching pairs of clusters between ܲଵ and ܲଶ . Then, we renumber the clustering indexes ܲଶ based on ܥbest matching pairs. We can see that above technique is a heuristic because we
228
get only a good result and not best results. We can get the best result using brute-force search. However, if the number of clusters is high, it is impossible.
Figure 4. Illustration of Mutual Information I(X,Y) We tested our algorithm on M IT dataset. This dataset contains 8 outdoor scene categories: coast, mountain, forest, open country, street, inside city, tall buildings and highways. There are 2688 color images, 256x256 pixels.
In the above methodology the most critical issue to be addressed is how to evaluate the clustering quality of an instance ݔ for the partition ܪ௧. Based on ܪ௧, the clustering quality is computed using (3). We can rewrite (3) as ܳܥ௧ ൌ ͳ െ ൫݄௧ǡௗ െ ݄௧ǡௗ൯. It means the larger ݄௧ǡௗ െ ݄௧ǡௗ is, the smaller ܳܥ௧ is or the clustering quality of instance ݔ is better. Based on the ܳܥindex, at each iteration ݐthe pseudoloss ߳ ௧ is computed using (2). Then, the weight distribution ݓ௧ାଵ for the next iteration is computed using (4). Using this formula, we can reduce the well-cluster points (whose clustering quality are high) and raise the weight of badly clustered data points. Thus, in the first iteration, the boostGM M algorithm will partition the original data set, while in the next iteration, our algorithm will cluster data points that were hard to cluster in the first iteration (ܰ௧ badly-clustered instances), and the next iteration will partition the hardly clustered instances in the previous iterations. For the early stopping of our algorithm, two stopping criteria were used. In particular, the algorithm terminates if GM M has a pseudoloss ߳ ௧ greater than 0.5 (in which case the partitioning result of the last iteration is not taken into account) or the pseudoloss does not further increase after three iterations. It is clear that almost all distributions in nature are the normal distribution so that in the case of not know clearly about feature of dataset, GM M is better than K-means. However, if we use only one GM M for clustering, each cluster is presented by Gaussian. Our method is using boosting to present each cluster by some Gausses, and these Gausses are combined with a compatible weight (like a GM M ) so that each cluster is presented by a GM M . GM M is better than GM M in presented data points.
4. EXPERIMENTAL RESULTS To test boost-GM M , we use Accuracy and Normalized M utual Information (NM I) to measure the quality of the final clustering solutions.
Figure 5. Examples of 8 outdoor scene categories. To construct the testing set, we mix images from categories. For example, 2x100 is 100 first images of coast and mountain; 4x200 is 200 first images of coast, mountain, forest and open-country.
Accuracy is therefore the number of true samples divided by the total of all the test samples. Normalized M utual Information between the label of testing set ܺ and final clustering solution Y: ܰ ܫܯሺܺǡ ܻሻ ൌ
Table 1: Time of feature extraction and running algorithms
ܫሺܺǡ ܻሻ Input
ඥܪሺܺሻ ܪ כሺܻሻ
Where ܫሺܺǡ ܻሻ ൌ ܪሺܺሻ ܪሺܻሻ െ ܪሺܺǡ ܻሻ. ܪሺܺሻ is the entropy of X while ܪሺܻሻ is the entropy of Y. H(X,Y) is the joint entropy of ܺ and ܻ.
229
T ime (in second) Feature Extraction
Kmeans
GMM
boostKmeans
boostGMM
2x100
90,339491
0,0588
0,0613
0,0879
0,1341
2x150
132,091160
0,0901
0,0958
0,1289
0,2576
2x200
171,601068
0,1399
0,1391
0,1724
0,3252
4x100
171,913414
0,1443
0,1467
0,2226
1,0720
4x150
251,784309
0,1950
0,2153
0,3297
2,3643
4x200
337,243440
0,2687
0,2712
0,3872
3,0982
8x100
337,572913
0,3293
0,3411
0,6023
6,5913
8x150
567,190846
0,5122
0,5560
0,8947
17,3812
8x200
734,957941
0,7108
0,7642
1,3500
25,7541
Because the initialization of GM M is random, the output of our algorithm is variable. Therefore, we execute algorithms ten times and computed the mean and the standard deviation (std):
1
݉݁ܽ݊ ൌ ݔҧ ൌ
kmeans GMM boost-kmeans boost-GMM
0.9
ͳ ݔ ݊
0.8
NMI
ୀଵ
0.7 0.6
ͳ ݀ݐݏൌ ඩ ሺݔ െ ݔҧ ሻଶ ݊
0.5 0.4
ୀଵ
2
3
4
5 Clusters
6
7
8
In the first test, we constructed the testing set from 2 categories to 8 categories with 100 images per categories. The results are shown in table 2, Figure 6 and Table 3, Figure 7.
