Research ArticleFast Image Search with Locality-Sensitive Hashing andHomogeneous Kernels Map
Jun-yi Li1,2 and Jian-hua Li1
1School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China2Electrical and Computer Engineering Department, National University of Singapore, Singapore 119077
Correspondence should be addressed to Jun-yi Li; [email protected]
Received 30 December 2013; Accepted 19 February 2014
Academic Editors: Y.-B. Yuan and S. Zhao
Copyright Β© 2015 J.-y. Li and J.-h. Li. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Fast image search with efficient additive kernels and kernel locality-sensitive hashing has been proposed. As to hold the kernelfunctions, recentwork has probedmethods to create locality-sensitive hashing, which guarantee our approachβs linear time; howeverexisting methods still do not solve the problem of locality-sensitive hashing (LSH) algorithm and indirectly sacrifice the loss inaccuracy of search results in order to allow fast queries. To improve the search accuracy, we show how to apply explicit featuremaps into the homogeneous kernels, which help in feature transformation and combine it with kernel locality-sensitive hashing.We prove our method on several large datasets and illustrate that it improves the accuracy relative to commonly used methods andmake the task of object classification and, content-based retrieval more fast and accurate.
1. Introduction
In Web 2.0 applications era, we are experiencing the growthof information and confronted with the large amounts ofuser-based content from internet. As each one can publishand upload their information to the internet, it is urgent forus to handle the information brought by these people frominternet. In order to organize and be close to these vision datafrom Internet, it has caused considerable concern of people.Therefore, the task of fast search and index for large video orimage databases is very important and urgent for multimediainformation retrieval such as vision search especially nowthe big data in some certain domains such as travel photodata from the website and social network image data or otherimage archives.
With the growth of vision data, we focus on two impor-tant aspects of problem including nearest neighbor searchand similarity metric learning. For metric learning, manyof the researchers have proposed some algorithms such asInformation-Theoretic metric learning [1]. As for nearestneighbors search, the most common situation and task for usis to locate the most similar image from an image database.Among all the methods, given the similarity of example
and query item, the most common method is to find allthe vision data among the vision database and then sortthem. However time complexity of this algorithm is too largeand also impractical. When we handle image or video data,especially, this complexity will not be calculated, because it isvery difficult for us to compute the distance of two items inhigher dimensional space and also vision datum is sparse, sowe cannot complete it by limited time.
Many researchers believe that linear scanning can solvethis problem; although we believe it is a common approachand not suitable for computing in large-scale datasets, itpromotes the development of ANN. LSH was used in ANNalgorithms. To get fast query response for high-dimensionalspace input vectors [1β5], when using LSH, we will sacrificethe accuracy. To assure a high probability of collision for simi-lar objects, randomized hash functionmust be computed; thisis also referred to in many notable locality-sensitive hashingalgorithms [6, 7].
Although, in object similarity search task, the LSH hasplayed an important role, some other issues and problemshave been neglected. In image retrieval, recognition, andsearch tasks, we find that they are very common:
Hindawi Publishing Corporatione Scientific World JournalVolume 2015, Article ID 350676, 9 pageshttp://dx.doi.org/10.1155/2015/350676
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(A) in the sample feature space, traditionally LSH ap-proaches can only let us get a relatively high collisionprobability for items nearby. As a lot of vision datasetscontainedmuch rich information, we can find that thecategory tags are attached to YouTube and Flickr dataand the class labels are attached toCaltech-101 images.However the low-level and high-level of vision sam-ples have great gap, which means that the gap low-level features and high-level semantic informationexist. To solve this problem, we intend to utilizethe side additional information for constructing hashtable;
(B) As tomanipulate nonlinear datawhich is linear insep-arable, we commonly use kernel method in visiontask because of its popularity. For instance, in visionmodel, objects are often modeled as BOF and kerneltrick is an important approach in classifying thesedata from low-dimension space to high-dimensionspace. However, how to create hash table in kernelspaces is a tough problem for us.
To verify our idea, we did several experiments in objectsearch task. For example, we show our results on the Caltech-101 [8] dataset and demonstrate that our approach is superiorto the existing hashing methods as our proposed algorithm.
