=Paper=
{{Paper
|id=None
|storemode=property
|title=Visualizable and Explicable Recommendations Obtained from Price Estimation Functions
|pdfUrl=https://ceur-ws.org/Vol-811/paper5.pdf
|volume=Vol-811
}}
==Visualizable and Explicable Recommendations Obtained from Price Estimation Functions==
https://ceur-ws.org/Vol-811/paper5.pdf
Visualizable and explicable recommendations
obtained from price estimation functions
Claudia Becerra and Alexander Gelbukh
Fabio Gonzalez Center for Computing Research (CIC)
Intelligent Systems Research Laboratory (LISI) National Polytechnic Institute (IPN)
Universidad Nacional de Colombia, Bogota Mexico DF, 07738, Mexico
[cjbecerrac,fagonzalezo]@unal.edu.co gelbukh@gelbukh.com
ABSTRACT assist decision-making, is a task that largely overwhelms hu-
Collaborative filtering is one of the most common approaches man capacities. Moreover, several studies have shown that
in many current recommender systems. However, historical this problem generates adverse e↵ects on people such as: re-
data and customer profiles, necessary for this approach, are gret due to the selected option, dissatisfaction due to poor
not always available. Similarly, new products are constantly justification for the decision, uncertainty about the idea of
launched to the market lacking historical information. We “best option”, and overload of time, attention and memory
propose a new method to deal with these “cold start” sce- (see [20]).
narios, designing price-estimation functions used for making Many recommender systems approaches have addressed
recommendations based on cost-benefit analysis. Experi- this problem through collaborative filtering [6] based on prod-
mental results, using a data set of 836 laptop descriptions, uct content (i.e. descriptions) and on customer informa-
showed that such price-estimation functions can be learned tion [2, 9]. This approach recommends products similar to
from data. Besides, they can also be used to formulate inter- those chosen by similar users. On the other hand, latent se-
pretable recommendations that explain to users how prod- mantics approaches [10] have been successfully used to build
uct features determine its price. Finally a 2D visualization affinity measures between products and users. Most of the
of the proposed recommender system was provided. aforementioned approaches have been applied in domains
with products such as books and movies that remain avail-
able long enough to collect enough historical data to build
Categories and Subject Descriptors a model [4, 12].
H.1.2 [User/Machine Systems]: Human information pro- While impressive progresses have been made in the field
cessing; H.4.2 [Types of Systems]: Decision support using collaborative filtering, the relevance of current ap-
proaches in domains with frequent changes in products is
still an open question [8]. For example, customer-electronics
General Terms domain is characterized by products with a very short life
Experimentation cycle in the market and a constant renewal of technologies
and paradigms. Collaborative approaches face two major
problems in this scenario [13]. First, product features are
Keywords constantly redefined, making difficult for users to identify
Apriori recommendation, Cold-start recommendation, Price relevant attributes. Second, historical sales product data
estimation functions become obsolete very quickly due to the frequent product
substitution. This problem of making automatic recom-
mendations without historical data is known as cold-start
1. INTRODUCTION recommendation [18].
The internet and e-commerce grow exponentially. As a In this paper, we propose a new cold-start method based
result, decision-making process about products and services on an estimate of the benefit to the user when purchasing
is becoming increasingly complex. These processes involve a product. This function is formulated as the di↵erence
hundreds and even thousands of choices and a growing num- between estimated and real prices. Therefore, our approach
ber of heterogeneous features for each product. This is recommends products with high benefit-cost ratio to find
mainly due to the introduction and constant evolution of “best-deals” on a data set of products. Figure 1 shows an
new markets, technologies and products. example of such recommendations based on utility functions
Unfortunately, human capacity for decision-making is too displaying 900 laptop computers. In this figure, the features
limited to address the complexity of this scenario. Studies in of laptops below the line in bold, indicating fair prices, do
psychology field have shown that human cognitive capacities not justify prices of laptops.
are limited from five to nine alternatives for simultaneous The rest of the paper is organized as follows. In Section
comparison [17, 14]. Consequently, making a purchasing de- 2, the necesary background and proposed method are pre-
cision at an e-commerce store that does not provide tools to sented. In Section 3, an evaluation methodology and some
data refinements are proposed and applied to the model.
