Top-Down Discovery of Cross-Level Web Browsing Sequences on Taxonomy

Top-Down Discovery of Cross-Level Web Browsing

Sequences on Taxonomy

Shyue-Liang Wang

Department of Information Management National University of Kaohsiung

Kaohsiung, Taiwan [email protected]

Wei-Shuo Lo

Department of Business Administration Mei-Ho Institute of Technology

Pingtun, Taiwan

Tzung-Pei Hong

Department of Computer Science and Information Engineering National University of Kaohsiung

Department of Computer Science and Engineering National Sun Yat-sen University

Kaohsiung, Taiwan [email protected]

ABSTRACT

others. In particular, many techniques for mining user browsing patterns have been

proposed in recent years. However, most of these works focus on mining browsing

patterns of web pages directly. In this work, we consider the problem of mining

generalized browsing patterns on both multiple-level and cross-level of taxonomy

comprised of web pages. We propose here an algorithm to discover these generalized

browsing patterns based on top-down level-wise searching approach. Example

demonstrating the proposed approach is given. Comparisons with the Generalized

Sequential Patterns (GSP) approach [16] and Apriori-Level approach [19] show that

the proposed top-down approach generates fewer candidate sequences. This

indicates that the proposed algorithm is more efficient in discovering cross-level web

browsing sequences.

Keywords: Web Mining, Browsing Patterns, Sequential Patterns, Cross-Level,

Taxonomy, Top-Down.

1. INTRODUCTION

Web mining can be viewed as the use of data mining techniques to automatically

documents and services [11]. It has been studied extensively in recent years due to

practical applications of extracting useful knowledge from inhomogeneous data

sources in the World Wide Web. Web mining can be divided into three classes: web

content mining, web structure mining and web usage mining [7]. Web content

mining focuses on the discovery of useful information from the web contents, data

and documents. Web structure mining deals with mining the structure of hyperlinks

within the web itself. Web usage mining emphasizes on the discovery of user access

patterns from secondary data generated by users’ interaction with the web.

In the past, several web mining approaches for finding user access patterns and user

interesting information from the World Wide Web were proposed [3-6, 15]. Chen

and Sycara proposed the WebMate system to keep track of user interests from the

contents of the web pages browsed [4]. It can thus help users to easily search data

from World Wide Web. Chen et. al. mined path-traversal patterns by first finding the

maximal forward references from log data and then obtaining the large reference

sequences according to the occurring numbers of the maximal forward references.

Cohen et. al. sampled only portions of the server logs to extract user access patterns,

which were then grouped as volumes [5]. Files in a volume could then be fetched

proposed the Web Utilization Miner to discover interesting navigation patterns. The

human expert dynamically specifies the interestingness criteria for navigation patterns,

which could be statistical, structural and textual. To discover the navigation patterns

satisfying the criteria, it exploits an innovative aggregated storage representation for

the information in the web server log. Web Site Information Filter System

(WebSIFT) [6] is a web usage mining framework that uses the content and structure

information from a Web site, and finally identifies interesting results from mining

usage data. WebSIFT divides the web usage mining process into three principal

parts that are corresponding to the three phases of usage mining: preprocessing,

pattern discovery, and pattern analysis. The input of the mining process includes

server logs (access, referrer, and agent), HTML files, and optional data. The

preprocessing process constructs a user session file with the input data to derive a site

topology and to classify the pages of a site. The user session file will be converted

to the transaction file and output to next phase. The pattern discovery process uses

the techniques such as statistics, association rules, clustering, sequential to generate

rules and patterns. In the pattern analysis process, the site topology and page

classification are fed into the information filter, the output of pattern discovery will be

Web browsing pattern is a kind of user access pattern that considers users’ browsing

sequences of web pages. In fact, it is similar to the discovery of sequential patterns

from transaction databases. The problem of mining sequential patterns was first

introduced in [1]. Let I={i1, i2, …, im} be a set of literals, called items. An itemset is a non-empty unordered set of items. A sequence is an ordered list of itemsets.

