在巨量資料的年代，我們很難直接針對這些高維度且高複雜度的資料直接做處理。此外，標記資料需要大量的時間、人力、甚至是金錢；相對的，未被標記的資料非常的多而且容易取得。半監督式學習利用可以利用少量標記資料加上大量的未標記資料對資料做分析處理。本研究是利用核化切片逆迴歸法來實現半監督式學習的方法，核化切片逆迴歸法主要是利用平均數、共變異矩陣與加權平均數、加權共變異矩陣解透過特徵值分解找到有效維度縮減的方向，其中只有加權平均數以及加權共變異矩陣需要用到標記資料所提供的訊息；所以我們近一步地把這個方法延伸到半監督式學習領域：取代了原本對平均數及共變異矩陣的估計，以往在半監督式學習領域裡，只有標記資料參與計算；在半監督式核化切片逆迴歸法中，我們利用標記資料以及未標記資料去估計平均數以及共變異矩陣，然而加權平均數及加權共變異矩陣依然只用有標記的資料去做計算。透過這個方法，我們有效的運用標記以及未標記的資料去計算有效維度縮減方向，並透過這個方向將資料投影到低維度空間，最後linear SSVM根據這些低維度資料建出分類模型。實驗結果顯示本方法能夠在短時間內有效且準確處理高維度資料。

In the big data age, the large and complex collection of data sets becomes difficult to process using on-hand database management tools or traditional data processing applications. In addition, due to the cost of collecting labeled data, we have much more unlabeled data than we do labeled data. Hence, the problem of utilizing both labeled and unlabeled data for machine learning tasks, known as known as semi-supervised learning (SSL), is attracting increasing attention. Sliced inverse regression (SIR) is a renowned supervised linear dimension reduction method and has been extended to nonlinear setting via the kernel trick. Projecting the data instances onto the e.d.r. subspace extracted by kernelized SIR (KSIR) and then applying a linear classification algorithm such as SVM is a very powerful tool for classification problems. The e.d.r. subspace is generated by solving a generalized eigenvalue problem that is defined by the sample covariance matrix and the between-class sample covariance matrix. Thus with a good estimation of these kernalized covariance matrices, we are able to extract a more accurate e.d.r. subspace for the purpose of classification. Based on this observation, we will apply KSIR to the SSL problem. We assume that the labeled instances inherit the probability distribution of the classes' data distribution. Thus, we can use these labeled and unlabeled data to estimate the kernalized sample covariance matrix and the between-class sample covariance matrix to generate the KSIR $e. d. r.$ subspace. This $e. d. r.$ subspace will embed the class characteristic information into each KSIR direction. The linear smooth SVM classifier is applied to the projection images of labeled data in the $e. d. r.$ subspace. The numerical results show that the proposed method's classification performance in a SSL setting is competitive with that of classifiers working under a supervised learning setting.

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