Copyright is held by the author/owner(s). Finally, in Section 4, some concluding remarks are briefly
RecSys’11, October 23–27, 2011, Chicago, Illinois, USA. discussed.
27
tor regression [19], provide better models with lower error
Figure 1: Graphic recommender based on price es- rates but also with lower interpretability.
timates This trade-o↵ can be overcome with a hybrid regression
Recommendation model as 3FML (three-function meta-learner) [3]. This meta-
regressor combines two di↵erent regression methods in a new
improved combined model in a way similar to other meta-
Recommendation algorithms such as voting, bagging and AdaBoost (see [1]).
Price estimation ($)
Unlike these methods, 3FML uses one regression method to
make price predictions and another to predict the error. As
fair long as the former regression method is weak, stable and
price interpretable, the latter can be any other regression method
regardless its interpretability. As a result, the combined re-
gression preserves the same interpretability level of the first
regressor but with lower error rate.
A linear regression model can be trained to learn param-
eters m by minimizing the least squared error from data
[15]. This first model can be used by 3FML to build a base
regression model f0 (x) with the full dataset. Then, this
model is used to divide the data into two additional groups
depending on whether the obtained price predictions were
Actual price ($) below or above the training price, given a di↵erence thresh-
old ✓. Next, using the same base-regression method, two ad-
ditional models f+1 (x) and f 1 (x) are trained with the pair
2. APRIORI RECOMMENDATIONS USING of subsets called respectively, upper model and lower model.
UTILITY FUNCTIONS Figure 3 illustrates upper, base and lower models compared
The general intuition of method is led by the lexicograph- to the target function, which is the price in a data set of
ical criterion [22]. That is, users prefer products that o↵er laptop computers. The three resulting models are combined
more value for their money. Clearly, this approach is not ap- using an aggregation mechanism – called mixture of experts
plicable to all circumstances, but it is general enough when [11] – with the following expression:
customer profiles are not available in cold-start scenarios.
P
When a user purchases a product xi , a utility function
utility(xi ) provides an estimation of the di↵erence between fˆ(xi ) = wl (xi )fl (xi ), (2)
l✏H
the estimated price f (xi ) and the market price yi , that is
utility(xi ) = f (xi ) yi . Thus, the products in the market having
P
are represented as a set X = {x1 , x2 ,..., xn , ..., xN }, where
each product xi is a vector characterized in a feature space wl (xi ) = 1, i 2 {1 . . . n} (3)
l✏H
RM . With these data, a regression model, learned from X
and the vector of prices y, generates price estimations f (xi ) H is a dictionary of experts consisting on the base model
required for calculation of the utility. Finally, the utility and two additional specialized models, H = {f 1 (x), f0 (x),
function is computed on all products thus providing an or- f+1 (x)}. The gating coefficient wli establishes the level of
dered list with the top-n apriori recommendations. relevance of the l model into the final price prediction for
Estimates of price f (xi ) can be obtained by a linear- the i-th product.
regression model as: In 3FML model, coefficients wli = wl (xi ) are obtained
X by chaining a membership function wl for each regression
f (xi ) = o + m xim . (1)
model to a function ↵ that depends on the errors of the
m2{1,...,M }
three models, wl (xi ) = wl (↵(f 1 (xi ), f0 (xi ), f+1 (xi ), yi )).
