The dimensionality of episodic images

The dimensionality of episodic images Vishnu Sreekumar (sreekumar.1@buckeyemail.osu.edu) Department of Psychology, Ohio State University Columbus, OH 43201 USA Yuwen Zhuang (zhuang.14@buckeyemail.osu.edu) Department of Computer Science and Engineering, Ohio State University Columbus, OH 43201 USA Simon J. Dennis (simon.dennis@gmail.com) Department of Psychology, Ohio State University Columbus, OH 43201 USA Mikhail Belkin (mbelkin@cse.ohio-state.edu) Department of Computer Science and Engineering, Ohio State University Columbus, OH 43201 USA Abstract spaces of corpora of different languages exhibited a two-scale structure (Doxas et al., 2010). Doxas et al. did a correlation dimension analysis on the paragraph spaces of text corpora taken from five different languages and genres. The corre- lation dimension is a measure of how points within a given distance r scales with that distance. The paragraph spaces were found to exhibit a low dimensional structure at short dis- tances and a higher dimensional structure at larger distances. This is similar to a “weave” structure. For example, if we zoom in to look at a thread that is part of a shirt, the observed dimensionality is one. If we zoom out to intermediate length scales, we would start observing a two dimensional structure. Further zooming out will further increase the dimensionality. The finding of this “weave” structure in natural language dis- course raises an important question regarding the origin of this constraint. Is this constraint one that is imposed by the cognitive system or is it a property of the input the system receives that is being mirrored by the cognitive system? We attempt to address this question in the current study. To in- vestigate this, we used a Microsoft TM Research SenseCam to capture images that can be thought of as representative of a person’s (visual) episodic experience. A dimensionality anal- ysis was then done on these images. Previous studies (Doxas, Dennis, & Oliver, 2010) show that natural language discourse exhibits a two-scale structure with a lower dimension at short distances and larger dimension at long distances. We attempt to search for the source of this constraint in the visual input that goes into forming episodic experiences in human beings. This information is assumed to be approximated well by images captured by a Microsoft TM Research SenseCam that our subjects used. The hypothesis is that if the same two scale structure is observed here, the constraint is possibly not one that is imposed by the cognitive system. We use and contrast two methods by which images can be represented: the traditional color histogram and a more recently developed color correlogram method. The color correlogram is established to work better for our current purposes. We observe hints of a two scale structure in the cor- relation dimension plots but these are not conclusive. Keywords: Episodic Memory; Correlation Dimension; Net- works; Graphs. Introduction The existing models of episodic memory assume a represen- tation of context. Retrieval of episodes involves reinstatement of context. The current literature does not address the nature of representation of context and the question of how the rep- resentation was formed in the first place. Our ultimate goal is to model contextual reinstatement as a search over episodic networks. We begin by looking at the images that people en- counter everyday. In a parallel study, graphs of these images are constructed and the structure of the graphs is investigated. People are extremely fast at isolating episodes from mem- ory. Such a search has to be fast and efficient. The graph has to satisfy certain properties for it to be efficiently searchable (Steyvers & Tenenbaum, 2005). We attempt to test the idea that contextual reinstatement can be modeled as a network search. One prerequisite for this model to be feasible is that the episodic network must be quickly searchable. We encode events into our memory as we encounter and experience them. What kinds of constraints are inherent to this input information? Such a question is motivated by pre- vious studies on natural language discourse where paragraph The paper is organized as follows. The next section out- lines the method used to capture and represent the images on which the dimensionality analysis is done. The Microsoft Re- search SenseCam device is described briefly. Two different image representation schemes and their corresponding dis- tance measures are discussed. The two methods are then con- trasted using a definition of a ratio that is based on the require- ment that these methods must, among other things, success- fully identify images that belong to the same contexts. The subsequent section describes the correlation dimension. The results section discusses the correlation dimension plots for the image sets obtained from different individuals. The paper concludes with a discussion of the structure that is observed in the correlation dimension plots of the image data.