Cluster analysis is reformulated as a problem of estimating the parameters of a mixture of multivariate distributions.The maximum-likelihood theory and numerical solution techniques are developed for a fairly general class of distributions. The theory is applied to mixtures of multivariate normals ("NORMIX") and mixtures of multivariate Bernoulli distributions ("Latent Classes"). The feasibility of the procedures is demonstrated by two examples of computer solutions for normal mixture models of the Fisher Iris data and of artificially generated clusters with unequal covariance matrices. This paper is addressed to the problem which has been variously called cluster analysis, Q-analysis, typology, grouping, clumping, classif ication, numerical taxonomy, and unsupervised pattern recognition. The variety of nomenclature may be due to the importance of the subject in such diverse fields as psychology, biology, signal detection, artificial intelligence, and information retrieval. Perhaps this multiplicity of names also indicates a certain confusion in the basic definition of the problem. This paper attempts to reformulate cluster analysis, with a resulting improvement in conceptual simplicity and statistical rigor. In this formulation cluster analysis will be viewed as a form of mixture analysis for finite mixtures of multivariate distributions.In clustering methodology, one is generally given a sample of N objects or individuals, each of which is measured on m variables. From this information alone, one must devise a classification scheme for grouping the objects into r classes. The number of classes and the characteristics of the classes are to be determined. If all the objects in a given class were identical to one another, the problem would be simple. However, in the usual situation the objects in a class differ on most or all of the measures. Most cluster analysis procedures try to measure the "similarity" between any two objects, and then try to group the objects so as to maximize within-class similarity. Unfortunately, the appropriate measure of similarity is a subject of some controversy. It would be desirable to derive a cluster analysis system without arbitrary assumptions about similarity. Such a system will be presented in this paper. JULY, 1970329

Interaction regions between adjacent solar wind streams have been identified between 1 and 5 AU using Pioneer 10 and 11 magnetic field and plasma measurements. Beyond 1 AU, a relatively large fraction of the interaction regions have been found to be accompanied by either forward shocks, reverse shocks, or shock pairs. The observations are consistent with previous theoretical proposals that the interaction between adjacent streams leads to the development of corotating interplanetary shocks.

Measurements of electron density and temperature by the Pioneer Venus orbiter electron temperature probe (OETP) are used to describe the dynamic behavior of the Venus ionosphere and to begin to relate this complex behavior to variations in the solar wind and the ionosheath magnetic field, parameters that are also measured by orbiter instruments. The average ionopause height rises from about 330 km at the subsolar point to 700 km at the dusk terminator and 1000 km at the dawn terminator, in both cases exhibiting a stronger dependence upon solar zenith angle than that reported from Venera 9 and 10 occultation data. The ionopause on the dayside tends to expand and contract with changes in solar wind pressure, becoming asymptotic to about 290 km at pressures above 4 × 10−8 dyn/cm² and rising to over 1000 km for pressures below 5 × 10−9 dyn/cm². The solar wind pressure, after correction for solar zenith angle, agrees approximately with the magnetic field pressure applied at the ionopause, confirming earlier suggestions that the pressure is conveyed to the ionosphere primarily by the magnetic field rather than by the shocked solar wind plasma. On the nightside the ionopause is much more highly variable, sometimes falling below 200 km or rising above 3500 km. The present Pioneer Venus orbit does not permit the true configuration to be measured. Within the nightside ionosphere itself, we find extreme spatial irregularities in the form of holes, horizontally stratified layers, detached plasma clouds, and dual temperature plasma in regions of low electron density. A scenario is developed to describe the process of ion pickup on the dayside in terms of solar wind pressure discontinuities inducing wavelike structure at the ionopause, which then is penetrated by ionosheath plasma and magnetic fields that remove ionospheric plasma impulsively in the form of detached plasma clouds. The energy released in this process may be responsible for the elevated electron temperatures observed in both the dayside and nightside of the Venus ionosphere.

Pioneer Venus observations are used in conducting a study of the location and structure of the Venus bow shock. The trace of the shock in the solar wind aberrated terminator plane is nearly circular at an altitude of 1.38 RV independent of interplanetary magnetic field orientation with an extrapolated subsolar height of 0.38 RV. Gas dynamic relations and scaling of the terrestrial analogue are used to determine the effective impenetrable obstacle altitude from the mean shock surface with the conclusion that it lies beneath the observed height of the ionopause. The short‐term variability in shock position is similar to that found at the earth, while over the long‐term bow shock, altitude varies by up to ∼35% in phase with the solar cycle owing to causes other than changing solar wind Mach number. In contrast to ionopause position, which is shown to be well determined by external pressure measurements, bow shock altitude is found to be only weakly dependent upon ionopause height and solar wind dynamic pressure. These results are interpreted in terms of interactions with exospheric neutrals and/or lack of complete deflection of the incident solar wind by currents induced in the ionosphere modifying the flow about Venus from that associated with a tangential discontinuity obstacle of nearly constant radius. The downstream bow shock is smaller in diameter than that of terrestrial case despite the larger Mach cone angle at 0.72 AU most probably due to the smaller relative size of the Venus magnetotail. A brief survey of shock structure with Pioneer Venus instrumentation shows general agreement as to the time and location of the shock crossings with a transition layer thickness of the order of the ion inertial length scale. The observed variation in bow shock structure and the foreshock with upstream parameters was similar to that seen at the earth.

The solar wind plasma analyzer on board Pioneer 11 provides first observations of low‐energy positive ions in the magnetosphere of Saturn. Measurable intensities of ions within the energy per unit charge (E/Q) range 100 eV to 8 keV are present over the planetocentric radial distance range ∼4–16 Rs in the dayside magnetosphere. The plasmas are found to be rigidly corotating with the planet out to distances of at least 10 Rs. At radial distances beyond 10 Rs, the bulk flows appear to be in the corotation direction but with lesser speeds than those expected from rigid corotation. At radial distances beyond the orbit of Rhea at 8.8 Rs, the dominant ions are most likely protons, and the corresponding typical densities and temperatures are 0.5 cm−3 and 106 °K, respectively, with substantial fluctuations. Identification of the mass per unit charge (M/Q) of the dominant ion species is possible in certain regions of Saturn’s magnetosphere via the angular distributions of positive ions. A large torus of oxygen ions is located inside the orbit of Rhea, and the densities are >10 cm−3 over the radial distance range ∼4–7.5 Rs. Density maxima appear at the orbits of Dione and Tethys where oxygen ion densities are ∼50 cm−3. The dominant oxygen charge states are O2+ and O3+ in the radial distance ranges ∼4–7 Rs and 7–8 Rs, respectively. The observations are suggestive of a decrease of ion energies to values less than the instrument energy threshold of E/Q=100 eV at the apparent inward edge of the torus at 4 Rs. Ion temperatures increase rapidly from ∼2 × 105 °K at 4 Rs to 5 × 106 °K at 7.3 Rs. It is concluded that the most likely source of these plasmas is the photodissociation of water frost on the surface of the ring material with subsequent ionization of the products and radially outward diffusion. The sources associated with the satellites Dione and Tethys are probably of lesser strength. The presence of this plasma torus is expected to have a large influence on the dynamics of Saturn's magnetosphere, since the pressure ratio β of these plasmas approaches unity at radial distances as close to the planet as 6.5 Rs. On the basis of these observational evidences it is anticipated that quasi‐periodic outward flows of plasma, accompanied by a reconfiguration of the magnetosphere beyond ∼6.5 Rs, will occur in the local night sector in order to relieve the plasma pressure from accretion of plasma from the rings.