This model is equivalent to an additive value function These membership functions wl (↵) are similar to those used
used in the decision-making model SAW (simple additive in fuzzy sets [23] but these satisfy the constraint given by
weighting) [5], but with coefficients m learned automat- eq. 3. Three examples of those functions are shown in Fig-
ically. Clearly, the recommendations obtained from these ure 2; one triangular and two Gaussian. Clearly, the range
estimates can be explained to users, since each term m xim of the error function ↵ must agree with the domain of the
represents the money contribution to the final price estimate membership functions. For instance, if the domain of the
provided by the m-th feature of the i-th product. membership functions is [0, 1], an appropriate function ↵i
The quality of the apriori recommendations obtained with must return a value close to 0.5 when yi is better modeled
the proposed method depends primarily on three factors: by f0 (xi ). Similarly, reasonable values for ↵i , if yi is better
the amount of training data, the accuracy of price estimates modeled by f 1 (xi ) or f+1 (xi ), are respectively 0.0 and 1.0.
f (xi ), and the ability to extract user-understandable expla- Such function ↵ can be arithmetically constructed (see
nations from the regression model. Certainly, linear models, [3] for triangular and Gaussian cases) and ↵i can be ob-
such as that of eq. 1, o↵er good interpretability, but in many tained for every xi . 3FML makes use of a second regres-
cases, these models generate high rates of error in their pre- sion method to learn a function for ↵i . This function is
dictions when the interactions among features are complex. called ↵-learner, which seeks to predict the same target yi
These models are known as weak regression models. On the but indirectly through the errors obtained by f 1 , f0 and
other hand, discriminative approaches, such as support vec- f+1 . The estimates obtained with ↵-learner are used in com-
28
Figure 2: Triangular and Gaussian membership Table 1: Attributes in Laptops 17 836 data set
functions Feature name Type % missing
Manufacturer Nominal 0.00%
Processor Speed Numeric 0.40%
Installed Memory Numeric 1.90%
Operating System Nominal 0.00%
Processor Nominal 0.20%
Memory Technology Nominal 7.20%
Max Horizontal Resolution Numeric 7.90%
Warranty-Days Numeric 15.50%
Figure 3: 3FML’s three regression models graph Infrared Nominal 0.00%
Bluetooth Nominal 0.00%
Docking Station Nominal 0.00%
Port Replicator Nominal 0.00%
Fingerprint Nominal 0.00%
Subwoofer Nominal 0.00%
Price ($)
External Battery Nominal 0.00%
CDMA Nominal 0.00%
Price Numeric 0.00%
of the entire data set. These resources allow the reader –
Laptop computers sorted by actual price
Target Base LMS Lower model Upper model
guided by a brief discussion – to qualitatively evaluate the
recommendations obtained with the proposed method.
3.1 Data
bination with the membership functions to get coefficients The data is a set of 836 laptop computers each represented
wl (xi ). Therefore, final predictions are obtained with a dif- by a vector of 69 attributes including price, which is the
ferent linear model for each target price yi . The resulting attribute to be estimated. Data were collected by Becerra1
model is also linear, but di↵erent for each product instance from several U.S. e-commerce sites (e.g. Pricegrabber, Cnet,
in function to xi : Yahoo, etc.), during the second half of 2007 within a month.
P A subset of 17 features was selected using the correlation-
fˆ(xi ) = ˆ0 (xi ) + ˆm (xi )xim , (4) based selection method proposed by Hall [7]. We call this
m✏ {1, ..., M }
dataset Laptops 17 836 ; all its features and percentage of
where missing values are shown in Table 1.
X X
ˆo (xi ) = lo wl (xi ) ;
ˆm (xi ) = lm wl (xi ). 3.2 Price estimation results
l2H l2H
For the construction of the price-estimation function, sev-
Clearly, the model in eq. 4 is as user-explainable as that eral regression methods were used, namely: least mean squares
of eq. 1. linear regression (LMS) [15], M5P regression tree [21, 16],
The e↵ect of ↵-learner in eq. 4 is that the entire data set support vector regression (SVR) [19] and three-function meta-
is clustered into three latent classes. These classes can be learner (3FML, described in previous section). 3FML pro-
considered as market segments namely: high-end, mid-range vides three interpretable linear models: upper, base and
and low-end products. Many commercial markets exhibit lower models, which can be associated with product classes.
