基于FCA的概念學(xué)習(xí)研究
發(fā)布時間：2019-06-29 15:03
【摘要】：隨著信息技術(shù)的不斷發(fā)展,人們獲取數(shù)據(jù)的方式不再單一,如電視、報紙、互聯(lián)網(wǎng)等,獲取數(shù)據(jù)的周期也在不斷減小。面對海量的結(jié)構(gòu)化、非結(jié)構(gòu)化、半結(jié)構(gòu)化的數(shù)據(jù),如何快速有效的從中挖掘出潛在的價值是當(dāng)前的研究熱點,同時也是機器學(xué)習(xí)面臨的挑戰(zhàn)和機遇。粗糙集理論是Pawlak于1982年提出,并廣泛應(yīng)用于數(shù)據(jù)挖掘、機器學(xué)習(xí)、決策分析等領(lǐng)域。形式概念分析(FCA)是由R.Wille于1982年提出的一種知識發(fā)現(xiàn)的數(shù)學(xué)工具,它被廣泛應(yīng)用于數(shù)據(jù)挖掘,聚類,分類等領(lǐng)域。粗糙集主要應(yīng)用于不確定性的知識表達(dá),FCA主要是挖掘同類事物與事物所具有的屬性之間的內(nèi)在關(guān)系,粗糙集和FCA結(jié)合可以挖掘事物與其所具有的屬性之間的不確定性關(guān)系。在多途徑獲取信息的時代,從單一的信息源獲取的信息往往是模糊或不完備的,因此將多個信息源獲取的信息融合起來就顯得非常有必要了,融合的目的是將多個信源的信息融合為一個信息量更大的信息體,使得融合有“1+12”的效果。本文正是基于FCA的主要特征概念學(xué)習(xí)和多源模糊概念學(xué)習(xí),研究了主要特征和信息融合的數(shù)學(xué)性質(zhì),同時設(shè)計了融合算法和模糊概念學(xué)習(xí)算法,并通過數(shù)值實驗驗證本文所提方法的有效性,本文的主要創(chuàng)新點如下:1.在形式背景中定義a主要特征,并用數(shù)學(xué)語言闡述了必然特征與似然特征的差別,研究形式背景中基礎(chǔ)比率對認(rèn)知的影響,結(jié)合基礎(chǔ)比率和a主要特征定義特征與概念之間的可信度,研究了可信度是如何表達(dá)擁有某一屬性(特征)的對象在屬于概念的可信程度,并討論了可信度與主要特征之間的關(guān)系。最后通過案例的計算過程來展示可信度在度量對象的歸屬問題上比單一的主要特征好,并驗證了模型的有效性和可行性。2.條件熵是信息的一種度量方式,基于條件熵的信息融合可以在減少冗余信息的同時提高分類的質(zhì)量,使得相似類更細(xì),即同一類別的對象之間的差別較小,不同類別之間的差別較大。在融合的基礎(chǔ)之上進(jìn)行模糊概念學(xué)習(xí),并根據(jù)提出的條件熵融合方法設(shè)計了對應(yīng)的條件熵融合算法,在此基礎(chǔ)上設(shè)計了基于對象信息和屬性信息的兩種模糊概念學(xué)習(xí)算法,然后使用UCI數(shù)據(jù)集設(shè)計了一系列的數(shù)值實驗,將本所提出的條件熵融合與傳統(tǒng)的均值融合進(jìn)行對比,驗證條件熵融合在減少冗余信息的同時提高了分類的質(zhì)量,而均值融合僅僅是運用統(tǒng)計方法將多源的信息進(jìn)行均值壓縮,不能提高分類的質(zhì)量。
[Abstract]:With the continuous development of information technology, the way for people to obtain data is no longer single, such as television, newspapers, the Internet and so on, and the cycle of obtaining data is also decreasing. In the face of massive structured, unstructured and semi-structured data, how to dig out the potential value quickly and effectively is not only the current research focus, but also the challenge and opportunity of machine learning. Rough set theory was put forward by Pawlak in 1982 and is widely used in data mining, machine learning, decision analysis and other fields. Formal concept analysis (FCA) is a mathematical tool of knowledge discovery proposed by R.Wille in 1982. It is widely used in data mining, clustering, classification and other fields. Rough set is mainly used in the knowledge representation of uncertainty. FCA is mainly to mine the internal relationship between the same kind of things and the attributes of the same kind of things. The combination of rough sets and FCA can mine the uncertain relationship between things and their attributes. In the era of multi-channel access to information, the information obtained from a single information source is often fuzzy or incomplete, so it is very necessary to fuse the information obtained from multiple information sources. The purpose of fusion is to fuse the information from multiple sources into a more informative information body, so that the fusion has the effect of "112". In this paper, based on the main feature concept learning and multi-source fuzzy concept learning of FCA, the mathematical properties of main features and information fusion are studied, and the fusion algorithm and fuzzy concept learning algorithm are designed, and the effectiveness of the proposed method is verified by numerical experiments. The main innovations of this paper are as follows: 1. This paper defines the main features of a in the formal background, and expounds the difference between the inevitable features and the likelihood features in mathematical language, studies the influence of the basic ratio on cognition in the formal background, and combines the basic ratio and the credibility between the main features of a definition of features and concepts, and studies how the credibility of the object with a certain attribute (feature) belongs to the concept. The relationship between credibility and main characteristics is also discussed. Finally, the calculation process of the case is used to show that the credibility is better than the single main feature in the problem of measuring the ownership of the object, and the effectiveness and feasibility of the model are verified. 2. Conditional entropy is a measure of information. Information fusion based on conditional entropy can reduce redundant information and improve the quality of classification, which makes similar classes finer, that is, the difference between objects of the same category is small, and the difference between different categories is large. On the basis of fusion, fuzzy concept learning is carried out, and the corresponding conditional entropy fusion algorithm is designed according to the proposed conditional entropy fusion method. On this basis, two fuzzy concept learning algorithms based on object information and attribute information are designed. Then a series of numerical experiments are designed using UCI dataset to compare the proposed conditional entropy fusion with the traditional mean fusion. It is verified that conditional entropy fusion can reduce redundant information and improve the quality of classification, while mean fusion only uses statistical method to compress multi-source information, which can not improve the quality of classification.