In order to test our algorithm performance on dataset,we design some experiments on certain visual task suchas Caltech-101 [8] and demonstrate that the performanceof algorithm in our paper is beyond the traditional LSHapproaches on the dataset, as hash functions can be calculatedbeyond many kernels. Arbitrary kernel in ANN is suitablein our scheme; actually we can find that a lot of similarityhashing functions can be accessed in the task of vision searchtasks based on content retrieval.
2. Homogeneous KernelIn our paper, we mainly focus on some similar kernels likeintersection, Jensen-Shannon, Hellingerβs, and π2 kernels. Inthe fields of machine learning and vision search, we oftenuse these kernels as learning kernels. These kernels have twocommon attributes: being homogeneous and additive. Theidea of kernel signature has been smoothly connected to thesekernels in this section. Meanwhile we can use pure functionsto represent these kernels. Also these attributeswill be appliedin Section 3 to obtain kernel featuremaps.Through the kernelfeature map, we can get their approximate expression.
Homogeneous Kernels. A kernel ππ: R+0Γ R+0
β R isπΎ-homogenous if
βπ β₯ 0 : ππ(ππ,ππ) = π
πΎππ(π, π) . (1)
When πΎ = 1, we believe that ππ(ππ,ππ) is homogeneous. Let
π = 1/βππ; we can obtain a πΎ-homogeneous kernel and wecan also write the formula as
ππ(π, π) = π
βπΎππ(ππ,ππ) = (ππ)
πΎ/2ππ(β
π
π,β
π
π)
= (ππ)πΎ/2π (log π β log π) .
(2)
Here the pure function
π (π) = ππ(ππ/2, πβπ/2
) , π β R (3)
is called the kernel signature.
Stationary Kernels. A kernel ππ : R+0Γ R+0β R is called
stationary kernels if
βπ β R : ππ (π + π, π + π) = π
π (π, π) . (4)
Let π = β(π + π)/2; the ππ (π, π) is represented as
ππ (π, π) = π
π (π + π, π + π)
= ππ (π β π
2,π β π
2) = π (π β π) ,
(5)
π (π) = ππ (π
2, βπ
2) , π β R. (6)
Here we call formula (6) kernel feature.In the field of machine learning or computer vision, most
of the homogeneous kernels are composed of the Jensen-Shannon, intersection, π2, and Hellingerβs kernels. So we canalso view them as additive kernels. In the next section, we willfocus on these kernels and their kernel maps. Table 1 showsthe details [9].
π2 Kernel. We define π(π, π) = 2ππ/(π + π) as the π2 kernel
[10, 11]. Here the π2 distance is then defined as π·2(π, π) =π2(π, π).
Jensen-Shannon (JS) Kernel.We define π(π, π) = (π/2)log2(π+
π)/π + (π/2)log2(π + π)/π as the JS kernel. Here the JS kernel
distance π·2(π, π) can be obtained by π·2(π, π) = πΎπΏ(π |
(π + π)/2) + πΎπΏ(π | (π + π)/2), where we import the conceptof Kullback-Leibler divergence computed by πΎπΏ(π | π) =
βπ
π=1ππlog2(ππ/ππ).
Intersection Kernel. We defined π(π, π) = min{π, π} as theintersection kernel [12]. The distance metric π·2(π, π) = βπ βπβ1is π1 distance between variants π and π.
Hellingerβs Kernel. We defined π(π, π) = βππ as the Hellingerβskernel and specified distance metric π·2(π, π) = ββπ β βπβ2
2
as Hellingerβs distance between variants π and π.The functionexpression π (π) = 1 is the signature of the kernel, which isconstant.
πΎ-Homogeneous Parameters. In previous research paper, wecan see that the homogeneous kernels are used by parametersπΎ = 1 and πΎ = 2. When πΎ = 2, the kernel becomes π(π, π) =ππ. Now, in our paper, we can derive the πΎ-homogeneouskernel by formula (2).
3. Homogeneous Kennel Map
When handling low-dimensional data which is inseparable,we should create kernel feature map π(π₯) for the kernel
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Table 1: Common kernels, signature, and their feature maps.