An itemset i is denoted as (i1, i2, …, im), where ij is an item. A sequence s is denoted as (s1

→

→

the items purchased in the transaction. All the transactions of a customer can

together be viewed as a sequence. This sequence is called a customer-sequence. A

customer supports a sequence s if s is contained in the customer-sequence for this

customer. The support for a sequence is the fraction of total customers who support

this sequence. A sequence with support greater than a user-specified minimum

support is called a large sequence. In a set of sequences, a sequence is maximal if it

is not contained in any other sequences. The problem of finding sequential patterns

is to find the maximal sequences among all sequences that have supports greater than

a certain user-specified minimum support.

proposed [1,2,12,14,16-22]. In application to web browsing patterns, techniques for

mining simple sequential browsing patterns and sequential patterns with browsing

times have been proposed [4,5,6,7,10,11,15]. However, most of these works focus

on mining browsing patterns of web pages directly. In this work, we consider the

problem of mining generalized browsing patterns on both multiple-level and

cross-level of taxonomy comprised of web pages. We propose here an algorithm to

discover these generalized browsing patterns based on top-down level-wise searching

approach. Comparisons with the Generalized Sequential Patterns (GSP) approach

[16] and Apriori-Level approach [19] are also discussed.

The rest of our paper is organized as follows. Section 2 reviews some related work

of mining sequential pattern. Section 3 presents the top-down mining algorithm of

generalized browsing patterns. Section 4 gives an example to illustrate the

feasibility of the proposed algorithm and shows the difference between the GSP

algorithm, the Apriori-Level algorithm, and the Top-Down algorithm. A conclusion

is given at the end of the paper.

Sequential pattern mining, similar to association rule mining, is the mining of

frequently occurring patterns that are related to time or other sequences. Many

algorithms for efficient mining of sequential patterns on single and multiple concept

levels have been proposed [1-5, 9-17,20-22]. This section reviews some of the basic

algorithms for discovering various types of sequential patterns.

For single concept level sequential pattern discovery, two main approaches have been

proposed. The first approach, called generate-and-test, uses a process of candidate

generation and testing to find frequent patterns. The second approach, called data

transformation, transforms the original data into a representation better suited for

frequent pattern mining.

For the generate-and-test approach, several different algorithms have been proposed

to find all frequent patterns in a dataset. The Apriori-All and GSP algorithms [1, 16]

accomplish this by employing a bottom-up search. The Apriori-All algorithm first

generates large itemsets from candidate itemsets that meet the minimum support

requirement on each pass. It then joins the large itemsets to form candidate

sequences. The large sequences are those candidate sequences with support greater

lead to poor performance due to large frequent pattern sizes. The SPADE algorithm

[21] is a generate-and-test approach with divide-and-conquer and efficient lattice

searching features. The candidate sequences are stored on a lattice and further

divided to equivalence classes. Depth-first and/or breadth-first searches are then

applied to each sub-lattice, which is induced by the equivalence relation, to search for

the large sequences with certain pruning strategies. It usually requires three database

scans, or only a single scan with some pre-processed information, thus minimizing the

I/O costs. Experimental results show that the SPADE performs better than the

previous Apriori-All algorithm.

For the data transformation approach, several different algorithms have been proposed.

The DSG (Direct Sequential pattern Generation) algorithm [20] is a graph-based

algorithm to find large sequences. It constructs an association graph to indicate the

associations between items and then traverse the graph to generate large sequences.

The algorithm needs to scan the database only once. However, the related

information may not fit in the main memory when the size of the database is very

large. The Free-Span and Prefix-Span algorithms [12, 14] are tree-based algorithm

to find large sequences. The general idea is to examine only the prefix subsequences

In each projected database, sequential patterns are grown by exploring only local

frequent patterns. To further improve mining efficiency, two kinds of database

projections are explored: level-by-level projection and bi-level projection, with an

optimization technique using pseudo-projection. Experimental results show that the

Prefix-Span performs better than the previous Apriori-All, GSP, and Free-Span

algorithms.

For multiple concept level sequential pattern discovery, a few algorithms have been

proposed. The GSP algorithm [16] is an extension of Apriori-All algorithm. The

algorithm consists of two phases: candidate generation and counting candidates.

However, each data sequence d is replaced with an “extended sequence” d’, where

each transaction d’i of d’ contains the items in the corresponding transaction di of d, as

well as all the ancestors of each item in di. For example, with the taxonomy shown

in Figure 1, a data sequence <(Legislative)> would be replaced with the extended

sequence <(Legislative, Central, Government)>. The algorithm will run on these

extended sequences and find all large sequences. The sequences thus discovered

contains itemsets that appeared on all levels of the taxonomy. The multiple-level

sequential pattern algorithm [2] is a top-down level-wise Apriori-All-based algorithm.

