Feature selection for clustering categorical data with an embedded modelling approach

Research on the problem of feature selection for clustering continues to develop. This is a challenging task, mainly due to the absence of class labels to guide the search for relevant features. Categorical feature selection for clustering has rarely been addressed in the literature, with most of the proposed approaches having focused on numerical data. In this work, we propose an approach to simultaneously cluster categorical data and select a subset of relevant features. Our approach is based on a modification of a finite mixture model (of multinomial distributions), where a set of latent variables indicate the relevance of each feature. To estimate the model parameters, we implement a variant of the expectation-maximization algorithm that simultaneously selects the subset of relevant features, using a minimum message length criterion. The proposed approach compares favourably with two baseline methods: a filter based on an entropy measure and a wrapper based on mutual information. The results obtained on synthetic data illustrate the ability of the proposed expectation-maximization method to recover ground truth. An application to real data, referred to official statistics, shows its usefulness.

How a cyber-physical system can efficiently obtain a snapshot of physical information even in the presence of sensor faults

We present a distributed algorithm for cyber-physical systems to obtain a snapshot of sensor data. The snapshot is an approximate representation of sensor data; it is an interpolation as a function of space coordinates. The new algorithm exploits a prioritized medium access control (MAC) protocol to efficiently transmit information of the sensor data. It scales to a very large number of sensors and it is able to operate in the presence of sensor faults.

The influence of health expenditures on household impoverishment in Brazil

OBJECTIVE To analyze the variation in the proportion of households living below the poverty line in Brazil and the factors associated with their impoverishment. METHODS Income and expenditure data from the Household Budget Survey, which was conducted in Brazil between 2002-2003 (n = 48,470 households) and 2008-2009 (n = 55,970 households) with a national sample, were analyzed. Two cutoff points were used to define poverty. The first cutoff is a per capita monthly income below R$100.00 in 2002-2003 and R$140.00 in 2008-2009, as recommended by the Bolsa Família Program. The second, which is proposed by the World Bank and is adjusted for purchasing power parity, defines poverty as per capita income below US$2.34 and US$3.54 per day in 2002-2003 and 2008-2009, respectively. Logistic regression was used to identify the sociodemographic factors associated with the impoverishment of households. RESULTS After subtracting health expenditures, there was an increase in households living below the poverty line in Brazil. Using the World Bank poverty line, the increase in 2002-2003 and 2008-2009 was 2.6 percentage points (6.8%) and 2.3 percentage points (11.6%), respectively. Using the Bolsa Família Program poverty line, the increase was 1.6 (11.9%) and 1.3 (17.3%) percentage points, respectively. Expenditure on prescription drugs primarily contributed to the increase in poor households. According to the World Bank poverty line, the factors associated with impoverishment include a worse-off financial situation, a household headed by an individual with low education, the presence of children, and the absence of older adults. Using the Bolsa Família Program poverty line, the factors associated with impoverishment include a worse-off financial situation and the presence of children. CONCLUSIONS Health expenditures play an important role in the impoverishment of segments of the Brazilian population, especially among the most disadvantaged.

Miocene lithological, foraminiferal and palynological data from the Belverde borehole (Portugal)

XVIII Jornadas de Paleontología, 2002

Contextual and individual indicators associated with the presence of teeth in adults

OBJECTIVE The objective of this study was to analyze whether socioeconomic conditions and the period of availability of fluoridated water are associated with the number of teeth present.METHODSThis cross-sectional study analyzed data from 1,720 adults between 20 and 59 years of age who resided in Florianópolis, SC, Southern Brazil, in 2009. The outcome investigated was the self-reported number of teeth present. The individual independent variables included gender, age range, skin color, number of years of schooling, and per capita household income. The duration of residence was used as a control variable. The contextual exposures included the period of availability of fluoridated water to the households and the socioeconomic variable for the census tracts, which was created from factor analysis of the tract’s mean income, education level, and percentage of households with treated water. Multilevel logistic regression was performed and inter-level interactions were tested.RESULTS Residents in intermediate and poorer areas and those with fluoridated water available for less time exhibited the presence of fewer teeth compared with those in better socioeconomic conditions and who had fluoridated water available for a longer period (OR = 1.02; 95%CI 1.01;1.02). There was an association between the period of availability of fluoridated water, per capita household income and number of years of education. The proportion of individuals in the poorer and less-educated stratum, which had fewer teeth present, was higher in regions where fluoridated water had been available for less time.CONCLUSIONS Poor socioeconomic conditions and a shorter period of availability of fluoridated water were associated with the probability of having fewer teeth in adulthood. Public policies aimed at reducing socioeconomic inequalities and increasing access to health services such as fluoridation of the water supply may help to reduce tooth loss in the future.

