• Proceedings of the Korea Contents Association Conference
• /
• 2007.11a
• /
• pp.217-220
• /
• 2007

LLE(Locally Linear Embedding) has been proposed to compute low dimensional, neighborhood preserving embeddings of high dimensional data. Here, we should perform whole processes of LLE when untrained patterns are presented. In this paper, we propose a training of MLPs(Multilayer Perceptrons) to perform the mapping of LLE from high dimensional data to low dimensional ones.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.517-523
• /
• 1998

In this paper we prove that a normed almost linear space \hat{X} can be embedded in a normed linear space X when a normed almost linear space X has a basis and splits as X=V+W. Also we have a metric induced by a norm on a normed almost linear space as a corollary.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.661-671
• /
• 2007

We investigate the number of knots and links in linear embeddings of $K_6$, the complete graph with 6 vertices. Concretely, we show that any linear embedding of $K_6$ contains either only one Hopf link, or three Hopf links and one trefoil knot.

• Journal of KIISE
• /
• v.42 no.2
• /
• pp.235-241
• /
• 2015

Locally linear embedding (LLE) [1] is a type of manifold algorithms, which preserves inner product value between high-dimensional data when embedding the high-dimensional data to low-dimensional space. LLE closely embeds data points on the same subspace in low-dimensional space, because the data points have significant inner product values. On the other hand, if the data points are located orthogonal to each other, these are separately embedded in low-dimensional space, even though they are in close proximity to each other in high-dimensional space. Meanwhile, it is well known that the facial images of the same person under varying illumination lie in a low-dimensional linear subspace [2]. In this study, we suggest an improved LLE method for face recognition problem. The method maximizes the characteristic of LLE, which embeds the data points totally separately when they are located orthogonal to each other. To accomplish this, all of the subspaces made by each class are forced to locate orthogonally. To make all of the subspaces orthogonal, the simultaneous Diagonalization (SD) technique was applied. From experimental results, the suggested method is shown to dramatically improve the embedding results and classification performance.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.7
• /
• pp.3353-3370
• /
• 2016

The way of combination of Product Perfect Codes (PPCs) is based on the theory of short codes constructing long codes. PPCs have larger embedding rate than Hamming codes by expending embedding columns in a coding block, and they have been proven to enhance the performance of the F₅ steganographic method. In this paper, the proposed modified product codes called MPCs are introduced as an efficient way to embed more data than PPCs by increasing 2^r₂-1-r₂ embedding columns. Unlike PPC, the generation of the check matrix H in MPC is random, and it is different from PPC. In addition a simple solving way of the linear algebraic equations is applied to figure out the problem of expending embedding columns or compensating cases. Furthermore, the MPCs over ℤ₄ have been proposed to further enhance not only the performance but also the computation speed which reaches O(n₁+σ). Finally, the proposed ℤ₄-MPC intends to maximize the embedding rate with maintaining less distortion , and the performance surpasses the existing improved product perfect codes. The performance of large embedding rate should have the significance in the high-capacity of covert communication.

• Journal of KIISE:Software and Applications
• /
• v.31 no.2
• /
• pp.182-188
• /
• 2004

This paper proposes to synthesize facial images from a few parameters for the pose and the expression of their constituent components. This parameterization makes the representation, storage, and transmission of face images effective. But it is difficult to parameterize facial images because variations of face images show a complicated nonlinear manifold in high-dimensional data space. To tackle this problem, we use an LLE (Locally Linear Embedding) technique for a good representation of face images, where the relationship among face images is preserving well and the projected manifold into the reduced feature space becomes smoother and more continuous. Next, we apply a snake model to estimate face feature values in the reduced feature space that corresponds to a specific pose and/or expression parameter. Finally, a synthetic face image is obtained from an interpolation of several neighboring face images in the vicinity of the estimated feature value. Experimental results show that the proposed method shows a negligible overlapping effect and creates an accurate and consistent synthetic face images with respect to changes of pose and/or expression parameters.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.11 no.7
• /
• pp.3594-3607
• /
• 2017

