Principal component discriminant analysis

The approach adopted involved two-stages. First the 11205 measurements in the mass spectrometry data were reduced to 14 scores by a principal component analysis of the centered but otherwise untreated and unscaled data matrix. Then a linear classifier was derived by linear discriminant analysis using these 14 scores as inputs. This number of scores was chosen by leave-one-out cross-validation on the training set, where it gave an overall error rate of 14%. Some indication of the information used in the classification may be obtained from an inspection of the coefficients of the linear classifier.     

Principal component analysis of scintimammographic images

The recent development of new gamma imagers based on scintillation array with high spatial resolution, has strongly improved the possibility of detecting sub-centimeter cancer in Scintimammography. However, Compton scattering contamination remains the main drawback since it limits the sensitivity of tumor detection. Principal component image analysis (PCA), recently introduced in scintimam nographic imaging, is a data reduction technique able to represent the radiation emitted from chest, breast healthy and damaged tissues as separated images. From these images a Scintimammography can be obtained where the Compton contamination is “removed”. In the present paper we compared the PCA reconstructed images with the conventional scintimammographic images resulting from the photopeak (Ph) energy window. Data coming from a clinical trial were used. For both kinds of images the tumor presence was quantified by evaluating the t-student statistics for independent sample as a measure of the signal-to-noise ratio (SNR). Since the absence of Compton scattering, the PCA reconstructed images shows a better noise suppression and allows a more reliable diagnostics in comparison with the images obtained by the photopeak energy window, reducing the trend in producing false positive.     

Principal component analysis for protein folding dynamics

Protein folding is considered here by studying the dynamics of the folding of the triple β-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.     

Principal component analysis of complex multijoint coordinative movements

Principal components analysis (PCA) has not been very much in vogue within the field of movement coordination even though it is useful to reduce data dimensionality and to reveal underlying data structures. Traditionally, studies of coordination between two joints have predominantly made use of relative phase analyses. This has resulted in the identification of principal constraints that govern the Central Nervous System’s organization and the control of coordination patterns. However, relative phase analyses on pairwise joints have some drawbacks because they are not optimal for revealing convergent patterns among multijoint coordination modes and for unraveling generic control strategies.In this paper, we present a method to analyze multijoint coordination based on the properties of PC, more specifically the eigenvalues and eigenvectors of the covariance matrix.The comparison between relative phase analysis and PCA shows that both provide similar and consistent results, underscoring the latter technique’s sensitivity to the study of coordination performance. In addition, it provides a method for automatic pattern detection as well as an index of performance for each joint within the context of the global coordination pattern.Finally, the merit of the PCA technique within the context of central pattern generators (CPG) will be discussed.     

Principal component analysis of DNA oligonucleotide structural data

The microstructure of a DNA helix is characterized by several base pair and base step parameters such as twist, rise, roll, propeller twist, etc., in addition to conformational parameters such as the backbone and the glycosidic torsion angles. Among these only a few, which are independent of all others and of each other, may be used to precisely characterize the helix. The problem however is to identify these independent parameters. We have used principal component analysis to identify a relatively small set of independent parameters, with which to characterize each DNA helix. We show that these principal components clearly discriminate between A and B DNA helical types. The calculations further suggest that the microstructure of a DNA helix is better characterized using dinucleotides.     

Principal component analysis based methods in bioinformatics studies

In analysis of bioinformatics data, a unique challenge arises from the high dimensionality of measurements. Without loss of generality, we use genomic study with gene expression measurements as a representative example but note that analysis techniques discussed in this article are also applicable to other types of bioinformatics studies. Principal component analysis (PCA) is a classic dimension reduction approach. It constructs linear combinations of gene expressions, called principal components (PCs). The PCs are orthogonal to each other, can effectively explain variation of gene expressions, and may have a much lower dimensionality. PCA is computationally simple and can be realized using many existing software packages. This article consists of the following parts. First, we review the standard PCA technique and their applications in bioinformatics data analysis. Second, we describe recent 'non-standard' applications of PCA, including accommodating interactions among genes, pathways and network modules and conducting PCA with estimating equations as opposed to gene expressions. Third, we introduce several recently proposed PCA-based techniques, including the supervised PCA, sparse PCA and functional PCA. The supervised PCA and sparse PCA have been shown to have better empirical performance than the standard PCA. The functional PCA can analyze time-course gene expression data. Last, we raise the awareness of several critical but unsolved problems related to PCA. The goal of this article is to make bioinformatics researchers aware of the PCA technique and more importantly its most recent development, so that this simple yet effective dimension reduction technique can be better employed in bioinformatics data analysis.     