Kernel π(π, π) Signature π (π) π (π€) Feature ππ(π)
Hellingerβs βππ 1 πΏ(π) βπ
π2
2ππ
π + πsech(π
2) sech(ππ) π
ππ€ log πβπ sech(ππ)
Intersection min{π, π} πβ|π|/2
2
π
1
1 + 4π2πππ€ log πβ
2π
π
1
1 + 4π2
JS π
2log2
π + π
π+π
2log2
π + π
π
ππ/2
2log2(1 + π
βπ) +
πβπ/2
2log2(1 + π
π)
2
log 4sech(ππ)1 + 4π2
πππ€ log π
β2
log 4sech(ππ)1 + 4π2
so that we can map our input data information in low-dimensional space to relatively high-dimensional (Hilbert)information space with β¨β , β β©:
βπ, π β π π·: πΎ (π, π) = β¨π (π) , π (π)β© . (7)
In order to compute the featuremaps and get approximatekernel feature maps expression for the homogeneous kernels,we should use Bochnerβs theorem by expanding the configu-ration of πΎ-homogeneous expression. Here we notice that ifa homogeneous kernel is Positive Definite [13], its signaturewill also be Positive Definite expression. The assumptioncondition is suitable for a stationary kernel. So, depending onformulae (2) and Bochnerβs theorem (9), we can derive theπ(π, π) and closed feature map.
We can compute the kernel density and feature mapclosed form [9] for most machine learning kernels. Table 1illustrates the results. Consider
π (π, π) = (ππ)π/2β«
+β
ββ
πβππ€π
π (π) ππ, π = log ππ
=β«
+β
ββ
(πβππ€ log πβπππ (π))
β
(πβππ€ log πβπππ (π)) ππ,
(8)
ππ€(π) = π
βππ€ log πβππΎπ (π). (9)
4. Kernelized Locality-Sensitive Hashing
To create and conduct the data association, we take theapproach of Kernelized LSH [14] which is also a hashtable-based algorithm. KLSH is proposed based on LSHalgorithm, which is more efficient and accurate for querysearch and matching. When searching the input query, theKLSH approach can quickly locate the possible similar andnearest neighbor items in the hash table and match it. Inaddition, KLSH has another characteristic: traditional LSHmethods can only find a part of hashes in the kernel space,while KLSH can locate all the possible hash tables in kernelspace. Moreover KLSH has been applied in the vision search
tasks by large scale datasets such as Tiny Image and otherdatasets [14].
Similar to LSH, constructing the hash functions for KLSHhas been the key problem for us. That means if we intendto compute the collision probabilities of input query and thedatabase points, we should compute the extent of similaritybetween them in the database as proposed by [15].
KLSH Principle. Any locality-sensitive hashing algorithm isbased on the probability of distribution of hash functionclusters. So we should compute the collision probability of abundle of points, for example,π and π:
ππ(β (π) = β (π)) = sim (π, π) . (10)
We can also view the problem as the issue of computingthe similarity of objects between π and π. Here sim(π, π)in the algorithm is the measure function of calculating thesimilarity, while β(π) and β(π) are randomly selected fromthe hash function cluster π». The instinct beyond this is thatwe find the fact that π and π will collide in the same hashbucket. So those objects which are significantly similar willbe more possible to be memorized in the hash table and thiseventually results in confliction [1].
We can derive the similarity function expression accord-ing to the vector inner product:
sim (π, π) = πππ. (11)
In [15, 16], the definition of LSH function has been extendedfrom formula (10) as
βπ(π) = {
1, if πππ β₯ 0,
0, else.(12)
Here we create a random hyper plane vector π. The distribu-tion of π fit has a zero-mean multi-Gaussianπ(0, Ξ£
π) distri-
bution. The dimensionality of π is the same with the inputvectorπ. This demonstrates that the statistical characteristicof input vector is uniquely matched with each hash function.
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Meanwhile this verification has been detailedly reported inthe LSH attribute in [17]. When we project on a point π,actually the sigh function we obtain in this process is a hashfunction and then we repeat it π times; a couple of hashes canbe created.We can also call this couple of hashes hash bucket.The hash bucket can be formed as
π (π) = β¨β1(π) , . . . , β
π‘(π) , . . . , β
π(π)β© . (13)
From (13), we can see that, after repeating π times, we can getone column of hash bucket (14); then repeating π times, wecan finally obtain the hash bucket π(π):ππ(π) = β¨β
1(π) , . . . , β
π‘(π) , . . . , β
π(π)β© (1 < π < π) .
