Chernoff Faces: a Useful Technique For Comparative Image Analysis and Representation

Linda L. Golden, University of Texas at Austin
Mayur Sirdesai, University of Texas at Austin
ABSTRACT - While consumer researchers often measure image in a decomposed attribute-by-attribute manner, it is easy to recognize that image is greater than the sum of its parts. Brand image is an important concept for consumer behavior and its relationship to choice behavior is being established in the literature. This paper presents a new approach for globally representing quantitative image impressions (data) and demonstrates its usefulness empirically. Using Chernoff face icons, the consumers' perceptions of multi-dimensional, multi-object attributes can be readily displayed for visual analysis.
[ to cite ]:
Linda L. Golden and Mayur Sirdesai (1992) ,"Chernoff Faces: a Useful Technique For Comparative Image Analysis and Representation", in NA - Advances in Consumer Research Volume 19, eds. John F. Sherry, Jr. and Brian Sternthal, Provo, UT : Association for Consumer Research, Pages: 123-128.

Advances in Consumer Research Volume 19, 1992      Pages 123-128

CHERNOFF FACES: A USEFUL TECHNIQUE FOR COMPARATIVE IMAGE ANALYSIS AND REPRESENTATION

Linda L. Golden, University of Texas at Austin

Mayur Sirdesai, University of Texas at Austin

[We gratefully thank New York University who contributed financially to the data collection, the University of Texas Research Institute and Mary R. Zimmer of the University of Georgia for her involvement. Sincere appreciation is also extended to Robert T. Green and the University of Texas Graduate School of Business for their support.]

ABSTRACT -

While consumer researchers often measure image in a decomposed attribute-by-attribute manner, it is easy to recognize that image is greater than the sum of its parts. Brand image is an important concept for consumer behavior and its relationship to choice behavior is being established in the literature. This paper presents a new approach for globally representing quantitative image impressions (data) and demonstrates its usefulness empirically. Using Chernoff face icons, the consumers' perceptions of multi-dimensional, multi-object attributes can be readily displayed for visual analysis.

Consumer researchers recognize the important relationship between consumer image perceptions and purchasing behavior. In fact, it has been said that most individuals base their purchasing actions on the type of image a product portrays (Jacoby and Mazursky 1984). Thus, because of the importance of the idea, consumer researchers and strategists have developed many ways to measure consumer image perceptions.

Image measurement and analysis techniques range from the traditional quantitative multi-variate ones, to qualitative data collection and analysis (see Zimmer and Golden 1988 for a review and content analysis application), to the recent introduction of information theoretic analysis for scaled image data (Golden, Brockett and Zimmer 1990). However, irrespective of analytical approach, the effective display of multidimensional findings is often very cumbersome and its meaning difficult to represent.

Brand and retail image is generally recognized to be multi-dimensional (Golden, Albaum and Zimmer 1987) and researchers often wish to compare image results across alternative product offerings. Indeed, one way of comparing images of competitive products is to substitute competitors' brand names with your own and evaluate the relative consumer responses across multiple attribute dimensions in order to develop a comparative assessment of consumer perceptions (Jacoby and Mazursky 1984). However, sometimes the informational analysis desired goes beyond the "Are the differences statistically significant?" to focus on "What does this mean?" and "How can I interpret or present it?"

This paper develops and empirically demonstrates the idea of using icons, specifically geometrically derived Chernoff faces, as a tool to comprehend and display multi-variate image data (in this case, retail store image data). Via SYSTAT the Chernoff face analysis program is now readily available and this technique has been shown to be more effective than many other icons for similarity comparisons (Wilkinson 1983). Chernoff faces can help behavioral analysts and strategists represent the results of image data in a simplified and comprehensive manner. In addition, Chernoff faces can be used as the sole method of analysis or combined with other statistical techniques to assess statistical effects, depending on the consumer analysts needs at the moment of inquiry.

The conceptual underpinnings of Chernoff faces are highly mathematical in nature (see Chernoff 1973), but the results allow for immediate visual comparisons across alternative image objects (such as stores or brands). No previous research has explored the usefulness of this technique for consumer behavior or image perceptions.

Chernoff Faces

A typical Chernoff face is a cartoon-like caricature of the human face developed through a series of highly mathematical and geometrical relationships (see Figure). Chernoff surmised that individuals can distinguish the subtle differences in each facial feature and can develop an image of a person based on these differences. He used this idea to create an image of multi-variate data sets where each variable was assigned a particular facial feature. Depending on the relative magnitudes of the data, the facial characteristics create a unique image for a given multi-variate data set.