The traditional feature extraction methods such as principal component analysis (PCA) cannot obtain the local structure of the samples, and locally linear embedding (LLE) cannot obtain the global structure of the samples. However, a common drawback of existing PCA and LLE algorithm is that they cannot deal well with the sparse problem of the samples. Therefore, by integrating the globality of PCA and the locality of LLE with a sparse constraint, we developed an improved and unsupervised difference algorithm called Sparse Difference Embedding (SDE), for dimensionality reduction of high-dimensional data in small sample size problems. Significantly differing from the existing PCA and LLE algorithms, SDE seeks to find a set of perfect projections that can not only impact the locality of intraclass and maximize the globality of interclass, but can also simultaneously use the Lasso regression to obtain a sparse transformation matrix. This characteristic makes SDE more intuitive and more powerful than PCA and LLE. At last, the proposed algorithm was estimated through experiments using the Yale and AR face image databases and the USPS handwriting digital databases. The experimental results show that SDE outperforms PCA LLE and UDP attributed to its sparse discriminating characteristics, which also indicates that the SDE is an effective method for face recognition.

• Journal of Broadcast Engineering
• /
• v.14 no.1
• /
• pp.81-84
• /
• 2009

This paper explores the possibility of describing objects from the change in the shape according to the change in viewpoint. Specifically, we sample the shapes from various viewpoints of a 3-D model, and apply dimension reduction by locally linear embedding. A low dimensional distribution of points are constructed, and characteristics of the object are described from this distribution. Also, we propose two 3-D retrieval methods by applying the iterative closest point algorithm, and by applying Fourier transform and measuring similarity by modified Housdorff distance, and present experimental results. The proposed method shows that the change of shape according to the change in viewpoint can describe the characteristics of an object.

• Smart Media Journal
• /
• v.8 no.2
• /
• pp.74-79
• /
• 2019

Traditional compound noun decomposition algorithms often face challenges of decomposing compound nouns into separated nouns when unregistered unit noun is included. It is very difficult for those traditional approach to handle such issues because it is impossible to register all existing unit nouns into the dictionary such as proper nouns, coined words, and foreign words in advance. In this paper, in order to solve this problem, compound noun decomposition problem is defined as tag sequence labeling problem and compound noun decomposition method to use syllable unit embedding and deep learning technique is proposed. To recognize unregistered unit nouns without constructing unit noun dictionary, compound nouns are decomposed into unit nouns by using LSTM and linear-chain CRF expressing each syllable that constitutes a compound noun in the continuous vector space.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.7
• /
• pp.2892-2913
• /
• 2016

Network virtualization promises to play a dominant role in shaping the future Internet by overcoming the Internet ossification problem. However, due to the injecting of additional virtualization layers into the network architecture, several new security risks are introduced by the network virtualization. Although traditional protection mechanisms can help in virtualized environment, they are not guaranteed to be successful and may incur high security overheads. By performing the virtual network (VN) embedding in a security-aware way, the risks exposed to both the virtual and substrate networks can be minimized, and the additional techniques adopted to enhance the security of the networks can be reduced. Unfortunately, existing embedding algorithms largely ignore the widespread security risks, making their applicability in a realistic environment rather doubtful. In this paper, we attempt to address the security risks by integrating the security factors into the VN embedding. We first abstract the security requirements and the protection mechanisms as numerical concept of security demands and security levels, and the corresponding security constraints are introduced into the VN embedding. Based on the abstraction, we develop three security-risky modes to model various levels of risky conditions in the virtualized environment, aiming at enabling a more flexible VN embedding. Then, we present a mixed integer linear programming formulation for the VN embedding problem in different security-risky modes. Moreover, we design three heuristic embedding algorithms to solve this problem, which are all based on the same proposed node-ranking approach to quantify the embedding potential of each substrate node and adopt the k-shortest path algorithm to map virtual links. Simulation results demonstrate the effectiveness and efficiency of our algorithms.