(14)
When given the value of π, we can get all the the hashfunctions located in the bucket; we can see the following:
π (π) =
{{{{{{{
{{{{{{{
{
β1,1 π
(π) β2,1 π
(π) β β β βπ ,1 π(π) β β β β
π‘,1 π(π)
.
.
....
.
.
....
.
.
....
β1,π π
(π) β2,π π
(π) β β β βπ ,π π(π) β β β β
π‘,π π(π)
.
.
....
.
.
....
.
.
....
β1,π π
(π) β2,π π
(π) β β β βπ ,π π(π) β β β β
π‘,π π(π)
}}}}}}}
}}}}}}}
}
, (1 < π < π; 1 < π < π‘) . (15)
Due to the fact that we compute the similarity measurefunction in high-dimensional kernel space, the similarityfunction can also be extended and written as
sim ((ππ, ππ)) = π (π
π, ππ) = π (π
π)π
π (ππ) . (16)
In formula (16), we use kernel function π(π) to constructπ (ππ, ππ) to complete the kernel mapping for the points of
mπand π
π. And π(π
π)ππ(ππ) is a product of projection on
hash function from theR space.The problem is that nothingis known about the data while in kernel space to generateπ from π(0, Ξ£
π). Therefore, in order to construct the hash
function, πneeds to be created so thatwe can quickly computethe πππ(π) function based on the kernel. Similar to normal
ππ, we could use only the kernel of π(π) to approximatelycompute the function of π
ππ(π). We should select a subset of
database to construct π. By the large number of central limittheory, if we intend to choose parts of database items from thewhole database to form the dataset π, the sample of kerneldata must be satisfied by the distribution with mean π andvariance Ξ£. The variable π§
πcan be written as
π§π=1
πβ
πβπ
π (ππ) . (17)
With the growth of variable π, the theory tells us thatthe vector οΏ½οΏ½
π= βπ‘(π§
πβ π) has also been satisfied by the
distribution of normal Gaussian.We used the whitening transform to obtain π:
π = Ξ£β1/2
οΏ½οΏ½π. (18)
The LSH function has been yielded:
β (π (π)) = {1, if π (π)π Ξ£β1/2οΏ½οΏ½
πβ₯ 0,
0, else.(19)
As analyzed above, we use kernel function to represent thedatabase data; then the statistical data like variance andmean
are uncertain. If we intend to estimate and calculate π andΞ£, we could sample the data from the database by KPCAand eigen decomposition in [18] and we let Ξ£ = πΞπ
π andΞ£β1/2
= πΞβ1/2
ππ; therefore we can obtain the hash function
β(π(π)):
β (π (π)) = sign (π (π)ππΞβ1/2πποΏ½οΏ½π) . (20)
From the above, we can see how to construct the hashfunction for the kernel matrix input vectors. In this case, welet the kernelmatrix input beπΎ = πΞ©π
π by decomposing theπΎmatrix. HereΞ© andΞ have the same nonzero eigenvalue; itis also viewed as another form of kernel matrix input. From[18], we compute the projection
Vππ‘π (π) =
π
β
π=1
1
βππ‘
π’π‘(π) π (π
π)π
π (π) . (21)
Here π’π‘and V
π‘are, respectively, the π‘th eigenvector of the
kernel matrix and its covariance matrix.As mentioned before, we choose π data points from the
database to form π(ππ); traversing all the π‘ eigenvectors and
conducting the computation yields
β (π (π)) = π (π)ππΞβ1/2
πποΏ½οΏ½π
=
π
β
π‘=1
βππ‘Vππ‘π (π)π Vππ‘οΏ½οΏ½π.
(22)
Substituting (21) into (22) yields
π
β
π‘=1
βππ‘(
π
β
π=1
1
βππ‘
π’π‘(π) π (π
π)π
π (π))
β (
π
β
π=1
1
βππ‘
π’π‘(π) π (π
π)π
οΏ½οΏ½π) .
(23)
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(1) Process Data(a) Obtain πΎmatrix from database throughout the π points.(b) Obtain π
π by randomly sampling a subset from the {1, 2, . . . , π}
(c) Project on πth subset to obtain βπ(π(π)).