The database is transformed to a filtered database by pruning those itemsets with

supports lower than the user specified minimum support. It then finds the large

k-sequences on the top level. The large 1-sequences of the next level can be

calculated from the filtered database of previous level. The process repeats itself by

calculating the large k-sequences and then the next level. The sequences discovered

contains itemsets that appeared on the same level of the taxonomy.

3. MINING OF GENERALIZED WEB BROWSING PATTERNS

In this section, we describe the proposed top-down data-mining algorithm to discover

generalized web browsing patterns from log data.

3.1 NOTATION

The following notation is used in our proposed algorithm:

n: the total number of log data;

m: the total number of files in the log data;

ni: the number of log data from the i-th client, 1≤i≤c;

Di: the browsing sequence of the i-th client, 1≤i≤c;

Did: the d-th log data in Di, 1≤d≤n_i;

Ig: the g-th file, 1≤g≤m;

α_{: the predefined minimum support value;}

Cr: the set of candidate sequences with r files;

r

L : the set of large sequences with r files.

3.2 THE TOP-DOWN ALGORITHM

The proposed algorithm, Top-Down algorithm, first finds all large one itemsets on

every level of the concept hierarchy. These itemsets are actually the large sequences

of size one, which are also called large 1-sequences. Based on these large 1-sequences,

it generates large sequences by performing a top-down level-wise searching. This step

basically finds the large sequences consisting itemsets on the same concept level. To

obtain sequences containing itemsets from different concept levels, large sequences of

current level must be joined with large sequences of upper levels. However, the

computational effort of joining can be reduced by first checking the ancestor

given two large 2-sequences, <x, y> and <y, z>, if x and y are on the same path or y

and z are on the same path of the concept hierarchy, then <x, z> is a large 2-sequence.

Steps of the proposed mining algorithm are described below.

INPUT: A server log, a predefined taxonomy of web pages, a predefined

minimum support valueα.

OUTPUT: A set of maximal generalized browsing patterns

STEP 1: Select the web pages with file names including .asp, .htm, .html, .jva .cgi

and close the connection from the log data; keep only the fields date,

time, client-ip and file-name. Denote the resulting log data as D.

STEP 2:Encode each web page with a file name using a sequence of number and

the symbol “*”, with the t-th number representing the branch number of

a certain web page on level t.

STEP 3:Form a browsing sequence Dj for each client cj by sequentially listing

his/her nj tuples (web page), where nj is the number of web page

browsed by client cj. Denote the d-th tuple in Dj as Djd.

STEP 4:Find the set of large itemsets with respect to each level of concept

hierarchies, level by level and from top to bottom. In fact, the large

of all large 1-sequences from all level is denoted as LS1.

STEP 5:Find the k-sequences from the large itemsets in the same level and then

find the k-sequences from the large itemsets of different levels. It starts

searching for large sequences on the top level and proceeds a top-down

level-wise searching.

(5.1) For level m=1, find all large k-sequences based on all large itemsets

of this level.

(5.2) For level m ≥ 2

(5.2.1) Find all large k-sequences on the current level.

(5.2.2) Find all large cross-level k-sequences between current level

and all upper levels in a level-by-level manner from current

level to top level. Perform ancestor transitivity checking for

cross-level candidate sequences with constituent itemsets

from levels that are at least two-level apart.

(5.2.3) Repeat tasks(5.2.1)and(5.2.2)until the lowest level is reached.

STEP 6:Find the maximal sequences by deleting those sequences that are

subsequences of others.

In this section, we describe an example to demonstrate the proposed mining

algorithm of generalized web browsing patterns. The example shows how the

proposed algorithm can be used to discover the generalized sequential patterns from

the web browsing log data shown in Table 1. In addition, the predefined taxonomy

for web pages is shown in Figure 1. The predefined minimum support α is set at

50 %.

