【摘要】：數(shù)據(jù)分類作為機(jī)器學(xué)習(xí)最基礎(chǔ)的學(xué)習(xí)任務(wù)之一,隨著網(wǎng)絡(luò)化信息化的發(fā)展,所需分類的數(shù)據(jù)復(fù)雜程度越來(lái)越高。多核學(xué)習(xí)因描述數(shù)據(jù)特征能力強(qiáng),是復(fù)雜數(shù)據(jù)集分類的有效方法理論。從分類角度看,數(shù)據(jù)集分為輸入數(shù)據(jù)部分,是數(shù)據(jù)的空間或?qū)傩孕畔?和相對(duì)應(yīng)的輸出數(shù)據(jù)部分,是數(shù)據(jù)的類別標(biāo)號(hào)信息。輸入數(shù)據(jù)樣本,來(lái)自自然世界或工程,其往往存在固有的制約或約束關(guān)系,這種關(guān)系本質(zhì)上可以用數(shù)學(xué)流形來(lái)描述。輸入數(shù)據(jù)樣本在其空間中所具備的流形約束,是數(shù)據(jù)的本征特征,是人來(lái)識(shí)別目標(biāo)的重要信息。然而,多核分類方法尚未充分利用輸入數(shù)據(jù)樣本的流形約束信息。為了利用輸入數(shù)據(jù)樣本的流形約束信息,本文提出了一種具有輸入數(shù)據(jù)樣本流形約束信息的監(jiān)督型的流形正則化多核分類模型。為獲取輸入數(shù)據(jù)樣本在其空間中的流形約束信息,需要描述它們?cè)诳臻g中的近鄰關(guān)系程度,本文應(yīng)用了能細(xì)致地評(píng)價(jià)數(shù)據(jù)間近鄰關(guān)系的Hellinge r(?)巨離；同時(shí),考慮了輸出數(shù)據(jù)所表達(dá)的類別標(biāo)號(hào)信息作用,即同類別數(shù)據(jù)間的近鄰關(guān)系程度比不同類數(shù)據(jù)間的近鄰關(guān)系程度較高的一般性知識(shí)。最后,本文給出了考慮標(biāo)號(hào)信息的監(jiān)督型的輸入數(shù)據(jù)樣本流形約束的流形正則項(xiàng),將其引入監(jiān)督型的多核分類模型,建立了一種具有輸入數(shù)據(jù)樣本流形約束的監(jiān)督型的流形正則化多核分類模型,給出了該模型的求解算法。監(jiān)督分類仿真試驗(yàn)對(duì)比的結(jié)果表明,本文提出的一種具有輸入數(shù)據(jù)樣本流形約束的監(jiān)督型的流形正則化多核分類模型是有效的。針對(duì)實(shí)際工程中,數(shù)據(jù)的輸出部分普遍是有標(biāo)號(hào)和無(wú)標(biāo)號(hào)同時(shí)存在的事實(shí),本文將具有輸入數(shù)據(jù)樣本流形約束的監(jiān)督型的流形正則化多核分類模型拓展成為一種半監(jiān)督的分類模型。首先,通過(guò)歐氏距離來(lái)獲取全體輸入數(shù)據(jù)樣本之間的近鄰關(guān)系,并以此得到輸入數(shù)據(jù)樣本的流形約束信息；然后,擴(kuò)展監(jiān)督型的流形正則化多核分類模型中的多核函數(shù)在全體輸入數(shù)據(jù)樣本下的矩陣并計(jì)算全體輸入數(shù)據(jù)樣本的流形約束信息的流形正則信息；從而,拓展模型成為能夠綜合利用有標(biāo)號(hào)和無(wú)標(biāo)號(hào)數(shù)據(jù)樣本的一種半監(jiān)督型的流形正則化多核分類模型。本文給出了這種半監(jiān)督型的流形正則化多核分類模型的求解算法、誤差分析和半監(jiān)督分類仿真試驗(yàn)對(duì)比,試驗(yàn)結(jié)果表明了該模型在半監(jiān)督分類中的有效性。針對(duì)本文給出的一種半監(jiān)督型的流形正則化多核分類模型,一方面為提高該模型的自適應(yīng)性和分類準(zhǔn)確性,本文提出了半監(jiān)督型的流形正則化多核分類模型中的多核函數(shù)的參數(shù)的自動(dòng)選擇方法；另一方面,本文改進(jìn)了半監(jiān)督型的流形正則化多核分類模型中的多核組合權(quán)值的約束形式,給出p范數(shù)約束多核組合權(quán)值的模型一般解。在提出的多核函數(shù)中的參數(shù)自動(dòng)選擇方面,本文通過(guò)改進(jìn)半監(jiān)督型的流形正則化多核分類模型的數(shù)學(xué)表達(dá)式并設(shè)計(jì)求解算法,將待選的核函數(shù)參數(shù)值轉(zhuǎn)化為算法的解,實(shí)現(xiàn)自動(dòng)地確定核函數(shù)參數(shù)的具體取值。在改進(jìn)多核組合權(quán)值的約束方面,通過(guò)將半監(jiān)督型的流形正則化多核分類模型中的多核組合權(quán)值的固定的1范數(shù)約束,改進(jìn)為一般性的p范數(shù)約束,并給出了p范數(shù)約束多核組合權(quán)值的半監(jiān)督流形正則化多核分類模型的求解定理及其證明。對(duì)于兩方面改進(jìn)后的半監(jiān)督分類模型,本文分別做了半監(jiān)督分類仿真試驗(yàn)對(duì)比。試驗(yàn)結(jié)果表明,本文提出的核函數(shù)參數(shù)自動(dòng)選擇的半監(jiān)督流形正則化多核分類模型和p范數(shù)約束多核組合權(quán)值的半監(jiān)督流形正則化多核分類模型是有效的。
[Abstract]:Data classification is one of the most basic learning tasks of machine learning. With the development of networked information, the data complexity of the required classification is getting higher and higher. Multi-core learning is an effective method for classification of complex data sets due to the strong ability of describing data features. From a classification point of view, the data set is divided into an input data portion, a spatial or attribute information of the data, and a corresponding output data portion, which is the category label information of the data. Input data samples, from natural world or engineering, often have inherent constraints or constraints, which can be described in nature by a mathematical manifold. The manifold constraints of the input data samples in their space are the intrinsic characteristics of the data and are important information for people to identify the target. However, the multi-core classification method has not fully utilized the manifold constraint information of the input data samples. In order to use the manifold constraint information of the input data samples, this paper presents a supervised manifold regularization multi-core classification model with input data sample manifold constraint information. In order to obtain the manifold constraint information of the input data samples in their space, it is necessary to describe their neighbor relation degree in space. ) At the same time, the class label information, which is expressed by the output data, is considered, that is, the degree of neighbor relation between the same class data is higher than that of the neighbor