Incremental Method of Generating Decision Implication Canonical Basis

Decision implication is an elementary representation of decision knowledge in formal concept analysis. Decision implication canonical basis (DICB), a set of decision implications with completeness and nonredundancy, is the most compact representation of decision implications. The method based on true premises (MBTP) for DICB generation is the most efficient one at present. In practical applications, however, data is always changing dynamically, and MBTP has to re-generate inefficiently the whole DICB. This paper proposes an incremental algorithm for DICB generation, which obtains a new DICB just by modifying and updating the existing one. Experimental results verify that when the samples in data are much more than condition attributes, which is actually a general case in practical applications, the incremental algorithm is significantly superior to MBTP. Furthermore, we conclude that, even for the data in which samples is less than condition attributes, when new samples are continually added into data, the incremental algorithm must be also more efficient than MBTP, because the incremental algorithm just needs to modify the existing DICB, which is only a part of work of MBTP.

The elementary representation of spatial and color vision in the human retina

The retina is the most accessible element of the central nervous system for linking behavior to the activity of isolated neurons. We unraveled behavior at the elementary level of single input units—the visual sensation generated by stimulating individual long (L), middle (M), and short (S) wavelength–sensitive cones with light. Spectrally identified cones near the fovea of human observers were targeted with small spots of light, and the type, proportion, and repeatability of the elicited sensations were recorded. Two distinct populations of cones were observed: a smaller group predominantly associated with signaling chromatic sensations and a second, more numerous population linked to achromatic percepts. Red and green sensations were mainly driven by L- and M-cones, respectively, although both cone types elicited achromatic percepts. Sensations generated by cones were rarely stochastic; rather, they were consistent over many months and were dominated by one specific perceptual category. Cones lying in the midst of a pure spectrally opponent neighborhood, an arrangement purported to be most efficient in producing chromatic signals in downstream neurons, were no more likely to signal chromatic percepts. Overall, the results are consistent with the idea that the nervous system encodes high-resolution achromatic information and lower-resolution color signals in separate pathways that emerge as early as the first synapse. The lower proportion of cones eliciting color sensations may reflect a lack of evolutionary pressure for the chromatic system to be as fine-grained as the high-acuity achromatic system.