Revealed Preference Dimension via Matrix Sign Rank

Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the market dimension is fixed. This paper solves the open problem of determining exactly which graphs are attainable as revealed preference graphs in $d$-dimensional markets. This is achieved via an exact characterization which closely ties the feasibility of the graph to the Matrix Sign Rank of its signed adjacency matrix. The paper also shows that when the preference relations form a partially ordered set with order-dimension $k$, the graph is attainable as a revealed preference graph in a $k$-dimensional market.Comment: Submitted to WINE `1

Structuring Consumer Preferences with the SEM Method

Structuring preferences has been developed with econometric models using functional flexible parametric form and the exploring the perceptions about expressed and latent needs using different multivariate approaches. Purpose of this research is to explore the demand for a new drink using the mean-end chain (MEC) theory and multivariate SEM procedure. The first part is dedicated to description of specialty foods for their capacity to create new niche markets. The MEC theory is introduced to explain the relations between attributes and consumers' perceptions of secondary needs revealed as benefit and values. The second part is dedicated to the empirical investigation of demand of a drink obtained from the "Olivello spinoso" a spontaneous plant. Empirical data were collected with "face to face sensorial test", and used to test the consumer perceptions for the product's attributes and preferences using the SEM approach. Conclusive remarks are in terms of suggestions about the modification of the product's attributes to increase the demand.Demand, Mean-End Chain, multivariate analysis, Specialty products, Niche market, customer satisfaction, SEM, Consumer/Household Economics,

Robust Principal Component Analysis?

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the L1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces

Defining block character

In this paper I propose a clear, efficient, and accurate method for determining if a block of contiguous buildings has an overall character. The work is needed because most contemporary design reviews presuppose the existence of visual character, but existing design principles are often too vague to make the required determination. Clarity is achieved by shifting from vague notions to a definite concept for block character: a design feature will be perceived as part of the overall character of that block if the frequency of the feature is greater than a critical threshold. An experiment suggested that the critical frequency was quite high: over 80%. A case history illustrates how the new concept of visual character could greatly increase the efficiency and accuracy of actual planning decisions.

SAVOIAS: A Diverse, Multi-Category Visual Complexity Dataset

Visual complexity identifies the level of intricacy and details in an image or the level of difficulty to describe the image. It is an important concept in a variety of areas such as cognitive psychology, computer vision and visualization, and advertisement. Yet, efforts to create large, downloadable image datasets with diverse content and unbiased groundtruthing are lacking. In this work, we introduce Savoias, a visual complexity dataset that compromises of more than 1,400 images from seven image categories relevant to the above research areas, namely Scenes, Advertisements, Visualization and infographics, Objects, Interior design, Art, and Suprematism. The images in each category portray diverse characteristics including various low-level and high-level features, objects, backgrounds, textures and patterns, text, and graphics. The ground truth for Savoias is obtained by crowdsourcing more than 37,000 pairwise comparisons of images using the forced-choice methodology and with more than 1,600 contributors. The resulting relative scores are then converted to absolute visual complexity scores using the Bradley-Terry method and matrix completion. When applying five state-of-the-art algorithms to analyze the visual complexity of the images in the Savoias dataset, we found that the scores obtained from these baseline tools only correlate well with crowdsourced labels for abstract patterns in the Suprematism category (Pearson correlation r=0.84). For the other categories, in particular, the objects and advertisement categories, low correlation coefficients were revealed (r=0.3 and 0.56, respectively). These findings suggest that (1) state-of-the-art approaches are mostly insufficient and (2) Savoias enables category-specific method development, which is likely to improve the impact of visual complexity analysis on specific application areas, including computer vision.Comment: 10 pages, 4 figures, 4 table