(d) Obtain π€ = πΎ1/2β ππ /π
(e) Project π€(π) onto the points in kernel space(f) Obtain hash bucket π
π(π)
(2) Query Processing(a) Obtain the same hash bucket in (29) from the database(b) Use Ann search for query matching.
Algorithm 1: KLSH algorithm.
Simplifying (23) yieldsπ
β
π=1
π
β
π=1
(π (ππ)π
π (π))
β (π (ππ)π
οΏ½οΏ½π)(
π
β
π‘=1
1
βππ‘
π’π‘(π) π’π‘(π)) .
(24)
SinceπΎβ1/2ππ
= βπ
π=1(1/βπ
π)π’π(π)π’π(π), we further simplify the
(24) yields
β (π (π)) =
π
β
π=1
π€ (π) (π (ππ)π
π (π)) , (25)
where π€(π) = βππ=1πΎβ1/2
πππ(π₯π)ποΏ½οΏ½π.
Through the above derived formula π€(π) we can obtainπ = βπ
π=1π€(π)π(π₯
π) which obeys random Gaussian distribu-
tion, then we can substitute (17) into π€(π):
π€ (π) =1
π
π
β
π=1
β
πβπ
πΎβ1/2
πππΎππ. (26)
We neglect the term of βπ, and finally the simplified π€(π)yields (27). π
π represents the unit vector for π.
And therefore hash function for kernel input will finallybe
π€ = πΎ1/2β ππ
π, (27)
β (π (π)) = sign(π
β
π=1
π€ (π) π (π,ππ)) . (28)
π is the kernel mapping matrix for pointsπ andππin space.
After several iterations, the hash function will form a hashbucket.
In order to get the suitable parameters in this process,we implement the query matching for several iterations.The detailed algorithm is illustrated finally in Algorithm 1.Considerππ(π)
=[β1(π (π)), β
2,π(π (π)), . . . , β
π‘,π(π (π)), . . . , β
π,π(π (π))],
(1 < π < π‘) , (1 < π < π) .
(29)
Figure 1: Datasets: Caltech-101 Example.
5. Experimental ResultIn the experiment, we proposed the homogenous kernel-hashing algorithm and verified the high efficiency on thedataset. In our scheme, homogenous kernel-KLSH methodmakes it possible to get the unknown feature embeddings.We use these features to conduct vision search task to locatethe most similar items in the database, and the neighbors wefind in the task will give their scores on the tags. The methodproved to be more effective and accurate than the linear scansearch.
In this part, we design and verify our algorithm on theCaltech-101 dataset in Figure 1. Caltech-101 dataset is a bench-mark on image recognition and classification, which has 101categories objects and each category has about 100 images,so 10000 images totally. In recent years, many researchershave done useful research on this dataset such us proposingsome important and useful image represent kernels [19].Also there are many published papers that focused on thisdataset, some of which are very valuable and significantlyhistoric. For example, papers [20β22], respectively, state theircontribution to the dataset. The author of [21] proposed thematching method for pyramid kernel of images histograms,while Berg [20] proposed and created the CORR kernel of
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50 100 150 200 250 300
0.58
0.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
Number of hash bits50 100 150 200 250 300
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0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.7
0.71
0.72
10 15 20 25 30 35 40 45 50 55 600.63
0.64
0.65
0.66
0.67
0.68
0.69
0.7
0.71
0.72
Value of n
Value of t
SIFT-RBF and π2 Lin scanSIFT-RBF and π2 KLSH
SIFT-RBF and π2 Lin scanSIFT-RBF and π2 KLSH
SIFT-RBF and π2 Lin scanSIFT-RBF and π2 KLSH
k-N
N ac
cura
cy
k-N
N ac
cura
cy
k-N
N ac
cura
cy
Figure 2: Hashing using a RBF-π2 kernel for SIFT based on homogenous kernels π2 (πΎ = 1/2). We choose π‘ = 30, π = 300, and π = 300 inour experiment.
image local feature using geometric blur for matching localimage similarity.
In our paper, we apply our algorithm to complete thevision classification and similar search task. The platform ofour benchmark is based on Intel 4 core 3.6GHZ CPU and16GB of memory and 2 TB hard disk.