this segmentation, e.g. computers, mobile phones, cars, etc. Finally, estimated price for each laptop was obtained with
the combination of these three models using eq. 4 with the
weights obtained from ↵-Learner and Gaussian membership
3. EXPERIMENTAL VALIDATION functions.
The aim of experiments is to build a model that provides a The performance of each method was measured using root-
cost-benefit ranking of a set of products where each product mean-square error (RMSE) defined as:
is represented as a vector of features. To assess the quality
of this ranking, two factors are observed. First, the error v
uP ⇣ ⌘2
of the price-estimation regression should be low to make u ˆ
t i f (xi ) yi
sure that this function provides a reasonable explanation RM SE = .
of the data set. Second, the model must be interpretable |X|
and discovered knowledge must be consistent with market The data set was randomly divided into 75% for training
data. For example, if a proposed model discovers a ranking and 25% for testing. Ten di↵erent runs of this partition ratio
of how much money each operating system contributes to were used for each method. These ten RMSE results were
laptop prices, this ranking should be in agreement the prices averaged and reported. Table 2 shows the results, their stan-
of retail versions of the same operating systems. dard deviation (in parentheses) and some model parameters.
In addition, the full features set of the top-10 recom-
1
mended products is provided along with a 2D visualization http://unal.academia.edu/claudiabecerra/teaching
29
The method with lowest RMSE was SVR with a complex-
ity parameter C = 100 using radial basis functions (RBF) Table 3: Proportions of operating systems ocur-
as kernel. However, interpretability of this model is quite rences in Laptops 17 836 data set
limited, given the embedded feature space induced by the Operating System # %
kernel. On the other hand, LMS and 3FML provide straight- Vista Home Premium (WinVHP) 251 30.02%
forward interpretation of coefficients, which represent the WinXP Pro (WinXPP) 208 24.88%
amount of the contribution of each feature to the product WinXP (WinXP) 151 18.06%
estimated price. Clearly, 3FML was the method that better Win. Vista Business (WinVB) 137 16.39%
coped with this interpretability-accuracy trade-o↵. Win. Vista Home Basic (WinVHB) 44 5.26%
Mac OS (MacOS) 34 4.07%
Win. Vista Ultimate (WinVU) 11 1.32%
Table 2: 10 runs average RMSE results for price Total 836 100%
estimates obtained with several regression methods
Regression model Avg. RMSE
M5P regression tree 239.70(21.57) Table 4: Retail prices for di↵erent editions of Win-
Least Mean Squares (LMS) 259.87(17.90) dows Vista
"-SVR, C = 100, linear kernel 258.93(16.93) O.S.! WinVHB WinVHP WinVB WinVU
3FML (LMS as base model) 233.48(14.76) Retail price* $199.95 $259.95 $299.95 $319.95
3FML ("-SVR, C = 100, linear kernel) 223.76( 8.57) *http://www.microsoft.com/windows/windows-
"-SVR, C = 100, RBF kernel = 7.07 230.23(12.27) vista/compare-editions (site consulted in September
2007)
3.3 Evaluation and feedback
string that contains — in most of cases – the manufacturer,
In this section the price estimation function obtained us-
the product family and the model (e.g. “Intel Core 2 Duo
ing 3FML is manually analyzed checking coherence of co-
Mobile T7200”). Unlike OS attribute, which has only seven
efficients with real facts of the market. Particularly, coef-
possible alternatives, Processor attribute has 133 possible
ficients for attributes operating system, processor and nu-
processor models. Moreover, the frequencies of occurrence
merical features are reviewed, and – when necessary – some
of each processor model exhibit a Zipf-type distribution (see
refinements are proposed to the data sets to deal with dis-
Figure 4). Thus, approximately half of the 836 laptops have
cussed issues.
only 8 di↵erent processors and more than 80 processors oc-
3.3.1 Operating System attribute analysis cur only in one laptop. Part of this sparseness is due to
missing information, abbreviations and formatting.
