本文選題：數(shù)據(jù)降維　切入點(diǎn)：非負(fù)矩陣分解　出處：《遼寧工業(yè)大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來，隨著多媒體技術(shù)的快速發(fā)展，獲得高質(zhì)量的圖像變得越來越容易，如何對這些高質(zhì)量的圖像進(jìn)行表示和分類成為最近的研究熱點(diǎn)。一方面，高質(zhì)量的圖像具有高維性，高維性使得圖像特征更加豐滿；另一方面，高維性卻給人們的處理帶來了困難，這些利于圖像表示的高維數(shù)據(jù)往往會(huì)造成“維度災(zāi)難”。所以，在對圖像進(jìn)行分類之前要進(jìn)行必要的降維表示。 目前，數(shù)據(jù)降維有許多方法，但大多數(shù)分解方法的結(jié)果中允許負(fù)值存在，很顯然這些負(fù)值在實(shí)際問題中沒有物理意義。非負(fù)矩陣分解方法則是在保證非負(fù)值的情況下進(jìn)行的降維。這種降維方法一方面使得數(shù)據(jù)得到了降維，數(shù)據(jù)具有純加性和一定的稀疏性，純加性凸顯了分解的合理性，稀疏性可以抑制外界對數(shù)據(jù)特征的影響，具有一定的魯棒性；另一方面對非負(fù)數(shù)據(jù)進(jìn)行分解時(shí)采用了簡單有效的迭代算法，通過不斷的學(xué)習(xí)得到了含有圖像局部特征的信息，符合人類認(rèn)知事物由部分到整體的感知過程。 圖像表示和分類是模式識別領(lǐng)域內(nèi)非常重要的課題。在圖像分類過程中，對圖像特征提取是否合理以及對圖像分類所用分類函數(shù)是否最優(yōu)將會(huì)直接影響圖像的分類結(jié)果。本文應(yīng)用了非負(fù)矩陣分解算法的相關(guān)理論對圖像數(shù)據(jù)進(jìn)行降維表示和局部特征提取，進(jìn)而進(jìn)行分類。本文針對圖像處理領(lǐng)域的內(nèi)容研究了稀疏約束非負(fù)矩陣分解、圖正則化非負(fù)矩陣分解、標(biāo)簽約束非負(fù)矩陣分解等理論。綜合這些理論本文提出了三種改進(jìn)的非負(fù)矩陣分解算法，包括基于稀疏約束的半監(jiān)督非負(fù)矩陣分解算法、基于稀疏約束的圖正則化半監(jiān)督非負(fù)矩陣分解、基于稀疏和先驗(yàn)約束的有監(jiān)督非負(fù)矩陣分解。在完成圖像降維和特征提取后，本文利用K均值進(jìn)行聚類，而對于監(jiān)督的非負(fù)矩陣分解算法為了使分類效果更好，本文結(jié)合了支持向量機(jī)理論進(jìn)行分類。本文在常見的人臉數(shù)據(jù)集和物體數(shù)據(jù)集上進(jìn)行了實(shí)驗(yàn)，實(shí)驗(yàn)表明本文的算法具有合理性和有效性。
[Abstract]:In recent years, with the rapid development of multimedia technology, it becomes more and more easy to obtain high quality images. How to represent and classify these high quality images has become a research hotspot. On the one hand, high quality images have high dimension. On the other hand, the high dimension makes it difficult for people to deal with it, and the high-dimensional data which is good for image representation will often cause "dimensionality disaster". The necessary dimensionality reduction representation should be made before the image is classified. At present, there are many methods to reduce the dimension of data, but the results of most decomposition methods allow negative values to exist. It is obvious that these negative values have no physical significance in practical problems. The non-negative matrix factorization method is a dimensionality reduction method that guarantees the non-negative values. On the one hand, this dimensionality reduction method results in the reduction of the dimension of the data. Data has pure additivity and certain sparsity, pure additivity highlights the rationality of decomposition, sparsity can restrain the external influence on data characteristics, and it has certain robustness. On the other hand, a simple and effective iterative algorithm is used to decompose the non-negative data. Through continuous learning, the information containing local features of the image is obtained, which accords with the perception process of human cognition from part to whole. Image representation and classification is a very important topic in the field of pattern recognition. Whether the image feature extraction is reasonable or not and whether the classification function used in image classification is optimal will directly affect the image classification results. This paper applies the theory of non-negative matrix decomposition algorithm to reduce the dimension of image data. Display and local feature extraction, In this paper, sparse constrained nonnegative matrix decomposition, graph regularized nonnegative matrix decomposition, and image processing are studied. This paper presents three improved nonnegative matrix factorization algorithms, including semi-supervised nonnegative matrix decomposition algorithm based on sparse constraints. The graph regularized nonnegative matrix decomposition based on sparse constraints and the supervised nonnegative matrix factorization based on sparse and prior constraints. After image reduction and feature extraction, K-means clustering is used in this paper. In order to make the classification effect better, the supervised non-negative matrix decomposition algorithm is combined with the support vector machine theory. Experiments show that the proposed algorithm is reasonable and effective.
【學(xué)位授予單位】：遼寧工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TP391.41;O151.21

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