# Classification of Hyperspectral In Vivo Brain Tissue Based on Linear Unmixing
## 2 Background  
The most basic approaches for BLU are principal component analysis (PCA) and independent component analysis (ICA) [18; 19]. These two methodologies have been applied to identify cancer by using HSI and BLU algorithms in previous studies. In [20; 21], PCA was considered to identify different types of cancer in anomalous cells and to distinguish between tumor and normal tissues of head and neck cancer. Meanwhile, ICA was suggested to perform the classification of colon tissue cells [22] and to detect the presence of keratinized tissues to identify oral cancer [23]. Nevertheless, neither algorithm, ICA and PCA, considers a joint non-negativity and normalized condition on the resulting end-members, so their formulations do not contribute to the end-members' physical interpretation. Other popular methods for non-negative datasets, such as multivariate curve resolution (MCR) or non-negative matrix factorization (NNMF), were used to identify breast cancer cells in HS microscopic images [24] or head and neck cancer in in vivo animal HS images [25], respectively. Another recent proposal is the extended blind end-member and abundance extraction (EBEAE) methodology that can be used for BLU in non-negative datasets by considering linearly independent end-members and normalized abundances. This method was previously used for biomedical imaging applications, including m-FLIM (multi-spectral fluorescence lifetime imaging) for chemometric analysis in oral cavity samples, OCT (optical coherence tomography) for macrophage identification in post-mortem artery samples, and in vivo brain tissue classification by using HSI [26]. Previous works in cancer detection have employed different machine learning approaches to classify HS in vivo brain data [27; 28; 29], including supervised and unsupervised algorithms, as well as deep learning methods. In [27], the use of a spatial-spectral algorithm was presented, where the differentiation among tissues was performed by using a combination of supervised and unsupervised machine learning methods. Thus, the supervised stage was based on support vector machine (SVM) classifier, K-nearest neighbor (KNN) filtering, and fixed reference t-distributed stochastic neighbors embedding (FR-t-SNE) dimensional reduction, where the unsupervised stage relied on the hierarchical K-means clustering algorithm. These two methods were combined by using a majority voting approach. In [28], deep learning approaches were explored, evaluating a 2D-CNN (two-dimensional convolutional neural network) and a 1D-DNN (one-dimensional deep neural network) against the use of SVM-based approaches to classify the samples. The processing framework in [28] involved both deep learning methods (2D-CNN and 1D-DNN), which increased the accuracy in the detection of tumor tissue with respect to the results obtained by each independent method. Finally, in [29], different optimization algorithms were explored to identify the most relevant wavelengths for the tumor margin delineation in the HS in vivo brain images. This methodology based on optimization algorithms revealed that with only 48 bands, the accuracy of the classification was not affected with respect to the reference results. In this context, linear unmixing by EbEAE is proposed to classify intraoperative HS images of in vivo brain tissue. The main goal is to develop alternative methods with accurate results, but requiring smaller training times compared to a supervised machine learning classifier (SVM-based algorithm). In this way, two methodologies are suggested that rely on identifying the characteristics of end-members related to the studied tissue classes by EbEAE. In the first one, by computing the minimum distance to the end-members' class sets, each pixel is labeled in the HS image. Meanwhile, the second one tries to isolate first the class related to the external materials or substances present in the surgical scenario, and then, the remaining pixels are labeled with the minimum distance philosophy to the tissue end-members' sets.