The paper presents a novel method for classifying human tumor samples using microarray gene expression data. The authors propose a two-step procedure: dimension reduction using Partial Least Squares (PLS) and classification using Logistic Discrimination (LD) or Quadratic Discriminant Analysis (QDA). They compare PLS with Principal Components Analysis (PCA) and demonstrate that PLS often outperforms PCA, especially in scenarios where the number of genes (p) exceeds the number of samples (N). The methods are applied to five different microarray datasets involving various human tumor samples, including normal versus ovarian tumor, Acute Myeloid Leukemia (AML) versus Acute Lymphoblastic Leukemia (ALL), Diffuse Large B-cell Lymphoma (DLBCL) versus B-cell Chronic Lymphocytic Leukemia (BCLL), normal versus colon tumor, and Non-Small-Cell-Lung-Carcinoma (NSCLC) versus renal samples. The stability of the classification results is assessed through re-randomization studies. The paper also illustrates a condition where PCA fails to predict well relative to PLS, highlighting the advantages of PLS in handling high-dimensional data.The paper presents a novel method for classifying human tumor samples using microarray gene expression data. The authors propose a two-step procedure: dimension reduction using Partial Least Squares (PLS) and classification using Logistic Discrimination (LD) or Quadratic Discriminant Analysis (QDA). They compare PLS with Principal Components Analysis (PCA) and demonstrate that PLS often outperforms PCA, especially in scenarios where the number of genes (p) exceeds the number of samples (N). The methods are applied to five different microarray datasets involving various human tumor samples, including normal versus ovarian tumor, Acute Myeloid Leukemia (AML) versus Acute Lymphoblastic Leukemia (ALL), Diffuse Large B-cell Lymphoma (DLBCL) versus B-cell Chronic Lymphocytic Leukemia (BCLL), normal versus colon tumor, and Non-Small-Cell-Lung-Carcinoma (NSCLC) versus renal samples. The stability of the classification results is assessed through re-randomization studies. The paper also illustrates a condition where PCA fails to predict well relative to PLS, highlighting the advantages of PLS in handling high-dimensional data.