【學(xué)位授予單位】：重慶理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP18
本文編號：2507909
[Abstract]:With the continuous development of information technology, the way for people to obtain data is no longer single, such as television, newspapers, the Internet and so on, and the cycle of obtaining data is also decreasing. In the face of massive structured, unstructured and semi-structured data, how to dig out the potential value quickly and effectively is not only the current research focus, but also the challenge and opportunity of machine learning. Rough set theory was put forward by Pawlak in 1982 and is widely used in data mining, machine learning, decision analysis and other fields. Formal concept analysis (FCA) is a mathematical tool of knowledge discovery proposed by R.Wille in 1982. It is widely used in data mining, clustering, classification and other fields. Rough set is mainly used in the knowledge representation of uncertainty. FCA is mainly to mine the internal relationship between the same kind of things and the attributes of the same kind of things. The combination of rough sets and FCA can mine the uncertain relationship between things and their attributes. In the era of multi-channel access to information, the information obtained from a single information source is often fuzzy or incomplete, so it is very necessary to fuse the information obtained from multiple information sources. The purpose of fusion is to fuse the information from multiple sources into a more informative information body, so that the fusion has the effect of "112". In this paper, based on the main feature concept learning and multi-source fuzzy concept learning of FCA, the mathematical properties of main features and information fusion are studied, and the fusion algorithm and fuzzy concept learning algorithm are designed, and the effectiveness of the proposed method is verified by numerical experiments. The main innovations of this paper are as follows: 1. This paper defines the main features of a in the formal background, and expounds the difference between the inevitable features and the likelihood features in mathematical language, studies the influence of the basic ratio on cognition in the formal background, and combines the basic ratio and the credibility between the main features of a definition of features and concepts, and studies how the credibility of the object with a certain attribute (feature) belongs to the concept. The relationship between credibility and main characteristics is also discussed. Finally, the calculation process of the case is used to show that the credibility is better than the single main feature in the problem of measuring the ownership of the object, and the effectiveness and feasibility of the model are verified. 2. Conditional entropy is a measure of information. Information fusion based on conditional entropy can reduce redundant information and improve the quality of classification, which makes similar classes finer, that is, the difference between objects of the same category is small, and the difference between different categories is large. On the basis of fusion, fuzzy concept learning is carried out, and the corresponding conditional entropy fusion algorithm is designed according to the proposed conditional entropy fusion method. On this basis, two fuzzy concept learning algorithms based on object information and attribute information are designed. Then a series of numerical experiments are designed using UCI dataset to compare the proposed conditional entropy fusion with the traditional mean fusion. It is verified that conditional entropy fusion can reduce redundant information and improve the quality of classification, while mean fusion only uses statistical method to compress multi-source information, which can not improve the quality of classification.
【學(xué)位授予單位】：重慶理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP18
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