We used π2 kernel for πΎ-homogeneous kernel maps (πΎ =1/2) and applied the nonlinear RBF-π2 kernel designed in[19, 23] to the SIFT-based local feature.Meanwhile we appliedand learnt the homogenous kernel map beyond it. Comparedwith the nonlearnt kernel, our learnt kernel has been moreaccurate. And we use KNN classifier, respectively, for KLSHand linear scan to compute the accuracy of classification. Wealso compare it with CORR [24] and the result proves to bebetter than them, here we use 15 images per class for trainingtask.
From Figure 2 we can see that the growth of parametersis closely related with accuracy. As is seen, the accuracyincreased with the increase of π, while it has little relationshipwith the number of π‘ and π. The value of (π, π‘, π) is chosen asπ = 300, π = 300, π‘ = 30 as the best parameters through aseries of experiments.
We find that the combination of these parameters canresult in better performance than the large-scale dataset.Meanwhile it can be seen that our approach with homoge-nous kernel map has higher accuracy than CORR-KLSHwithmetric learning [25].
Figure 3 illustrates that our method is superior to otherexisting approaches [25β28] tested on this dataset. Compar-ing with other kernel classifiers, our classifier with RBF-π2kernel for local features performs better. In Table 2 we cansee that the result of ours has higher accuracy with π = 15
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5 10 15 20 25 3010
20
30
40
50
60
70
80
Number of training examples per class
Mea
n re
cogn
ition
rate
per
clas
s
[19][27][26][21][23][25]
[7]Ours[1][4][16, 24]
Caltech-101 categories data set
Figure 3: Comparison against existing techniques on the Caltech-101.
2 4 6 8 10 12 14 16 18 200.52
0.54
0.56
0.58
0.6
0.62
0.64
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0.68
0.7
Number of nearest neighbors
Prob
abili
ty o
f acc
urat
e mat
ch
2 4 6 8 10 12 14 16 18 201.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Number of nearest neighbors
CPU
sect
ion
SIFT-RBF and π2 with homogenous kernel SIFT-RBF and π2 with homogenous kernel
Figure 4: Classification beyond CPU load performance.
and π = 30 than other papersβ results including better than[24] which obtains the result by 61% for π = 15 and 69.6%for π = 30. More clearly, it has improved the result by 16%several years ago.
In order to find the best parameters in our experimentfor NN search for our scheme, we should take into accountthe balance between performance and CPU time. Thereforehere we conducted to analyze the performance and CPU timeof different of π (π = 2, 3, . . . , 20) for NN search. Figure 4
illustrates the accuracy and CPU time by each π in ourdataset.
The author of [26] proposed the method by combiningKPCA and normal LSH. That means computing hashingbeyond the KPCA. However this method has apparentdisadvantage because KPCA will bring on the loss of inputinformation although it can reduce the dimensionality in theprocessing, while KLSH can solve this problem to assure theintegrity of input information to compute the LSH.Therefore
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Table 2: Accuracy of Caltech-101.
#train Ours [18] [29] [30] [31] [32] [33]15 68.5 59.05 56.4 52 51 49.52 4430 75.2 66.23 64.6 N/A 56 58.23 63
we found that our method has high accuracy and betterperformance than the algorithm in [26].
6. Conclusions
In our paper, we properly use the concept of homogeneouskernel maps to help us to solve the problem of approximationof those kernels, including those commonly used in machinelearning such as π2, JS, Hellingerβs, and intersection kernels.Combining with the KLSH scheme, it enables us to haveaccess to any kernel function for hashing functions. Althoughour approach is inferior to linear scan search in time but itcan guarantee that the search accuracy will not be affected.Moreoverwe do not need to consider the distribution of inputdata; to some extent, it can be applicable for many otherdatabases as Flicker and Tiny Image. Experimental resultsdemonstrate that it is superior to standard KLSH algorithm.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgments
The authors would like to thank Brian Kulis from UCBerkeley University for helpful comments on experimentsand also they should thank Professor Yan Shuicheng foradvice on their paper. The work was supported in part bythe National Program on Key Basic Research Project (973Program) 2010CB731403/2010CB731406.
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