Figure 7. The NMI of partitioning on the testing set of 100 images per categories
Table 2. Accuracy of partitioning on the testing set of 100 images per categories
In the second test, we constructed the testing set from 2 categories to 8 categories with 150 images per categories. The result are shown in Table 4, Figure 8 and Table 5, Figure 9.
Accuracy
Kmeans
Input
mean
std
GMM mean
std
boost-Kmeans boost-GMM mean
std
mean
Table 4. Accuracy of partitioning on the testing set of 150 images per categories
std
2x100 0,9750 0,0000 0,9850 0,0000 0,9750 0,0000 0,9850 0,0000
Accuracy
3x100 0,6893 0,0649 0,7307 0,0720 0,7207 0,0387 0,7613 0,0065
Input
4x100 0,7365 0,0470 0,7580 0,0690 0,7600 0,0000 0,7925 0,0000
2x150
0,9767 0,0000 0,9900 0,0000 0,9767 0,0000 0,9900 0,0000
5x100 0,5916 0,0654 0,6248 0,0761 0,6268 0,0721 0,6588 0,0463
3x150
0,6907 0,0627 0,7142 0,0931 0,7089 0,0809 0,7253 0,0927
6x100 0,5457 0,0436 0,5510 0,0534 0,5520 0,0556 0,5953 0,0432
4x150
0,7183 0,0467 0,7563 0,1198 0,7377 0,0033 0,8093 0,0098
7x100 0,5486 0,0371 0,5683 0,0524 0,5626 0,0254 0,5940 0,0189
5x150
0,5499 0,0259 0,588 0,0263 0,5579 0,0251 0,6165 0,0194
8x100 0,5262 0,0410 0,5205 0,0432 0,5300 0,0337 0,5625 0,0291
6x150
0,4698 0,0497 0,5456 0,0392 0,4802 0,0443 0,5731 0,0337
7x150
0,4808 0,0202 0,5503 0,0198 0,5084 0,0159 0,5674 0,0061
8x150
0,4603 0,0399 0,5113 0,0301 0,4652 0,0235 0,5428 0,0258
1 kmeans GMM boost-kmeans boost-GMM
std
GMM mean
std
boost-Kmeans boost-GMM mean
std
mean
std
1 kmeans GMM boost-kmeans boost-GMM
0.9
0.8 Accuracy
Accuracy
0.9
Kmeans mean
0.7
0.8 0.7 0.6
0.6
0.5
0.5
2
3
4
5 Clusters
6
7
8
0.4
2
3
4
5 Clusters
6
7
8
Figure 6. The Accuracy of partitioning on the testing set of 100 images per categories
Figure 8. The Accuracy of partitioning on the testing set of 150 images per categories
Table 3. NMI of partitioning on the testing set of 100 images per categories
Table 5. NMI of partitioning on the testing set of 150 images per categories
NMI Input
Kmeans mean
std
GMM mean
std
boost-Kmeans boost-GMM mean
std
mean
NMI
std
Input
Kmeans mean
std
GMM mean
Std
boost-Kmeans boost-GMM mean
std
mean
std
2x100 0,8381 0,0000 0,8888 0,0000 0,8381 0,0000 0,8888 0,0000
2x150 0,8433 0,0000 0,9291 0,0000 0,8433 0,0000 0,9291 0,0000
3x100 0,4727 0,0152 0,5150 0,0232 0,4725 0,0151 0,5240 0,0032
3x150 0,4864 0,0257 0,5218 0,0275 0,4861 0,0254 0,5282 0,0242
4x100 0,5188 0,0123 0,5692 0,0249 0,5250 0,0000 0,5817 0,0000
4x150 0,5056 0,0188 0,6076 0,0561 0,5110 0,0032 0,6214 0,0133
5x100 0,4507 0,0224 0,4972 0,0343 0,4555 0,0182 0,4964 0,0184
5x150 0,3815 0,0154 0,4558 0,0103 0,3799 0,0167 0,4566 0,0135
6x100 0,3927 0,0134 0,4143 0,0115 0,3885 0,0226 0,4232 0,0135
6x150 0,3396 0,0049 0,4032 0,0107 0,3386 0,0042 0,4042 0,0183
7x100 0,4243 0,0097 0,4576 0,0170 0,4302 0,0036 0,4683 0,0066
7x150 0,3649 0,0049 0,4138 0,0033 0,3574 0,0054 0,4146 0,0041
8x100 0,4147 0,0168 0,4524 0,0278 0,4098 0,0135 0,4619 0,0186
8x150 0,3486 0,0149 0,4177 0,0237 0,3553 0,0162 0,4224 0,0127
230
1
1
0.9 0.8
0.9
boost-GMM
0.7
0.6
0.5
0.5
0.4
0.4
3
4
5 Clusters
6
7
2
8