Some studies using Chernoff faces have been conducted in the political, psychological and medical areas (see Wang 1978). One published paper, related to business, developed the faces as a representation of the mathematical results of the financial performance and future predictions for various types of businesses, using faces as a visual indicator of past performance and current status (Huff, Mahajan and Black 1981). However, most of the work has been conducted in the area of statistics, using Chernoff faces as a method of clustering multidimensional data (Jacob 1983, Jacob et. al 1976). In fact, this was the original purpose behind the development of Chernoff Faces: Visual clustering of multi-dimensional statistical data. This paper focuses on a useful consumer behavior application of Chernoff faces and the mathematics of the theoretical framework behind the technique is left to its discussion in other literature (see Chernoff 1973).

FIGURE

CHERNOFF FACIAL ATTRIBUTES AND RELATIONSHIP OF IMAGE PERCEPTION VARIABLES WITH FACE CHARACTERISTICS

PURPOSE AND FOCUS OF THE RESEARCH

Marketers often measure consumer image perceptions via numerous attribute ratings (Golden, Albaum and Zimmer 1987, Golden, Brockett, Albaum and Zatarain 1991, Golden 1991). As such, image is a multi-dimensional concept. This necessitates the analysis and depiction of image results across multiple objects for multiple image dimensions. Chernoff faces provide a method by which these image results can be compared and depicted in a comprehensible manner.

This paper compares consumer image perceptions of two mass-merchandise retail store chains (Sears and K-Mart) across nineteen different image attributes developed from an extensive review of the literature. Data on these nineteen attributes were collected as part of a survey conducted via a nationwide consumer mail panel (see the methodology section for details).

The paper shows how Chernoff Faces can make readily visible the consumers' comparative image perceptions both across brands (stores) and within various patronage market segments (intra-store comparison). Thus, the usefulness of the technique for image display is not limited to inter-brand comparisons but also includes intra-brand comparisons across specific consumer segments of interest (in this case, segmentation by purchase/store trip frequency).

METHODOLOGY

Data Collection and Description

Chernoff faces were developed from the quantitative results of a nationwide survey of 453 consumer mail panel members. The final sample generally represented the geographical distribution of the United States and was 58.1 percent female. The respondents' annual household income distribution was: 17.5 percent earned less than $10,000 per year, 25.8 percent earned between $10,000 and $19,999 per year, 23.1 percent earned between $20,000 and $29,999 per year, 15.7 percent earned between $30,000 and $39,999 per year, 7.7 percent earned between $40,000 and $49,999 per year and 10.2 percent earned $50,000 or more per year. Nearly 16 percent of the respondents were under 30 years old, 22.7 percent were between 30 and 39 years, 16.8 percent were between 40 and 49 years, 19.0 percent were between 50 and 59 years and 25.8 percent were over 60 years old. Ten percent of the respondents had less than a high school education, 35.9 percent were high school graduates, 26.6 percent had some college education and 27.5 percent had four or more years of college.

In the survey instrument, respondents were asked to indicate their perceptions of both Sears and K-Mart on a seven-point numerical comparative scale (see Golden, Albaum and Zimmer 1987 and Golden 1991), an economical semantic differential-type scale format for image comparisons across multiple image objects and dimensions. The numerical comparative scale has also been shown to result in good quality data (Albaum and Golden, forthcoming).

The image dimensions used in this study were identified through an exhaustive literature review. The retail store image dimensions retrieved from the literature were then culled to:

(1) reflect a comprehensive array of image attribute dimensions,

(2) represent attributes most frequently investigated in the literature, and

(3) reduce redundancy in attribute dimensions.

This process resulted in the isolation of nineteen image attributes whose bi-polar scale construction translated to: inconvenient/convenient location, low/high price, dirty/clean, hard/easy to get credit, cluttered/spacious, unpleasant/pleasant atmosphere, low/high quality merchandise, dull/exciting, bad/good selection, unsophisticated/sophisticated customers, unfriendly/friendly salespersons, low/high caliber, dislike/like, unhelpful/helpful salespersons, bad/good reputation, uncongested/congested, not enjoyable/ enjoyable, hard/easy to exchange merchandise, bad/good value. In the numerical comparative scale presented to respondents, the left most extreme point of each bi-polar adjective pair was represented by "1", with the right extreme being represented by "7".

