Short paper, CHI’2000, Copyright ACM
Physics-based Graphical Keyboard Design Michael Hunter
Shumin Zhai
Barton A Smith
IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, +1 (408) 927 1112
[email protected] {zhai, basmith}@almaden.ibm.com ABSTRACT
Built upon the Fitts’ law and digraph model developed by MacKenzie and colleague [2, 3], we introduce two physicsbased methods to graphical keyboard design. One method uses physical simulation of digraph springs and the other uses a Monte Carlo method. Both methods produced keyboard layouts comparable to existing best designs by trial-and-error methods. We also correct an error in previous predictions and concluded that the upper bound performance of a graphical keyboard should be at 42 to 44 wpm. The effect of varying key size and the use of multiple space keys are discussed. Keywords
Graphical keyboard, soft keyboard, text entry, input. PREVIOUS WORK
Graphical keyboards (GK) for text-entry computing devices such as PDAs have been used and studied in the literature. A fundamental contribution on the topic is the model proposed by MacKenzie and colleagues [2, 3] that predicts user’s performance using GK. There are essentially two components in this model. One is Fitts’ law, which predicts the mean time to move the tapping stylus from one key (i) to another (j) for given distance (Dij) and key size (Wj). The other is the statistical transition (digraph) probability (Pij) for example in English between each pair of 27 keys (A to Z, and Space key). The mean time in seconds for typing a character is: 27
t =a+∑ i =1
27
∑ j =1
Pij Dij + 1 Log 2 4 .9 Wi
(1)
This equation allows typing speed in words per minute (wpm) to be calculated, assuming five characters per word. Since the model does not incorporate visual scanning or learning, the prediction is considered to be the upper bound of a user’s performance. Note that, the Fitts’ law coefficient used in (1) is based on average human tapping performance. Some users can tap faster than the average Fitts law prediction. Based on this model, MacKenzie and Zhang [2] predicted 43.2 wpm performance for the QWERTY layout. “Following substantial trial and error”, MacKenzie and Zhang designed a new layout, OPTI, whose performance was predicted to be 58.2 wpm. This is a very high performance for text entry, faster than most people’s 10 finger typing speed on a physical keyboard. Actual users
reached 44.3 wpm after 20 sessions of text entry, each for 45 minutes, on the OPTI design [2]. The goal of the current study is to replace the trial-anderror approach with more systematic approaches to the design of key layout. We first thoroughly analyzed their model and found a calculation error in their predictions. The OPTI Keyboard used 4 space keys. There are hence multiple character-space-character paths that had to be handled differently from other character-character transitions. In calculating the probability of characterspace-character transitions, MacKenzie and Zhang overlooked that fact that the probability of the second segment of the path (space-character) had to be conditional probability, since the two segments are serial. After correcting this error, we found the upper bound of the OPTI design to be at 40.3 wpm and of the QWERTY design to be 27.6 wpm. 40 wpm is still much higher than legible handwriting speed, suggesting the graphical keyboard to be a worthwhile approach to text entry. Using the corrected model, we explored two physics-based design methods. One could envision exhaustive logarithmic searching approach to design the optimal GK. However, the complexity of such a search is 0(n!) = 1028 . The Dynamic Simulation Method
With a mechanical simulation package (Working Model), we constructed springs between every pair of the 27 keys whose initial positions are randomly placed with spaces between the keys. The elasticity of a spring is proportional to the transitional probability between the two keys, so that the keys with the strongest transitional probability would be pulled together with greater force. There were viscous forces between the circle shaped keys and between the keys and the table surfaces. At the end of the simulation, all keys were pulled together as a basis of a candidate GK design. The performance of the design was then calculated according to model (1) and compared with existing designs. Note that such a simulation process does not ensure an optimal design. The final positions of the keys may not be at the minimum energy state, because some keys could block others from entering a lower energy state. Two methods were used to reduce deadlock states. First, we experimented with different initial states, until a satisfactory GK is achieved. Second, each spring had an extended segment that has adjustable length, which held the key apart. The length of this segment can be manually adjusted in the dynamic simulation process, until a satisfactory layout, evaluated by equation (1) is achieved.