Rabies in the state of São Paulo: the rodents question

The authors looked over the epidemiological data on the aggression by rodents in the period 1976-1985 in the records of the Instituto Pasteur in the State of São Paulo (Brazil). They observed that out of 367 379 people attacked, 22 250 were victims of rodents. Mainly responsible for these accidents were urban rodents, whose capture, however, was a limiting factor for the sending of samples to the laboratory. Laboratory diagnosis carried out in 1 083 samples of rodents did not show any positive case in the period, in spite of the presence of rabies in other animals species. It is conclude that, as rabies is rare among rodents, tests are necessary for the identification of the virus whenever suspicion of a positive case occurs; in addition, in the absence of reported cases of human death caused by rabies related to rodents, possibility exists for a reduction of antirabies treatments following exposure to these animals.

Comparison study of procedures for aspiration of biopsy samples

Introduction: The samples obtained from fine needle aspiration in liquid base cytology (FNAC) are often limited by scarce cellularity compared to the amount of colloid and presence of blood. Accordingly, it was important to test alternative technical procedures so as to maximize the cellularity of each sample. Objective: To compare the morphological features and cellularity of the three procedures in the FNAC cytodiagnosis of the thyroid. Methods: A total of 31 cases were each subjected to a cell block and ThinPrep preparation as well as a routine smear. The observation and analysis was performed using an optical microscope. Cytological diagnosis of each cell block case was objectively analysed for cellularity, presence of background and cellular preservation. Each smear and ThinPrep case was analysed for the presence or absence of cells. The data was analysed with Microsoft Excel (Office 2010) and SPSS (Statistical Package of Social Science) version 15.0 for Windows. Results: Of 31 cases, only 20 had thyroid cells in the cell block and ThinPrep preparations, however, all smear cases contained thyroid cells. Some background was found in 30 Cell block cases with only 5 of these containing well preserved cells for cytodiagnosis. Conclusions: As indicated by the results, smear is the most appropriate procedure for FNAC of the thyroid.

Potential infectivity of blood from HBsAG asymptomatic carriers due to the presence of HBV-DNA and comparison with other markers of hbv infection

Serum samples from 356 HBsAg positive asymptomatic carriers, which were titrated by reverse passive hemagglutination, were analysed for the presence of HBV-DNA, HBsAg and IgM anti-HBc. The samples were divided in three classes, according to the titers of HBsAg and IgM anti-HBc and the distribution of HBV-DNA and HBsAg among these classes was studied. In the high titer class of HBsAg, 65% of samples have one or both markers against only 19% in the low titer class. From the total of 356 samples, 121 gave positive results for IgM anti-HBc (33.9%). From these, 38.9% of HBV-DNA and 47.9% of HBeAg were observed, whereas in samples with absence of IgM anti-HBc, 18.3% and 16.6% were respectively found. A higher frequency of agreement between all these markers was found in the class of high titers of HBsAg; however, HBV-DNA was detected in the low titer class of HBsAg and little or no IgM anti-HBc, showing potential blood infectivity even in HBsAg positive borderline samples.

Deep crustal structure across a young passive margin from wide-angle and reflection seismic data (The Sardinia Experiment) - I. Gulf of Lion's margin

The conjugate margins system of the Gulf of Lion and West Sardinia (GLWS) represents a unique natural laboratory for addressing fundamental questions about rifting due to its landlocked situation, its youth, its thick sedimentary layers, including prominent palaeo-marker such as the MSC event, and the amount of available data and multidisciplinary studies. The main goals of the SARDINIA experiment, were to (i) investigate the deep structure of the entire system within the two conjugate margins: the Gulf of Lion and West Sardinia, (ii) characterize the nature of the crust, and (iii) define the geometry of the basin and provide important constrains on its genesis. This paper presents the results of P-wave velocity modelling on three coincident near-vertical reflection multi-channel seismic (MCS) and wide-angle seismic profiles acquired in the Gulf of Lion, to a depth of 35 km. A companion paper [part II Afilhado et al., 2015] addresses the results of two other SARDINIA profiles located on the oriental conjugate West Sardinian margin. Forward wide-angle modelling of both data sets confirms that the margin is characterised by three distinct domains following the onshore unthinned, 33 km-thick continental crust domain: Domain I is bounded by two necking zones, where the crust thins respectively from 30 to 20 and from 20 to 7 km over a width of about 170 km; the outermost necking is imprinted by the well-known T-reflector at its crustal base; Domain II is characterised by a 7 km-thick crust with anomalous velocities ranging from 6 to 7.5 km/s; it represents the transition between the thinned continental crust (Domain I) and a very thin (only 4-5 km) "atypical" oceanic crust (Domain III). In Domain II, the hypothesis of the presence of exhumed mantle is falsified by our results: this domain may likely consist of a thin exhumed lower continental crust overlying a heterogeneous, intruded lower layer. Moreover, despite the difference in their magnetic signatures, Domains II and III present the very similar seismic velocities profiles, and we discuss the possibility of a connection between these two different domains.