Table 3 shows the distribution of the di↵erent operating
The Processor attribute, as found in the data set, can
systems into the entire data set of laptops and the abbrevi-
generate a detrimental e↵ect on the price-estimation func-
ations that we use to refer them at Table 5 and Table 4.
tion. Besides, coefficients could hardly be explained and
In order to evaluate the portion of the price estimation
their evaluation against market facts could lead to mislead-
model related to operating system (OS) attribute, coeffi-
ing results. Thus, the model was withdrawn from Processor
cients of this feature are compared with related Microsoft’s
attribute and it was renamed as Proc. Family. In addition,
retail prices. Table 4 shows public retail prices for Windows
the data set was enriched manually adding the following four
Vista published at 2007-3Q. In spite that at that date,
processor related attributes:
Windows Vista operating system had already six months
of launched, many brand new laptops still had pre-installed • L2-Cache: processor cache in Kibibytes (210 bytes).
previous Windows XP . Thus, we consider for analysis Win-
dows XP Pro equivalent to Windows Vista Business , as • Hyper Transport: frontal bus clock rate in Mhz.
well as, Windows XP equivalent to Windows Vista Home
• Thermal Design: maximum dissipated power in watt.
Premium . This assumption is also coherent with the ob-
served behavior in Microsoft’s price policy that keeps prices • Process Technology: CMOS technology in nanometre.
of previous product releases invariable during version tran-
sition periods. This new data set is referred as Laptops 21 836 data set.
It is interesting to highlight the behavior of 3FML model Performance results of new price-estimation functions are
with Windows Vista Ultimate . Although this OS version shown in Table 6. Clearly, SVR and 3FML obtained sub-
occurs only at 1.32% of instances (see Table 3), it is cor- stantial improvements using this new data set.
rectly recognized as the most expensive OS (see Table 4) by Similarly to the analysis made for OS attribute, processors
the upper model. This fact corrects an erroneous tendency families also have a consumer-value ranking given by their
recognized by base and lower models. In general terms, for technology, which can be compared to a ranking taken from
other OS versions, 3FML managed to predict similar order- an interpretable price-estimation function. The technology
ing as that of retail prices. ranking of Intel processors is: (1st) Core 2 Duo , Core
Duo , Core Solo , Pentium Dual Core and Celeron .
3.3.2 Processor attribute coefficients Same for AMD’s processors: (1st) Turion , Athlon and
2
As shown in Table 1, Laptops 17 836 data set has two fea- Sempron . We extracted a ordering for processor fami-
tures to describe the main processors of laptops , they are: 2
see http://www.notebookcheck.net/Notebook-
Processor Speed (numeric) and Processor (nominal). The Processors.129.0.html for a short description of mobile
former is the processor clock rate and the latter is a text processor families (site consulted in June 2011)
30
5
Table 7: Processor families rankings obtained from
Table 5: 3FML base, upper and lower model coeffi- 3FML price-estimation function
cients s.o for operating system attribute Upper model Lower model