relation among the different class data. In the end, this paper gives a manifold regularized multi-core classification model with a supervised type of input data sample manifold constraint, considering the manifold regular term of the supervised type input data sample manifold constraint of the reference label information, and establishing a supervised type manifold regularized multi-core classification model with input data sample manifold constraint. The algorithm of this model is given. The results of the comparison of supervised classification simulation tests show that a supervised manifold regularization multi-core classification model with input data sample manifold constraints is effective. In the actual project, the output part of the data is generally the fact that the reference number and the no-label are present at the same time. In this paper, a supervised type manifold regularization multi-core classification model with input data sample manifold constraints is expanded into a semi-supervised classification model. First, the neighbor relation between all input data samples is obtained by the Euclidean distance, and the manifold constraint information of the input data sample is obtained; and then, the multi-kernel function in the extended-supervised manifold regularized multi-core classification model is used for the matrix of all input data samples and the manifold regular information of the manifold constraint information of all the input data samples is calculated; therefore, The expansion model is a kind of semi-supervised manifold regularized multi-core classification model which can comprehensively utilize the data samples with the label and the no-label. In this paper, the solution algorithm, the error analysis and the semi-supervised classification simulation test of the semi-supervised manifold regularized multi-core classification model are presented. The results show the effectiveness of the model in the semi-supervised classification. In order to improve the self-adaptability and classification accuracy of the model, a semi-supervised manifold regularized multi-core classification model is presented in this paper. On the one hand, the automatic selection method of the parameters of a multi-kernel function in a semi-supervised manifold regularization multi-core classification model is proposed. On the other hand, In this paper, the constrained form of multi-core combined weight in a semi-supervised manifold regularized multi-core classification model is improved, and a model general solution of a p-norm constrained multi-core combined weight is given. In this paper, by improving the mathematical expression of the semi-supervised manifold regularization multi-core classification model and designing the solution algorithm, the kernel function parameter value to be selected is transformed into the solution of the algorithm. And the specific value of the kernel function parameter is automatically determined. in the aspect of improving the constraint of the multi-core combined weight, the general p-norm constraint is improved by the fixed 1-norm constraint of the multi-core combination weight in the semi-supervised manifold regularization multi-core classification model, The solution theorem of the semi-supervised manifold regularized multi-core classification model with p-norm constrained multi-core combined weight and its proof are given. In this paper, the semi-supervised and semi-supervised classification model is compared with the two-aspect improved semi-supervised classification model. The experimental results show that the semi-supervised manifold regularized multi-core classification model and the semi-supervised manifold regularized multi-core classification model of the auto-selected semi-supervised manifold regularized multi-core classification model and the p-norm constrained multi-core combined weight are effective.
【學(xué)位授予單位】：北京科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP181

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