In the third test, we constructed the testing set from 2 categories to 8 categories with 200 images per categories. The result are shown in Table 6, Figure 10 and Table 7, Figure 11. Table 6. Accuracy of partitioning on the testing set of 200 images per categories Accuracy
Kmeans std
GMM
mean
mean
std
mean
std
mean
2x200
0,9675 0,0000 0,9725 0,0000 0,9650 0,0000 0,9725 0,0000
3x200
0,6920 0,0977 0,7420 0,0686 0,7413 0,0016 0,7890 0,0061
4x200
0,7007 0,0391 0,7652 0,1170 0,7000 0,0644 0,8007 0,0410
5x200
0,5274 0,0368 0,603 0,0553 0,5528 0,0345 0,6598 0,0315
6x200
0,4828 0,0353 0,5762 0,0161 0,4888 0,0244 0,6037 0,0108
7x200
0,4774 0,0155 0,5499 0,0219 0,4820 0,0214 0,5806 0,0132
8x200
0,4707 0,0368 0,5449 0,0353 0,4851 0,0114 0,5579 0,0159
4
5 Clusters
6
7
8
[1]
Table 7. NMI of partitioning on the testing set of 200 images per categories
Input
Kmeans mean
std
GMM mean
Std
boost-Kmeans boost-GMM mean
std
mean
NM I
Kmeans
0,5022
0,3630
GM M
0,6187
0,4671
boost-Kmeans
0,5141
0,3668
boost-GM M
0,6533
0,4925
6. REFERENCES
Figure 10. Illustration the Accuracy of partitioning on the testing set of 200 images per categories
NMI
Accuracy
In this paper, we proposed boost-GMM algorithm, which is based on boosting, to cluster scenes. Although, our algorithm has a running time longer than that of other algorithms, the results is better. Because the information in an image is huge, in our future work, we will study a better feature and better measure to apply to cluster image. We will also study a dimensional other than PCA. Another task is applying boost-GM M to clustering object images.
0.5 3
8
5. CONCLUSION
0.6
2
7
We also tested object images, but the results are low although the results of boost-GM M is better than other methods, because Gist feature is not efficient in clustering object images.
0.7
0.4
6
From Tables 2 to 8, we can see that the results of “boost-GM M ” are mostly better than those of other methods. But our method costs much more time, which can be seen in Table 1. Another problem is the results of 3 categories is lower than 4 categories because we used PCA to reduce the dimension from 960 to 30, but PCA can not hold all of the important features.
kmeans GMM boost-kmeans boost-GMM
0.8
5 Clusters
Std
1 0.9
4
The result of testing on total M IT set are shown in Table 8. Table 8. Performance of partitioning on MIT set
boost-Kmeans boost-GMM
Input
3
Figure 11. Illustration the NMI of partitioning on the testing set of 200 images per categories
Figure 9. Illustration the NMI of partitioning on the testing set of 150 images per categories
Accuracy
0.7
0.6
2
GMM boost-kmeans
0.8 NMI
NMI
kmeans
kmeans GMM boost-kmeans boost-GMM
[2]
Std
2x200 0,7944 0,0000 0,8267 0,0000 0,7831 0,0000 0,8267 0,0000
[3]
3x200 0,5089 0,0137 0,5072 0,0350 0,5036 0,0022 0,5446 0,0083 4x200 0,5067 0,0046 0,6057 0,0581 0,5092 0,0031 0,6176 0,0255
[4]
5x200 0,3907 0,0019 0,4805 0,0170 0,3977 0,0058 0,4871 0,0130 6x200 0,3402 0,0026 0,4018 0,0109 0,3465 0,0048 0,4196 0,0056
[5]
7x200 0,3624 0,0041 0,4398 0,0085 0,3686 0,0082 0,4484 0,0043 8x200 0,3615 0,0137 0,4456 0,0160 0,3742 0,0160 0,4479 0,0050
231
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