Base model Upper model Lower model Intel Core2 Duo 7.4(0.8) Intel Core2 Duo 7.6(0.5)
S.O. s.o S.O. s.o S.O. s.o Intel Core Duo 7.2(1.2) Intel Core Solo 6.2(1.7)
WinVU 323.3 WinVB 185.6 WinVB 127.3 Intel Core Solo 5.3(2.1) AMD Athlon 5.7(3.8)
WinVB 260.3 WinXPP 184.5 WinXPP 127 Intel Celeron 5.1(1.7) Intel Core Duo 4.8(2.1)
WinXPP 249.8 MacOS 169.2 MacOS 95.2 PowerPC 4.6(2.6) AMD Turion 4.8(1.8)
MacOS 245.9 WinVU 96.4 WinVHP 24.7 Pent DualCore 3.7(1.4) Pent DualCore 4.3(2.1)
WinVHP 116.7 WinVHP 57 WinVU 0.0 AMD Sempron 3.4(2.4) PowerPC 4.3(3.1)
WinXP 94.3 WinXP 27.8 WinVHB 0.0 AMD Turion 3.3(1.8) Intel Celeron 3.3(1.3)
WinVHB 0.0 WinVHB 0.0 WinXP -7.1 AMD Athlon 1.8(1.4) AMD Sempron 2.8(2.3)
Base model
Intel Core Solo 8.5(0.7)
Figure 4: Distribution of Processor attribute
Intel Core2 Duo 8.3(0.7)
2.00 Intel Core Duo 6.8(0.9)
1.80 Pent DualCore 5.1(1.4)
1.60 Intel Celeron 5.0(0.7)
log(frequency)
1.40 AMD Turion 3.7(1.1)
1.20 PowerPC 2.9(2.1)
1.00 AMD Sempron 2.6(1.8)
0.80
AMD Athlon 2.1(1.3)
0.60
0.40
0.20 Table 8: coefficients for numerical attributes from
0.00 3FML model with Laptops 21 836 data set
1 34 67 100 Feature name Upper Base Lower
processor models ranked by data set frequency 0 0.23 0.12 0.06
Warranty Days 0.04 0.01 -0.01
Installed Memory -0.11 0.17 0.10
Max. Horizontal Resolution 0.12 0.37 0.15
lies by their corresponding coefficients from 3FML models. Processor Tech. 0.30 0.08 0.05
Results for this ranking – means and standard deviation – Thermal Desing -0.01 -0.37 -0.27
making 10 runs with di↵erent samples of 75% training and Hyper Transport -0.02 0.25 0.05
25% test are shown in Table 7. L2-Cache 0.08 0.16 0.11
Results in Table 7 show how upper model better ordered Processor Speed -0.03 0.25 0.17
processor families with high technological ranking. Simi-
larly, lower model does a similar work recognizing Sempron
family at the lowest rank. Besides, these coefficients also shows that this e↵ect a↵ects
prices more at mid-range and low-end laptop-market seg-
3.3.3 Numerical attributes coefficients ments. Similarly, Max. Horizontal Resolution attribute re-
This subsection present a brief discussion on the interpre- veals that this feature has greater impact on the mid-range
tation of coefficients extracted from the price-estimation laptop market prices.
function for some numeric attributes (shown in Table 8). Interestingly, there is a phenomenon revealed by the fea-
Although this interpretation is clearly subjective, it reveals tures that are easy perceived by users, such as Installed
some laptop-market facts, which were extracted in an unsu- Memory, Max. Horizontal Res. (number of horizontal pixels
pervised way from the data. on screen), L2-Cache and Processor Speed. That is: those
For instance, consider Thermal Design attribute. Neg- features have considerably less e↵ect on prices in high-end
ative values in the coefficients reveal a fact: the lesser than in mid-range and low-end market segments. This phe-
power the CPU dissipates, the higher the laptop’s price. nomenon can be explained by the fact that “luxury” goods
justify their price more by attributes such as brand-label,
exclusive features and physical appearance rather than for
Table 6: RMSE for regression price estimates in their configuration.
