• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권2호
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• pp.121-125
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• 2015

In this paper, we propose a method that extracts features from character patterns using the fractal dimension of chaos theory. The input character pattern image is converted into time-series data. Then, using the modified Henon system suggested in this paper, it determines the last features of the character pattern image after calculating the box-counting dimension, natural measure, information bit, and information (fractal) dimension. Finally, character pattern recognition is performed by statistically finding each information bit that shows the minimum difference compared with a normalized character pattern database.

• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.93-103
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• 2016

In the paper, we discuss dimension reduction of predictors ${\mathbf{X}}{\in}{{\mathbb{R}}^p}$ in a regression of $Y{\mid}{\mathbf{X}}$ with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors ${\mathbf{X}}$ are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central $k^{th}$-moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of ${\mathbf{X}}$ are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of ${\mathbf{X}}$ and the conditional distribution of $Y{\mid}{\mathbf{X}}$. A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.

• 음성과학
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• 제4권2호
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• pp.25-39
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• 1998

This paper deals with fuzzy correlation dimension for an appropriate speech recognition. The proposed fuzzy correlation dimension has absorbed time variation value of strange attractor as utilizing fuzzy membership function at calculation of integral correlation when the results of proposed dimension are applied to speech recognition fuzzed correlation dimension is superior to speech recognition, and correlation dimension is superior to speaker discrimination.

• 대한수학회논문집
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• 제39권2호
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• pp.303-311
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• 2024

In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring (R, 𝔪), any homologically finite complex X with a finite Cohen-Macaulay dimension possesses a finite CM-resolution. This means that there exists a bounded complex G of finitely generated R-modules, such that G is isomorphic to X and each nonzero G_i within the complex G has zero Cohen-Macaulay dimension.

• 한국주조공학회지
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• 제5권4호
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• pp.283-288
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• 1985

The melt of highly purified Zn was poured by top pouring process into the open green sand mold, that was made by using the 3-plane L-sections pattern. After skin was formed, the unsolified melt was poured out by rolling-over. The thicknesses of skin for each different of castings were investigated with one dimension. The results obtained and could be summerzed as follows: 1) While the 3-plant L-sections castings were solidifying in the mold, solidification blocks of different section modulus in the castings were formed, i.e. 1-dimension divergency block, 2-dimension heat divergency block, 3-dimension heat divergency block, 2-dimension heat convergency block, and 3-dimension heat convergency block. 2) When the chill plate was set up to the mold in order to change section modulus artificially, heat divergency blocks and heat convergency blocks according to the shape of chill plate were revealed.

• 한국통신학회논문지
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• 제19권6호
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• pp.1140-1148
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• 1994

본 논문에서는 음성신호의 프랙탈 차원을 이용하여 한국어 모음인식 실험을 수행하였다. 프랙탈 차원은 Minkowski-Bouligand 차원을 사용하였으며, 형태학적 커버링(morphological covering) 방법을 이용하여 구하였다. 프렉탈 차원과 더불어 기존에 우수한 음성 인식 파라메타로 알려져 있는 LPC 켐스트럼(cepstrum)을 함께 사용하였으며, 프랙탈 차원의 음성인식에의 유용성 여부를 조사하였다. 다양한 자음환경에서의 모음인식 실험결과, LPC 켐스트럼 만을 사용하는 경우 및 프렉탈 차원과 LPC 켐스트럼을 함께 사용하는 경우의 모음 오인식율이 각각 5.6% 및 3.2%로 얻어졌다. 이는 LPC 켑스트럼에 프렉탈 차원을 추가함으로써 오인식되는 데이터가 40%이상 감소되는 결과이며, 프랙탈 차원이 음성인식에 있어서 유용한 특징 파라메터임을 보여준다.

• 농촌지도와개발
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• 제9권2호
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• pp.215-231
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• 2002

The objectives of this study were (1) to measure the level of satisfaction on rural for local public service. (2) and analyse variables related to the public service. Reviewing the literature and related studies for theoretical framework, Six criteria characterize public service : (1) responsiveness. (2) convenience, (3) speed, (4) correctness, (5) pleasantness, (6) equality, which are reflected in the instrument of this study. By the results of analysis, two dimensions (convenience, responsiveness) and total satisfaction are related to their residential lengths of the same rural area. For the total public service satisfaction gender, age, educational level, income level, occupation, and residential years explained in 13.3% For the convenience dimension their variables accounted for 22.4%. For responsiveness dimension their variables interpreted in 23.2%. For speed and correctness dimension their variables explained in 21.6%. For pleasantness dimension their variables accounted for local public services in 15.3%. For equality dimension their variables explained in 16.2%.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.43-57
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• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.759-769
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• 2005

We first discuss jump discontinuity in higher dimension, and then prove a local convergence theorem for wavelet approximations in higher dimension. We also redefine the concept of Gibbs phenomenon in higher dimension and show that wavelet expansion exhibits Gibbs phenomenon.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권2호
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• pp.522-539
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• 2021

In order to solve the problems of the existing audio fingerprint method when extracting audio fingerprints from long speech segments, such as too large fingerprint dimension, poor robustness, and low retrieval accuracy and efficiency, a robust audio fingerprint retrieval method based on feature dimension reduction and feature combination is proposed. Firstly, the Mel-frequency cepstral coefficient (MFCC) and linear prediction cepstrum coefficient (LPCC) of the original speech are extracted respectively, and the MFCC feature matrix and LPCC feature matrix are combined. Secondly, the feature dimension reduction method based on information entropy is used for column dimension reduction, and the feature matrix after dimension reduction is used for row dimension reduction based on energy feature dimension reduction method. Finally, the audio fingerprint is constructed by using the feature combination matrix after dimension reduction. When speech's user retrieval, the normalized Hamming distance algorithm is used for matching retrieval. Experiment results show that the proposed method has smaller audio fingerprint dimension and better robustness for long speech segments, and has higher retrieval efficiency while maintaining a higher recall rate and precision rate.