Principal component analysis for clustering gene expression data

MOTIVATION: There is a great need to develop analytical methodology to analyze and to exploit the information contained in gene expression data. Because of the large number of genes and the complexity of biological networks, clustering is a useful exploratory technique for analysis of gene expression data. Other classical techniques, such as principal component analysis (PCA), have also been applied to analyze gene expression data. Using different data analysis techniques and different clustering algorithms to analyze the same data set can lead to very different conclusions. Our goal is to study the effectiveness of principal components (PCs) in capturing cluster structure. Specifically, using both real and synthetic gene expression data sets, we compared the quality of clusters obtained from the original data to the quality of clusters obtained after projecting onto subsets of the principal component axes. RESULTS: Our empirical study showed that clustering with the PCs instead of the original variables does not necessarily improve, and often degrades, cluster quality. In particular, the first few PCs (which contain most of the variation in the data) do not necessarily capture most of the cluster structure. We also showed that clustering with PCs has different impact on different algorithms and different similarity metrics. Overall, we would not recommend PCA before clustering except in special circumstances.     

Principal component analysis of gene frequencies of Chinese populations

Principal components (PCs) were calculated based on gene frequencies of 130 alleles at 38 loci in Chinese populations, and geographic PC maps were constructed. The first PC map of the Han shows the genetic difference between Southern and Northern Mongoloids, while the second PC indicates the gene flow between Caucasoid and Mongoloids. The first PC map of the Chinese ethnic minorities is similar to that of the second PC map of the Han, while their second PC map is similar to the first PC map of the Han. When calculating PC with the gene frequency data from both the Han and ethnic minorities, the first and second PC maps most resemble those of the ethnic minorities alone. The third and fourth PC maps of Chinese populations may reflect historical events that allowed the expansion of the populations in the highly civilized regions. A clear-cut boundary between Southern and Northern Mongoloids in the synthetic map of the Chinese populations was observed in the zone of the Yangtze River. We suggest that the ancestors of Southern and Northern Mongoloids had already separated before reaching Asia. The ancestors of the Southern Mongoloids may result from the initial expansion from Africa or the Middle East, via the south coast of Asia, toward Southeast Asia, and ultimately South China. Upon reaching the Yangtze River, they might even have crossed the river to occupy the nearby regions for a period of time. The ancestors of the Northern Mongoloids probably expanded from Africa via the Northern Pamirs, first went eastward, then towards the south to reach the Yangtze River. The expansion of the Northern Mongoloids toward the south of the Yangtze River happened only in the last 2 or 3 thousand years.     

Principal component analysis of gene frequencies of Chinese populations

Principal components (PCs) were calculated based on gene frequencies of 130 alleles at 38 loci in Chinese populations, and geographic PC maps were constructed. The first PC map of the Han shows the genetic difference between Southern and Northern Mongoloids, while the second PC indicates the gene flow between Caucasoid and Mongoloids. The first PC map of the Chinese ethnic minorities is similar to that of the second PC map of the Han, while their second PC map is similar to the first PC map of the Han. When calculating PC with the gene frequency data from both the Han and ethnic minorities, the first and second PC maps most resemble those of the ethnic minorities alone. The third and fourth PC maps of Chinese populations may reflect historical events that allowed the expansion of the populations in the highly civilized regions. A clear-cut boundary between Southern and Northern Mongoloids in the synthetic map of the Chinese populations was observed in the zone of the Yangtze River. We suggest that the a     

浙江省丝瓜种质资源主成分分析和聚类分析

为进行丝瓜品种选育,以32个不同丝瓜种质资源为研究材料,调查结瓜习性、叶缘、瓜棱、雌花节率等共22个性状,对得到的性状数据采用DPS软件进行主成分分析和系统聚类分析。结果表明:22个性状可综合为5个主成分,其累积贡献率达81.308%,根据前5个主成分与性状的相关性,选出14个影响力较大的性状。在主成分分析的基础上,对32个丝瓜种质资源进行了系统聚类分析,在欧氏距离的水平上首先将其划分成2大类,又可进一步划分为6个亚类。     