Respondents were also asked to indicate how frequently they shopped at Sears and K-Mart. For the intra-store Chernoff face analysis, responses to this question were divided in order to represent Infrequent Shoppers (once a year or less), Moderately Frequent Shoppers (two to twelve times a year), and Frequent Shoppers (more than twelve times a year). The survey queried respondents about other issues and scale formats not relevant for this paper.

Chernoff Face Analysis

The mean and variances were computed for all nineteen attributes across the three shopping frequency categories. Based on these data, Chernoff faces were constructed using the SYSTAT software (Wilkinson 1988, pages 380-381). Twenty variables can be included in a single Chernoff face analysis; thus, the nineteen image attributes were within the possible computing range. Chernoff faces were developed for each store and each patronage frequency group separately.

Since an individual can perceive changes in some facial characteristics better than in others, it is feasible to assign the most important variables to features such as the curvature of the mouth, half-face height, half-length of eyes, and length of brow (Soete and Corte 1985) to get a better understanding of the image created. The Figure displays summary information on the mathematical construction of a Chernoff face and the particular facial characteristics that have been associated with each image attribute in this research.

RESULTS

Tables 1 and 2 present the results of the analysis for Sears and K-Mart, respectively. Mean ratings for each image attribute and the group size (n) are presented, as well as the resultant Chernoff face compilation.

Instructive of the usefulness of Chernoff faces is for the reader to place his or her hand over the faces and try to interpret the comparative image of Sears and K-Mart for the various shopping frequency groups from the numerical data alone. The comparison becomes very cognitively complex and difficult to summarize. However, when one's hand is removed from the Chernoff faces, a visual comparison of the image across stores and shopper frequency categories becomes immediately apparent. In addition to being a sophisticated mathematical representation, Chernoff faces provide a very quick and lucid image analysis when compared to the process of analyzing numerical results across each attribute. Thus, the resultant usefulness of Chernoff faces for image analysis and comparative image representation.

Focusing on Table 1, it is immediately apparent from the Chernoff faces that image perceptions become more "favorable" as one moves from the "infrequent shoppers" group to the "frequent shoppers" group. The association between shopping frequency and image perceptions is very quickly visualized.

TABLE 1

PERCEPTION OF SEARS THROUGH SHOPPING FREQUENCIES

These same general results hold for Table 2, K-Mart. However, comparing the results for Sears (Table 1) and K-Mart (Table 2), Chernoff faces also demonstrate that the constellation of image attributes for K-Mart within the moderate and frequent shoppers is somewhat stronger than for the same shopper groups at Sears. Referring to the Figure which lists the facial characteristics associated with the various image dimensions, the mouth is associated with perceptions of location convenience. Thus, the up-turned mouth for K-Mart in Table 2 illustrates a stronger positive image perception of location convenience vis-a-vis that perceived for Sears (as shown in Table 1).

Likewise, two other important facial characteristics are the position of the pupils and the slant of the eyes. These are associated with the over-all affect toward the store (dislike-like) and perceptions of the customers' sophistication, respectively. For both Sears and K-Mart, persons who shopped more frequently at the stores liked the stores better and perceived the stores as having more sophisticated customers. These results are depicted by the pupils moving inwards as the perceptions of positive affect increase and the eyes slant more outward as the perceptions of customer sophistication increase. The direction of change for each attribute represented by a given facial feature is indicative of the direction of the attribute rating on the numerical comparative scale results.

An attribute-by-attribute analysis can be conducted in this manner; however, this is not the primary advantage of Chernoff faces because an attribute-by-attribute analysis can also be seen rather readily from the tables. The advantage of Chernoff

TABLE 2

PERCEPTION OF KMART THROUGH SHOPPING FREQUENCIES

faces is the rapid visualization of the global image represented by the constellation of attributes. For example, across all attributes, the perceptions of K-Mart among moderate shoppers appear to be more positive (looking at the constellation of attributes represented by the whole face) than do the perceptions of Sears among its moderately frequent shoppers. The same can be said about the "frequent shoppers," as the K-Mart frequent shoppers display slightly more general enthusiasm than do the Sears frequent shoppers.

In using Chernoff faces to graphically represent multi-variate data, the researcher should keep in mind that an attribute-by-attribute comparison may mislead the viewer into believing there are strong differences where no statistically meaningful differences exist. For the brand image example presented in this paper, the appropriate focus is on the rapid visualization advantage of the global image and not on over-emphasis of attribute-by-attribute comparisons. Otherwise, the value of Chernoff faces analysis may be obscured or the usefulness abused.