The performance of the best design by dynamic simulation is 41.6 wpm. Fitts Energy and the Metropolis Method
We also explored another physics-based approach - the Metropolis Method. We realized that the GK design problem was very similar to searching the minimum energy state in statistical physics [1]. Designing a high performance keyboard is just like searching the structure of a molecule. Applying such an approach, we wrote a program that does a Monte Carlo “random walk” in the GK design space. In each step of the walk, the algorithm picks a key and moves it in a random direction by a random amount to reach a new configuration. The level of “Fitts energy” in the new configuration, based equation (1), is then evaluated. Whether the new configuration is kept as the starting position for the next iteration step depends on the following Metropolis function [4]:
W (A → B) = e =1
− ∆E
kT
if ∆E > 0 if ∆E ≤ 0
(2)
In equation (2), W (A-B) is the probabilty of changing from configuration A (old) to configuration B (new), ∆E is the energy change, k is a coefficient, T is “temperature”, which could be adjusted. The use of equation (2) is what makes the Metropolis method superior to our previous spring model, because the search does not always move towards a local minimum. It occasionally allows moves with positive energy change in order to be able to climb out of a local energy minimum. The random walk process starts from a random initial state and iterates according to the Metropolis function. The search process was also “annealed” by adusting temperature over time, until a sufficiently low energy solution was achieved. Annealing was controlled by operator evaluation of the energy descent. As the energy started to climb, a lower temperature was used, and resumed with the best previous energy state. The best GK design that we produced with the Metropolis search method, shown in Figure 1, has a predicted performance of 43.7 wpm.
Split Space Keys and Varying Key Size
Given the frequent use of the space key, the OPTI design [2] used 4 space keys, so that a user can pick a space key that makes the shortest character-space-character distance. This means that the user has to look a step ahead of typing, which requires difficult cognitive effort. Indeed, it was found that users selected the correct space key less than 50% of the time [2]. Considering that problem, plus the cost of taking additional GK area, which increases the travel distances between many keys, we decided to use only one space key in our design process. Since the space key is more frequently used, we first hypothesized that the space key should take relatively greater area than other keys. In fact, we believed the size of all keys should be proportional to their frequency of occurrence in the English language. This proved to be a problematic idea, because the most frequently used keys were always (correctly) optimized towards the center of the keyboard. If these keys were larger, the travelling distances for all pairs across these center keys would also increase, making the overall wpm lower than designs with a constant key size. Due to space constraint, we omit a quantitative analysis on the effect of varying key size. Conclusion
With the two physics-based approaches, we produced graphical keyboard designs with performance of 41.6 and 43.7 wpm. This is comparable to (or slightly better than) the level achieved by means of large amount of trial-anderror experimentation by MacKenize and Zhang whose layout has four space keys and assumes optimal selection among them. We revealed what systematic methods can achieve and what we should expect from a “good” layout. Based on MacKenzie, et al., we introduced two physicsbased design methods, breaking away from purely intuition/experience-based design. We corrected an error in previous predictions and concluded that the upper bound on performance of graphical keyboards should be 42 to 44 wpm. We also found that a single space key is superior and that varying key size did not increase performance. ACKNOWLEDGMENTS
We sincerely thank Scott MacKenzie for sharing his spreadsheet model and for numerous fruitful discussions. REFERENCES
Figure 1. The 43.7 wpm layout designed by Metropolis method
1.
Binder, K, Heermann, D.W., Monte Carlo Simulation in Statistical Physics, Springer-Verlag, 1988.
2.
MacKenzie, I.S., Zhang, S.X, The Design and Evaluation of High Performance Soft Keyboard, Proc. CHI 99, pp 25-30
3.
Soukoref, W., MacKenzie, I.S. Theoretical upper and lower bounds on typing speeds using a stylus and keyboard, Behaviour & Information Technology 14 (1995), 379-379
4.
http://www.npac.syr.edu/users/gcf/cps713montecarlo
