值譜分群演算法乃是將數據中的每個資料點視為一個圖(Graph)的頂點V，並將資料點(即頂點)之間的相似度量化為頂點之間的連接邊E。如此可得到一個基於相似度的無方向之加權圖G(V,E)。於是，資料分群問題就利用此一加權圖轉化為圖的劃分問題，並利用圖論劃分準則使劃分後的子圖(Sub-graph)內部相似度最大，相對的，子圖之間的相似度最小，而達成分群的目的。本研究基於先前的研究基礎，探討限制式分群(Constraints Clustering)中之必連(Must-Link,ML)限制條件對值譜分群結果的影響。由於值譜分群核心結構-距離矩陣(distance matrix)可透過相似度矩陣及最近鄰居法(k-NN)產生鄰近矩陣(affinity matrix)。本研究設定兩種必連限制:(1)必連限制在鄰近矩陣內、(2)必連限制在鄰近矩陣外，以探討此兩種限制對分群的變化。本研究實驗使用三個公開的UCI資料，分別針對所提出之演算法進行實驗。實驗分群結果利用評比指標 Adjusted Rand Index (ARI)來比較有限制與沒有限制時之分群結果。實驗結果發現必連限制在鄰近矩陣內對分群結果之ARI會產生較大的變異。此外，必連限制在鄰近矩陣外會使得值譜分群結果較沒有必連限制時產生較大的差異，而且ARI在特定之限制數量後會進行收斂。

Spectral clustering algorithm considers data points as vertexes in the undirected graph where the vertex set is V=[v_1,v_2,…, v_n ] and each edge between two vertexes v_i and v_j have a non-negative weight value (w_ij) by the similarity function. Thus, spectral clustering is based on the graph partition theory as it treats the data clustering problem as a graph partitioning problems. The objective of graph partition is to cluster data points to maximize the similarity of inner sub-graph of data points as well as to minimize the similarity between sub-graphs. This research aims to investigate the impact of clustering results when Must-Link constraints are applied under spectral clustering. Based on process of spectral clustering, the affinity matrix is generated from the similarity matrix where k-nearest neighborhood method is used to determine the closer data points. Two kind of ML constraints can be applied either in or out of affinity matrix: (1) ML constraints on affinity matrix of k-NN, and (2) ML constraints on affinity matrix of non k-NN. A series of experiments by using three UCI datasets were conducted to compare the clustering results under these two conditions. Adjusted Rand Index (ARI) was used to compare the clustering results with or without the mentioned constrains. The experimental results show the variation of ARI is larger when ML constraints on affinity matrix are applied. Furthermore, the dramatic drop of ARI appears if ML constraints on affinity matrix of non k-NN are applied. However, the descending of ARI will converged after certain number of ML constraints.

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