Contributions to the Eocene palaeontology and stratigraphy of Beira Alta, Portugal II - New Late Eocene mammalian remnants from Coja (Portugal) and the presence of Palaeotherium magnum Cuvier

The presence of Palaeotherium magnum in the fauna from Coja is recorded. It is well in agreement with the earlier reporting to the Montmartre level from the Ludian stage. Field data as well as compatibility with the remaining taxa and the identical fossilization of all the specimens indicate that all the vertebrate fossils come from the same horizon in the lithostratigraphic unit "Arcoses de Côja".

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Fast unsupervised extraction of endmembers spectra from hyperspectral data

Linear unmixing decomposes an hyperspectral image into a collection of re ectance spectra, called endmember signatures, and a set corresponding abundance fractions from the respective spatial coverage. This paper introduces vertex component analysis, an unsupervised algorithm to unmix linear mixtures of hyperpsectral data. VCA exploits the fact that endmembers occupy vertices of a simplex, and assumes the presence of pure pixels in data. VCA performance is illustrated using simulated and real data. VCA competes with state-of-the-art methods with much lower computational complexity.

Multi-scale vegetation classification using earth observation data of the Sundarban mangrove forest, Bangladesh.

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Hepatocellular carcinoma in Brazil: report of a national survey (Florianópolis, SC, 1995)

In order to investigate epidemiological aspects of hepatocellular carcinoma (HCC) in Brazil, basic informations about cases diagnosed from January 1992 to December 1994 were requested to several medical centers of different Brazilian States. A simple questionnaire included age, sex, alcohol abuse (over 80g/day), associated liver cirrhosis, persistent HBV infection (HBsAg), HCV infection (anti-HCV) and serum levels of alpha fetoprotein. 287 cases, over 16 years old, from 19 medical centers of 8 States (Pará, Bahia, Minas Gerais, Espirito Santo, Rio de Janeiro, São Paulo, Paraná and Rio Grande do Sul) were analysed. The results showed: (a) Mean age was 56.3 ± 14.4 for men and 54.7 ± 16.8 yr for women and the male/female ratio was 3.4:1. (b) 69.6% were caucasians, 21.8% mullatoes, 4.8% orientals and 3.7% blacks. (c) HBsAg (+) in 77/236 cases (41.6%) without differences between males and females. (d) Anti-HCV (+) in 52/193 cases (26.9%). (e) 7/180 cases were positive both for HBsAg and anti-HCV (3.8%). (f) There was chronic alcoholism in 88/235 cases (37%). (g) HCC was found in cirrhotic livers in 71.2% of 202 cases in which the presence or absence of cirrhosis was reported. (h) Alpha-fetoprotein above 20 ng/ml was found in 124/172 cases (72%) and above 500 ng/ml only in 40 cases (23.2%). These results showed that the HCC in Brazil has an intermediate epidemiological pattern as compared to those from areas of low and high incidence of the tumor. In spite of the high frequency of the association of HCC with the HBV and/or HCV infections, 42% of 180 cases were negative both for HBsAg and anti-HCV, indicating the possible role of other etiological factors. The comparison of data from different States showed some regional differences: higher frequency of associated HBsAg in Pará, Bahia, Minas Gerais and Espírito Santo, higher frequency of associated HCV infection in Rio de Janeiro, São Paulo and States of the Southern region and low frequency of associated liver cirrhosis in Salvador and Rio de Janeiro (55.5 and 50% respectively). Further investigation will be necessary to study the presence of other possible etiological factors as aflatoxins, suggested by the favourable climatic conditions for food contamination by fungi in the majority Brazilian regions