數位科技的發展及網際網路的盛行，使得巨量的資訊以驚人的速度快速的成長。這些資料都是來自於許多不同的來源，並且使用於不同的用途，因此常出現各種不同的資料型態，例如二值向量 (binary vectors)、多維的數值向量、名義屬性 (nominal attributes)、規則、模糊資料等等。如何有效處理這些不同型態的異質資料，並且在大量的資料中分析出有用的知識、趨勢、或是異常的規則，已經是資訊時代的一項重要課題。近年來知識發掘 (knowledge discovery in databases, KDD) 與資料探勘 (data mining) 的發展，應用了統計方法、機器學習、類神經網路、模糊理論、遺傳演算法等多項技術，正是為了能在大量的資料中找出有用的知識以提供決策分析之需。然而對於異質資料的處理，仍有一些缺失必須克服。首先，目前的技術多僅能處理單一型態的資料，無法直接輸入多種型態的異質資料。異質資料必須事先轉換，但轉換之後常會造成失真的問題。雖然運用模糊數可以同時表示數值及語意的資料，但實際上仍是轉換為數值而處理。而且這種運算的方式，並不適用於無序的名義屬性。其次，傳統的近似函數大都為單一型態的資料而設計，不能直接用來比較混合型態的物件。再者，資料探勘的目標是為了將大量的資料簡化為濃縮的概念。在精簡的過程中為了保持與原始資料的一致性，常必須進行極為耗時的檢查。而且大部分的簡化技術，也不適用於異質的資料型態。
本論文主要著重在前述異質資料學習的幾項關鍵問題，包含異質資料與概念的表示方式、異質物件的相似函數、以及異質概念的一致性學習。首先，本論文結合了數學網絡 (mathematical lattice) 與模糊集合理論，設計出模糊區域 (fuzzy region) 與模糊範例 (fuzzy exemplar) 的表示法，可以同時表示二元數值、精確數值、精確區間、名義屬性、精確規則、模糊數、模糊區間、離散模糊集合、模糊規則等不同資料型態的任意結合。這樣的表示方式，可以用於表示原始的異質資料，也可以表示學習後的異質概念或規則。其次，本論文提出適用於異質資料與概念的相似函數，包含距離函數、有向性的距離函數、以及隸屬度函數。傳統用於離散模糊集合的相似函數，大都必須計算兩個集合的交集程度。若兩者並無交集，其相似程度即為零。這樣的特性可能會降低系統一般化的能力。本論文所提出的相似函數，是將兩相異名義值以機率計算的值差距離 (value difference metric, VDM)，擴充應用於異質模糊集合的比較。這樣就可以得到異質特徵空間中任兩者合理的相似程度，即使兩者並沒有任何交集。再者，本論文以數學網絡理論為基礎，提出一個能有效率維持一致性的學習程序。這樣的程序在縮減樣本大小的學習過程中，可以確保與原始樣本的一致性，卻不必每次都進行耗時的檢查。這個學習程序能依照特徵空間中異質樣本的分佈，在單一資料週期內自動形成合適的判斷區域，並且藉由階層化的學習架構，漸進得到高度精簡的異質概念。這樣不但可以有效降低記憶空間的需求，提高後續分類的速度，卻仍然能維持分類結果與原始資料的一致性。
透過實際資料的實驗結果可以發現，本論文所提出的架構不但可以直接處理各種不同的異質資料與規則，對於所有特徵空間的異質樣本，也都可以計算出其合理的相似程度。而且學習所得的精簡概念，不但大幅降低了記憶空間的需求，其分類結果的一致性，也優於其他的學習方法。再者，簡化過程中不必為了維持一致性而進行耗時的檢查，也大幅提高了學習的速度。這些結果說明本論文所提出的解決方案，結合了數學網絡與模糊集合理論，可以成功應用於不同型態異質的資料，並且能在大量的資料中快速分析出精簡的知識，以作為後續決策分析之需。

Advances in digital technology and Internet have led to the fast growth of huge amounts of information at a phenomenal rate. Such information is gathered from various resources and applied to different applications. Thus, there are disparate types of information such as binary vectors, multidimensional vectors of numbers, nominal attributes, rules, fuzzy data, etc. Dealing properly with heterogeneous data and discovering useful knowledge, trends, and anomalies from vast amounts of data is one of the grand challenges of the information age. In recent years, knowledge discovery in databases (KDD) and data mining which merges together statistics, machine learning, neural networks, fuzzy set theory, genetic algorithms and related areas aims at extracting useful knowledge from large collections of data. However, there still remain deficiencies in the treatment of disparate, heterogeneous information. Firstly, recent approaches always handle only a single data type rather than deal with disparate types of data directly. The disparate heterogeneous data should be transformed into a single data type in advance, but the transformation may cause the problem of distortion. Although fuzzy numbers can express both numeric and linguistic data, they are still treated in the numeric way. Such treatment is not proper for nominal data since they are usually discrete unordered attributes. Secondly, previously proposed similarity measures usually focus on a single data type and cannot be used directly in the comparison of mixed types of information. Furthermore, data mining try to find a reduced set of representatives, but most approaches employ exhaustive verification for maintaining the consistency with the original data. Also, most reduction methods cannot be applied to disparate heterogeneous data.
This research focuses mainly on the critical issues in learning disparate heterogeneous data, including the representation of heterogeneous data and concepts, the similarity measures of heterogeneous objects, and consistency-based learning for heterogeneous concepts. First, this research combines mathematical lattice and fuzzy set theories to design a representation scheme with fuzzy regions and fuzzy exemplars. This representation can express any combination of disparate types of data including binary numbers, crisp numbers, crisp intervals, nominal attributes, crisp rules, fuzzy numbers, fuzzy intervals, discrete fuzzy sets, fuzzy rules, etc. Such representation can be used to represent both the original heterogeneous data, and the discovered heterogeneous concepts or rules. Next, this research proposes a new class of similarity measures that can be applied to heterogeneous data and concepts, including distance measures, directed distance measures, and inclusion measures. A problem with previous similarity measures used to for discrete fuzzy sets is that they should, in most cases, calculate the intersection of two sets. If there is no intersection their similarity will be zero. Such property may decrease the generalization ability of a learner. The suggested similarity measures are based on the value difference metric (VDM) between nominal attributes calculated using probability. The concept of value difference metric is extended and applied for the comparison of heterogeneous fuzzy sets. In this way, the reasonable similarity of any two objects in the discrete universe can be appropriately obtained, even if there is no intersection. Moreover, this research proposes an efficient consistent learning procedure based on mathematical lattice theory. According to this learning procedure, the consistency with the original samples can be ensured while reducing the sample size without doing time consuming verifications. This learning procedure can follow the distribution of heterogeneous data in the feature space, and automatically form a suitable decision region in a single pass through the data. Highly reduced heterogeneous concepts can be gradually condensed following the hierarchical learning scheme. This not only is able to reduce the memory requirement, raise the classification speed, but also is able to sustain the consistency of the classification results with the original data.
The experimental results of real world data sets indicated that the proposed approach can directly process disparate types of data sets and rules, and calculate reasonable similarity of all heterogeneous samples in the feature space. Moreover, the condensed concepts obtained by the proposed learning scheme greatly reduced the memory requirement, and the consistency of the classification result is better than other learning methods. Since the reduction process does not have to go through exhaustive verification for consistency, the learning speed is greatly raised. These results suggest that the proposed approach which combines mathematical lattice and fuzzy set theories that can be applied effectively on disparate types of heterogeneous data. It can rapidly obtain greatly condensed knowledge in the overwhelming information for the need of decision analysis.

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