We present a fractal technique for addressing geometric analogy problems from the Raven's Standard Progressive Matrices test of general intelligence. In this method, an image is represented fractally, capturing its inherent self-similarity. We apply these fractal representations to problems from the Raven's test, and show how these representations afford a new method for solving complex geometric analogy problems. We present results using the fractal algorithm on all 60 problems from the Standard Progressive Matrices version of the Raven's test.
We report a novel approach to addressing the Raven’s Progressive Matrices (RPM) tests, one based upon purely visual representations. Our technique introduces the calculation of confidence in an answer and the automatic adjustment of level of resolution if that confidence is insufficient. We first describe the nature of the visual analogies found on the RPM. We then exhibit our algorithm and work through a detailed example. Finally, we present the performance of our algorithm on the four major variants of the RPM tests, illustrating the impact of confidence. This is the first such account of any computational model against the entirety of the Raven’s.
The Raven's Progressive Matrices (RPM) test is a commonly used test of general human intelligence. The RPM is somewhat unique as a general intelligence test in that it focuses on visual problem solving, and in particular, on visual similarity and analogy. We are developing a small set of methods for problem solving in the RPM which use propositional, imagistic, and multimodal representations, respectively, to investigate how different representations can contribute to visual problem solving and how the effects of their use might emerge in behavior.
Fitzgerald, Tesca (Georgia Institute of Technology) | McGreggor, Keith (Georgia Institute of Technology) | Akgun, Baris (Georgia Institute of Technology) | Goel, Ashok K. (Georgia Institute of Technology) | Thomaz, Andrea L. (Georgia Institute of Technology)
Learning by observation is an important goal in developing complete intelligent robots that learn interactively. We present a visual analogy approach toward an integrated, intelligent system capable of learning skills from observation. In particular, we focus on the task of retrieving a previously acquired case similar to a new, observed skill. We describe three approaches to case retrieval: feature matching, feature transformation, and fractal analogy. SIFT features and fractal encoding were used to represent the visual state prior to the skill demonstration, the final state after the skill has been executed, and the visual transformation between the two states. We discovered that the three methods (feature matching, feature transformation, and fractal analogy) are useful for retrieval of similar skill cases under different conditions pertaining to the observed skills.
Graphical models offer techniques for capturing the structure of many problems in real-world domains and provide means for representation, interpretation, and inference. The modeling framework provides tools for discovering rules for solving problems by exploring structural relationships. We present the Structural Affinity method that uses graphical models for first learning and subsequently recognizing the pattern for solving problems on the Raven's Progressive Matrices Test of general human intelligence. Recently there has been considerable work on computational models of addressing the Raven's test using various representations ranging from fractals to symbolic structures. In contrast, our method uses Markov Random Fields parameterized by affinity factors to discover the structure in the geometric analogy problems and induce the rules of Carpenter et al.'s cognitive model of problem-solving on the Raven's Progressive Matrices Test. We provide a computational account that first learns the structure of a Raven's problem and then predicts the solution by computing the probability of the correct answer by recognizing patterns corresponding to Carpenter et al.'s rules. We demonstrate that the performance of our model on the Standard Raven Progressive Matrices is comparable with existing state of the art models.