Laptops 21 836 data set 3.4 Recommendations for users
Regression model RMSE
"-SVR (C = 1, lineal kernel ) 254.56(11.75) 3.4.1 Top-10 recommendations
"-SVR (C = 100, RBF kernel, ) 219.16( 9.88) After the quantitative evaluation (i.e. regression error)
3FML* 220.91(10.97) and qualitative assessment (i.e. agreement with market facts)
* Base model: "-SVR, C = 1, lineal kernel. ↵-Learner: "- using 3FML model, the resulting functions provided reason-
SVR, C = 100, RBF kernel. able estimates of price and support elements to explainable
31
Figure 5: Visualization of 836 laptops recommendation ranking
Profit
$400
$200
$0
-$200
-$400
Price
$450 $550 $650 $750 $850 $950 $1050 $1150 $1250 $1350 $1450 $1550 $1650 $1750 $1850
recommendations such as rankings and weights of attributes. 3.4.2 2D Visualization
After obtaining the estimates of prices, the profit for each Ordered lists are the most common format to present rec-
laptop is calculated from the di↵erence between this esti- ommendations to users. However, despite having such an
mate and real price. Table 9 shows the top-10 recommen- ordination, establish the most appropriated choice for a par-
dations with the highest profit among all 836 laptops. ticular user is a difficult task. Therefore, we propose a novel
The first and second top-ranked laptops have similar con- visualization method for our recommender system. The pur-
figurations, but even small di↵erences make comparison dif- pose of this is to enable users to build a mental model of the
ficult at first sight. The second laptop has better price, more market. When users do not have a clear aim or a defined
memory, docking station and ports replicator slots. Unlike, budget, this tool provides a rough idea of the number of
the former has higher screen resolution and a fingerprint sen- options and prices. In addition, visualization can help the
sor. These di↵erences can be compared quantitatively with short-term memory decreasing cognitive load and highlight
the help of coefficients provided by the model. However, a the recommended options.
better explanation of the #1 recommended choice is a mar- The proposed 2D visualization is shown in Figure 5. The
ket fact extracted from the obtained manufacturer ranking horizontal axe represents actual price and the vertical axe
showed in Table 10. The three regression models identify represents the profit, which is the di↵erence between the es-
the Lenovo brand better ranked than HP . Therefore, timated and actual price. Each laptop is represented as a
the first recommended laptop becomes a “best deal” given bubble, where larger radius and warmer colors (darker gray
the standard prices of Lenovo at the time. Similarly, rec- in the grayscale version) means higher profit-price di↵er-
ommendations #7, #9 and #10 seem to get their high user ences. Besides, the number of ranking was included in the
profit not because of their configuration features, but be- top-99 recommendations.
cause of their label Sony , which do better positions on the This visualization highlights other “best deals” that are
ranking of manufacturers than its counterparts. hidden in the ranking list. For instance, consider recom-
Second and third recommendations only di↵er in Proces- mendation #53 (see Figure 5 in the coordinates $1550 price
sor Speed attribute. Clearly, the estimated cost of that dif- and $260 profit). Perhaps this is an interesting option to
ferentia is the numerical di↵erence between their estimated consider if user’s budget is over $1500. Similarly, recom-
prices, which is $42. Nevertheless, their real price di↵erence mendation #26 can be quickly identified as the best option
is $50. This explains the order of position in the ranking for buyer on a low budget.
assigned by the recommender system to the #2 and #3 rec- The proposed visualization also allows a qualitative as-
ommendations. More pair-wise comparisons and evaluations sessment of the price-estimation function. For instance, con-
could be made but are omitted due to space limitations. sider the laptops above $1300, this function has difficulties
These paired comparisons become cognitively more diffi- to predict prices using the current set of features, which in
cult when the number of features, di↵erences and instances turn appears to be very e↵ective for mid-range prices. This
increases. However, the proposed recommender method pro- problem could be solved indentifying and adding to the set
vides reasonable explanations no matter how much data is of attributes those distinctive features of high-end laptops,
involved, and these can be provided by user request. This namely: shockproof devices, special designs, colors, housing
is important because cold-start recommender systems need materials, exclusive options, etc.
to establish trust in users due of the lack of collaborative
support.
