距離決策下的模糊聚類集成模型
doi: 10.11999/JEIT171065
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遼寧工程技術(shù)大學(xué)工商管理學(xué)院 ??葫蘆島 ??125105
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遼寧工程技術(shù)大學(xué)軟件學(xué)院 ??葫蘆島 ??125105
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遼寧工程技術(shù)大學(xué)電子與信息工程學(xué)院 ??葫蘆島 ??125105
基金項(xiàng)目: 國(guó)家自然科學(xué)基金青年科學(xué)基金(61401185)
Fuzzy Clustering Ensemble Model Based on Distance Decision
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School of Business Administration, Liaoning Technical University, Huludao 125105, China
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School of Software, Liaoning Technical University, Huludao 125105, China
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School of Electronic and Information Engineering, Liaoning Technical University, Huludao 125105, China
Funds: The Young Scientists Fund of the National Natural Science Foundation of China (61401185)
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摘要: 模糊聚類是近年來(lái)使用的一類性能較為優(yōu)越的聚類算法，但該類算法對(duì)初始聚類中心敏感且對(duì)邊界樣本的聚類結(jié)果不夠準(zhǔn)確。為了提高聚類準(zhǔn)確性、穩(wěn)定性，該文通過(guò)聯(lián)合多個(gè)模糊聚類結(jié)果，提出一種距離決策下的模糊聚類集成模型。首先，利用模糊C均值(FCM)算法對(duì)數(shù)據(jù)樣本進(jìn)行多次聚類，得到相應(yīng)的隸屬度矩陣。然后，提出一種新的距離決策方法，充分利用得到的隸屬度關(guān)系構(gòu)建一個(gè)累積距離矩陣。最后，將距離矩陣引入密度峰值(DP)算法中，利用改進(jìn)的DP算法進(jìn)行聚類集成以獲取最終聚類結(jié)果。在UCI機(jī)器學(xué)習(xí)庫(kù)中選擇9個(gè)數(shù)據(jù)集進(jìn)行測(cè)試，實(shí)驗(yàn)結(jié)果表明，相比經(jīng)典的聚類集成模型，該文提出的聚類集成模型效果更佳。Abstract: Fuzzy clustering is a kind of clustering algorithm which shows superior performance in recent years, however, the algorithm is sensitive to the initial cluster center and can not obtain accurate results of clustering for the boundary samples. In order to improve the accuracy and stability of clustering, this paper proposes a novel approach of fuzzy clustering ensemble model based on distance decision by combining multiple fuzzy clustering results. First of all, performing several times clustering for data samples by using FCM (Fuzzy C-Means), and corresponding membership matrices are obtained. Then, a new method of distance decision is proposed, a cumulative distance matrix is constructed by the membership matrices. Finally, the distance matrix is introduced into the Density Peaks (DP) algorithm, and the final results of clustering are obtained by using the improved DP algorithm for clustering ensemble. The results of the experiment show that the clustering ensemble model proposed in this paper is more effective than other classical clustering ensemble model on the 9 data sets in UCI machine learning database.
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表 1 算法實(shí)現(xiàn)流程