Principal component analysis of gene frequencies and the origin of Basques

The genetic peculiarity of the Basque population has long been noted. We aim to describe Basque distinctiveness in space and assess the internal Basque heterogeneity. All these aspects are relevant to the question of the origin of Basques. After a thorough literature search, a data base was created containing all the available data on gene frequencies in the Iberian Peninsula and France. Twenty-nine systems, comprising 71 alleles, were used to carry out a principal component (PC) analysis. The results show a sharp peak in the first PC in the Basque area, which remains even when the geographic scope is widened to include western Europe. As demonstrated by “wombling” analysis, the steeper slope in the first PC is found to the east of the Basque area, along the Pyrenees. Measures of genetic heterogeneity (such as F_ST values) within the Basque country, as compared to those for non-Basques, do not show a particular internal substructuration in the Basque population. The genetic results support a scenario in which the Basques are the product of in situ differentiation around the time of the Last Glacial Maximum (18,000 B .P .), in agreement with archaeological and linguistic data. Isolation from the surrounding populations has allowed the differentiation to last for millennia, but has erased the differences existing among Basques. © 1994 Wiley-Liss, Inc.     

Principal component analysis of the elongation of metacarpal and phalangeal bones

A hypothesis that the first principal component computed from the covariance matrix of logarithms reflected the specific growth rates of corresponding bones was taken to analyze the growth pattern of the tubular bones of the hand. The total length of 19 tubular bones of the right hand was measured on standardized radiographs of Japanese children (33 boys, 33 girls). Metacarpals in boys and bones of the fifth digit in girls showed higher growth coefficients. The second, third and fourth proximal, and the third and fourth middle phalanges showed lower coefficients for both sexes. These observations suggest the signs of proximal row dominance in boys and of fifth ray dominance in girls in the elongation of the hand bones. A marked sex difference was found in the fifth middle phalanx. In girls the growth coefficients of this bone was much larger than any other bones, but was moderate in boys.     

Principal component analysis of the conformational freedom within the EF-hand superfamily

A database of nonredundant structures of EF-hand domains--i.e., pairs of helix-loop-helix motifs--has been assembled, and the six angles among the four helices re-determined. A principal component analysis of these angles allows us to use two such components (PC1 and PC2) to describe the system retaining 80% of the total variance. A PC2 against PC1 plot representation allows us to represent in a compact way the full range of structural diversity of EF-hand domains, their grouping into protein families, and the variation for each family upon calcium and peptide binding.     

鹅膏属真菌形态特征的主成分与聚类分析

本研究选取了《中国真菌志·第二十七卷·鹅膏科》中27个物种及变种,对这些分类单元的菌托形状、菌褶颜色、担子大小等形态学特征进行统计,依据这些形态学特征进行主成分和聚类分析,得到各物种及变种与各个形态学特征之间的关联程度。通过聚类分析将27个物种及变种分为四大类,最终结果与鹅膏属分类情况一致,验证了上述分析方法在鹅膏属分类研究领域具有可行性与准确性。     

中国蜱类不同宿主类型的主成份分析和聚类分析

中国分布的蜱类宿主涉及爬行纲、鸟纲、哺乳纲等3纲20目,约130余种.主成份分析结果表明,9个主成份的累积贡献率仪达到70%以上,进一步的因子载荷分析发现只有极少数蜱类具有宿主特异性;聚类分析结果与其大致相同.因此,中国多数蜱类无明显的宿主特异性,宿主的生态特异性决定了蜱类的分布和宿主范围.     

Principal component analysis of evoked neuronal firing pattern in the human brain

Evoked firing activity (EFA) in neurons of the human thalamic reticular nucleus (Rt) was recorded by microelectrodes using extracellular recording techniques in the course of stereotaxic surgery for dyskinesia. Activity was induced by functionally significant verbal and sensory stimuli together with performance of goal-directed behavioral actions (BA). Use of the principal component method and construction of peristimulus covariance matrices are suggested in view of the presumably convergent nature of EFA in Rt neurons, taking the form of superposing independent components of response and variability in these in the course of BA testing and performance for the purpose of analyzing EFA and interneuronal correlations. The multivariate pattern of Rt EFA time courses during the action of functionally significant stimuli was revealed; this reflects different stages in performance of BA. The dynamics of components of response are revealed and occurrence of rapidly developing interneuronal correlations in functionally significant stages of goal-directed BA are described. Findings point to the efficacy of the suggested approach applied to analysis of EFA neurons.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 22, No. 6, pp. 811–818, November–December, 1990.