CONCLUSION

A brand or a store's image is greater than the sum of its parts (Zimmer and Golden 1988). Similarly, the constellation of a person's facial expressions is greater than the sum of its parts; thus, faces can be a useful mechanism for globally representing image response data. As consumer researchers continually recognize the relevance of image perception for choice behavior, it becomes more important to be able to accurately and precisely portray the results of image analyses. Facial representations provide a useful mechanism for so doing.

Although highly mathematical in nature and originally developed by Chernoff for the purpose of visual clustering, Chernoff faces do not circumvent the usefulness of other statistical analyses to discern meaningful differences in response data. Chernoff faces do provide a quick and accurate technique for the depiction of comparative image data, and the main advantage comes from the fact that each data point does not need to be compared with others in the same category, rather, an overall image gestalt can be illustrated for visual comparison purposes.

Extending the usefulness of Chernoff faces, this paper showed the development of Chernoff faces for image comparisons both within and between brands. Inter-brand comparisons allow immediate visualizations of image differences between or among consumer choice alternatives. However, focus on comparisons of specific segments of interest within a brand (intra-brand) quickly reveals the relationships between image perceptions and behavior.

This study focused on retail store image (between and within alternative brands of mass merchandisers), but the same technique can be used for any other type of image portrayal situation for which the researcher has voluminous data and an accurate visual representation of results is desired. In addition, Chernoff faces can be used to augment other types of statistical analyses that focus on significant differences between image attributes. They provide consumer researchers with an additional tool for more complete analysis, understanding and representation of the relationships between image perceptions and behavior.

REFERENCES

Albaum, Gerald and Linda L. Golden (forthcoming), "Alternative Measurement Formats for Multiple Comparisons Across Multiple Image Objects," Journal of Global Marketing.

Chernoff, Herman (1973), "Using Faces to Represent Points in K-Dimensional Space Graphically," Journal of the American Statistical Association, 68 (June), 361-368.

Golden, Linda L., Patrick L. Brockett, Gerald Albaum and Juan Zatarain (1991), "The Golden Numerical Comparative Scale: Economies with No Loss of Data Quality," Working Paper, University of Texas at Austin.

Golden, Linda L. (1991), "Results of Tests on the Golden Numerical Comparative Scale," American Statistical Association 1990 Proceedings of the Section on Survey Research Methods, Alexandria: American Statistical Association, 677-682.

Golden, Linda L., Patrick L. Brockett and Mary R. Zimmer (1990), "An Information Theoretic Approach for Identifying Shared Information and Asymmetric Relationships Among Variables," Multivariate Behavioral Research, 25 (October), 479-502.

Golden, Linda L., Gerald Albaum and Mary R. Zimmer (1987), "The Numerical Comparative Scale: An Economical Format for Retail Image Measurement," Journal of Retailing, 63 (4), 393-410.

Huff, David L., Mahajan, Vijay and Black, William. C.(1981), "Facial Representation of Multivariate Data," Journal of Marketing, 45 (Fall), 53-59.

Jacob, Robert J. K. (1983), "Investigating the Space of Chernoff Faces," in Recent Advances in Statistics, M. H. Rizvi, J. S. Rustagi and D. Siegmund (Eds.), New York: Academic Press, 449-468.

Jacob, Robert J. K., Egeth, H. E. and Bevan, W. (1976), "The Face as a Data Display,", Human Factors, 18, 189-200.

Jacoby, Jacob and Mazursky, David (1984), "Linking Brand and Retailer Images - Do the Potential Risks Outweigh the Potential Beenfits?," Journal of Retailing, 69 (Summer), 105-122.

Soete, Geert D. and Corte, Wilfried D.(1985), "On the Perceptual Salience of Features of Chernoff Faces for Representing Multivariate Data," Applied Psychological Measurement, 9 (September), 275-280.

Wang, Peter C., ed.(1978), Graphical Representation of Multi-Variate Data, New York: Academic Press.

Wilkinson, Leland (1988), Sysgraph, Evanston: Systat, Inc.

Wilkinson, L. (1983), Fuzzygrams, Cambridge, MA: Harvard Computer Graphics Week.

Zimmer, Mary R. and Linda L. Golden (1988), "Impressions of Retail Stores: A Content Analysis of Consumer Images," Journal of Retailing, 64 (3), 265-293.

----------------------------------------