輸入：實(shí)驗(yàn)數(shù)據(jù)集 $\small {{X}}{\rm{ = \{ }}{{x}_{i}}{\rm{|}}{i}{\rm{ = }}{1,2,}·\!·\!·\!{,}{n}{\rm{\} }}$，基聚類器運(yùn)算次數(shù) $\small {m}$，實(shí)驗(yàn)數(shù)據(jù)集的總類簇?cái)?shù) $\small C$ 輸出：數(shù)據(jù)集 $\small {{X}}{\rm{ = \{ }}{{x}_{i}}{\rm{|}}{i}{\rm{ = }}{1,2,}·\!·\!·{,}{n}{\rm{\} }}$的聚類集成標(biāo)簽Q 步驟 1 獲取基聚類FCM的聚類結(jié)果： (1) 判斷基聚類器運(yùn)算次數(shù)是否小于 $\small {m}$； (2) 利用范圍在(0,1)之間的隨機(jī)數(shù)初始化模糊隸屬度 $\small {{{U}}_{j}},\;{j} = {1,2,}·\!·\!·\!{,}{m}$，滿足式(1)的約束條件； (3) 通過(guò)式(2)計(jì)算 $\small C$個(gè)類簇的中心 $\small {c}_{k}^{j}{(}{k} = {1,2,}·\!·\!·\!{,}{C})$； (4) 通過(guò)式(1)計(jì)算FCM的目標(biāo)函數(shù)，若 $\small {J_{hj}}(u,c)$小于設(shè)定閾值，或相對(duì)上次計(jì)算的目標(biāo)函數(shù)的變化量 $\small \Delta {J_{hj}}$小于閾值，則迭代終止； (5) 利用式(3)重新計(jì)算新的模糊隸屬度 $\small {{{U}}_j}$，返回(3)； (6) 保存模糊隸屬度 $\small {{U}_j}$, $\small j = j + 1$，返回(1)； 步驟 2 構(gòu)建累積距離矩陣： (1) 利用式(8)計(jì)算每次得到的隸屬度矩陣 $\small {{{U}}_j},\ j = 1,2,·\!·\!·\!,m$對(duì)應(yīng)的最大隸屬類信息矩陣 $\small {{{L}}_j}$； (2) 利用式(9)計(jì)算單個(gè)隸屬度矩陣 $\small {{{U}}_{j}}$與信息矩陣 $\small {{{L}}_j}$構(gòu)造出的隸屬相似矩陣 $\small {{{U}}\!_j}\!^\prime $為例進(jìn)行距離矩陣的構(gòu)建； (3) 重復(fù)執(zhí)行 $\small {m}$次(2)，得到累積隸屬相似矩陣 $\small {{{U}}^\prime }$； (4) 利用式(10)構(gòu)建累積距離矩陣 $\small {{D}}$； 步驟 3 基于DP的聚類集成： (1) 利用步驟2得到的累積距離矩陣 $\small {{D}}$計(jì)算數(shù)據(jù)樣本間的兩兩距離 $\small {d_{ij}}$，并確定截?cái)嗑嚯x $\small {d_c}$； (2) 按照式(4)和式(5)分別計(jì)算數(shù)據(jù)樣本 $\small {x_i}$的局部密度 $\small {\rho _i}$和與更高局部密度的點(diǎn)的距離 $\small {\delta _i}$； (3) 利用式(11)中的 $\small {\gamma _i}$選擇前K個(gè)密度峰值點(diǎn)作為集成聚類中心 $\small \{ {{c}_{k}}{,}{k} = {1,2,}·\!·\!·\!{,}{C}\} $，對(duì)非數(shù)據(jù)中心的數(shù)據(jù)樣本進(jìn)行歸類； (4) 計(jì)算聚類的邊界區(qū)域，排除光暈點(diǎn)的干擾。 
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表 2 實(shí)驗(yàn)數(shù)據(jù)集信息
序號(hào) 1 2 3 4 5 6 7 8 9 數(shù)據(jù)集 parkinsons wdbc ionosphere german iris wine waveform vehicle x8d5k 數(shù)據(jù)樣本數(shù) 195 569 351 1000 150 178 5000 846 1000 屬性 22 30 34 24 4 13 21 18 8 類別數(shù) 2 2 2 2 3 3 3 4 5
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表 3 5種聚類方法的RI比較結(jié)果
序號(hào) FCM CSP HGP MCL 本文 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 1 0.579 0.068 0.638 0.012 0.607 0.007 0.613 0.016 0.646 0.003 2 0.723 0.047 0.833 0.013 0.812 0.019 0.841 0.021 0.852 0.010 3 0.563 0.057 0.628 0.015 0.617 0.017 0.613 0.007 0.662 0.014 4 0.625 0.039 0.729 0.016 0.746 0.006 0.731 0.004 0.758 0.009 5 0.786 0.034 0.832 0.023 0.822 0.015 0.852 0.016 0.887 0.006 6 0.732 0.041 0.856 0.011 0.859 0.017 0.826 0.008 0.863 0.013 7 0.628 0.037 0.646 0.007 0.638 0.014 0.637 0.011 0.641 0.015 8 0.547 0.022 0.627 0.021 0.593 0.014 0.616 0.005 0.635 0.007 9 0.715 0.033 0.816 0.004 0.849 0.005 0.834 0.010 0.866 0.008 平均值 0.655 0.042 0.734 0.014 0.727 0.013 0.729 0.011 0.757 0.009
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表 4 5種聚類方法的NMI比較結(jié)果
序號(hào) FCM CSP HGP MCL 本文 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 均值 標(biāo)準(zhǔn)差 1 0.412 0.043 0.483 0.004 0.488 0.007 0.474 0.006 0.516 0.002 2 0.536 0.028 0.576 0.008 0.619 0.007 0.577 0.012 0.634 0.016 3 0.512 0.063 0.568 0.006 0.567 0.003 0.544 0.008 0.574 0.002 4 0.499 0.052 0.582 0.011 0.612 0.005 0.594 0.008 0.625 0.004 5 0.692 0.025 0.783 0.016 0.808 0.015 0.747 0.012 0.813 0.014 6 0.645 0.026 0.721 0.007 0.736 0.004 0.712 0.009 0.742 0.003 7 0.525 0.020 0.585 0.011 0.564 0.007 0.579 0.002 0.591 0.004 8 0.118 0.016 0.135 0.004 0.136 0.002 0.133 0.005 0.142 0.006 9 0.632 0.034 0.724 0.012 0.716 0.011 0.712 0.008 0.742 0.010 平均值 0.508 0.034 0.573 0.009 0.583 0.007 0.564 0.008 0.598 0.007
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