32
Table 9: Detailed top-10 ranked recomendations
Recommendation rank ! #1 #2 #3 #4 #5
Horizontal Resol. 900 pixels 800 pixels 800 pixels 1536 pixels 768 pixels
Memory Tech. DDR2 DDR2 DDR2 DDR2 DDR2
Inst. Memory 512 MB 1024 MB 1024 MB 1024 MB 1024 MB
Family Core Duo Core Duo Core Duo Core2 Duo Core2 Duo
Processor Speed 1830 GHz 1830 GHz 2000 GHz 1500 GHz 2000 GHz
L2 Cache ?* ? ? 2048 kB 4096 kB
Hyper Transp ? ? ? 667 Mhz 667 Mhz
Thermal Design ? ? ? 35 34
Process Tech. ? ? ? 65nm 65nm
Manufacturer Lenovo HP HP Lenovo HP
Op. System WinXPP WinXPP WinXPP WinVB WinXPP
Warranty Days 1095 1095 1095 365 W 1095 W
IBDPFWC** YNYYYNN YYYYYNN YYYYYNN NNYYNNN YYYYYNN
Actual Price $ 899 $ 795 $ 845 $ 875 $ 849
Estimated Price $ 1,438 $ 1,319 $ 1,361 $ 1,383 $ 1,332
Profit $ 539 $ 524 $ 516 $ 508 $ 483
Recommendation rank ! #6 #7 #8 #9 #10
Horizontal Resol. 1050 pixels 800 pixels 800 pixels 800 pixels 800
Memory Tech. DDR2 DDR2 DDR2 DDR2 DDR2
Inst. Memory 1024 MB 1024 MB 1024 MB 512 MB 1024 MB
Family Core Duo Core2 Duo Core Duo Core Duo Core2 Duo
Processor Speed 2000 GHz 2160 GHz 1830 GHz 1660 GHz 2000 GHz
L2 Cache 2048 kB 4096 kB ?* 2048 kB 4096 kB
Hyper Transp 667 Mhz 667 Mhz ? 667 Mhz 800 Mhz
Thermal Design 31 W 34 W ? 31 W 35 W
Process Tech. 65nm 65nm ? 65nm 65nm
Manufacturer Lenovo Sony HP Sony Sony
Op. System WinXP Pro WinXP Pro WinXP Pro WinXP Pro V Business
Warranty Days 365 365 1095 365 365
I BDPFWC** NYNNYNN NYYYNNN YYYYYNN NNYYNNNN NYYYYNN
Actual Price $ 845 $ 1,060 $ 868 $ 649 $ 1,080
Estimated Price $ 1,312 $ 1,526 $ 1,319 $ 1,093 $ 1,522
Profit $ 467 $ 466 $ 451 $ 444 $ 442
* Question mark stands for missing values.
** Initials I B D P F W C stand for Infrared, Bluetooth, Docking Station, Port Replicator, Fingerprint, Subwoofer and CDMA.
Table 10: Average ranking of Manufacturer attribute using 3FML at Laptops 21 836 data set
Base model Upper model Lower model
Asus 10.6(0.7) Dell 10.0(0.9) Asus 10.2(0.8)
Sony 9.6(1.2) Fujitsu 9.2(1.0) Fujitsu 9.6(1.5)
Fujitsu 8.4(1.4) Sony 7.4(1.8) Sony 8.1(1.2)
Dell 7.9(0.9) Asus 6.8(1.8) Dell 7.3(1.4)
Apple 7.0(2.4) Apple 6.1(1.3) Apple 6.7(2.0)
Lenovo 6.5(1.6) Lenovo 4.1(2.4) Lenovo 5.2(1.5)
Toshiba 5.0(1.2) Gateway 4.0(2.9) Toshiba 4.7(1.5)
Acer 4.7(1.2) Averatec 3.8(1.3) Acer 3.9(1.3)
HP 2.3(0.7) Acer 3.6(1.3) HP 3.4(1.7)
Averatec 2.1(1.3) HP 3.3(1.9) Gateway 1.9(0.8)
Gateway 1.9(1.0) Toshiba 2.4(1.5) Averatec 1.9(2.1)
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