Table 1 A part of log data used in the example

Date Time Client-IP Server-IP Server

-port File-name 2007-06-01 05:39:56 140.117.72.1 140.117.72.88 11 News.htm 2007-06-01 05:40:08 140.117.72.1 140.117.72.88 11 Exective.htm 2007-06-01 05:40:10 140.117.72.1 140.117.72.88 11 Stock.htm …….. …….. …….. …….. …….. …….. 2007-06-01 05:40:26 140.117.72.1 140.117.72.88 11 University.htm …….. …….. …….. …….. …….. …….. 2007-06-01 05:40:52 140.117.72.2 140.117.72.88 11 Golf.htm 2007-06-01 05:40:53 140.117.72.2 140.117.72.88 11 Stock.htm …….. …….. …….. …….. …….. …….. 2007-06-01 05:41:08 140.117.72.3 140.117.72.88 11 Golf.htm …….. …….. …….. …….. …….. …….. 2007-06-01 05:48:38 140.117.72.4 140.117.72.88 11 Closing connection …….. …….. …….. …….. …….. …….. 2007-06- 05:48:53 140.117.72.5 140.117.72.88 11 Golf.htm

01 …….. …….. …….. …….. …….. …….. 2007-06-01 05:50:13 140.117.72.6 140.117.72.88 11 Stock.htm …….. …….. …….. …….. …….. …….. 2007-06-01 05:53:33 140.117.72.6 140.117.72.88 11 Closing connection

Figure 1 The predefined taxonomy used in this example

The proposed data-mining algorithm proceeds as follows.

STEP 1: Select the web pages with file names including .asp, .htm, .html, .jva .cgi

and close the connection from Table 1. Keep only the fields date, time,

client-ip and file-name. Denote the resulting log data as Table 2.

Government Entertainment Business Sport Education

Central Local TV Music Investment Management Ball Stellar School Extension

L an g u ag e C o m p u te r H ig h sc h o o l U n iv er si ty T ig er W o o d s B ec k h am G o lf F o o tb al l M ar k et in g M IS F o u n d S to ck C la ss ic al F as h io n D is co v er y N ew s K ao h si u n g T ai p ei L eg is la tiv e

Table 2 The resulting log data for web mining

Client-IP Server-IP Server-port File-name

140.117.72.1 140.117.72.88 11 News.htm 140.117.72.1 140.117.72.88 11 Exective.htm 140.117.72.1 140.117.72.88 11 Stock.htm …….. …….. …….. …….. 140.117.72.1 140.117.72.88 11 University.htm …….. …….. …….. …….. 140.117.72.2 140.117.72.88 11 Golf.htm 140.117.72.2 140.117.72.88 11 Stock.htm …….. …….. …….. …….. 140.117.72.3 140.117.72.88 11 Golf.htm …….. …….. …….. …….. 140.117.72.4 140.117.72.88 11 Closing connection …….. …….. …….. …….. 140.117.72.5 140.117.72.88 11 Golf.htm …….. …….. …….. …….. 140.117.72.6 140.117.72.88 11 Stock.htm …….. …….. …….. …….. 140.117.72.6 140.117.72.88 11 Closing connection

STEP 2: Each file name is encoded using the predefined taxonomy shown in Figure

1. Results are shown in Table 3.

Table 3 Codes of file names

Code File name Code File name

111 Executive.htm 1** Government.htm

211 News.htm 2** Entertainment.htm

212 Discovery.htm 3** Business.htm

321 Found.htm 5** Education.htm 411 Football.htm 11* Central.htm 412 Golf.htm 12* Local.htm 421 Tiger Woods.htm 21* TV.htm 511 University.htm 22* Music.htm 512 Highshool.htm 31* Investment.htm 32* Management.htm 41* Ball.htm 42* Stellar.htm 51* School.htm 52* Extension.htm

STEP 3: The web pages browsed by each client are listed as a browsing sequence.

Each tuple is represented as (web page), as shown in Table 4. The

resulting browsing sequences from Table 4 are shown in Table 5.

Table 4 The web pages browsed with their duration

Client-ID (Web page)

1 (111) 1 (211) 1 (231) 2 (112) 2 (111) 2 (231) 3 (111) 3 (211) 4 (211) 4 (313) 4 (323) 4 (421)

Table 5 The browsing sequences formed from Table4

Client ID Browsing sequences

1 (111), (211), (231), (222)

2 (112), (111), (231)

3 (111), (211)

4 (211), (313), (323), (421), (534)

STEP 4: Find the set of large itemsets with respect to each level of concept

hierarchies, level by level and from top to bottom. In fact, the large

itemsets in each level are the large 1-sequences for that level. The set of

all large 1-sequences from all level is denoted as LS1. The candidate and

large 2-sequence at level-1 are shown in Table 6, where ▲ represents

large sequence.

Table 6 Candidate and Large 2-sequence at level-1

1** 2**

1** 0 3▲

2** 0 1

STEP 5: Find the k-sequences from the large itemsets in the same level and then

find the k-sequences from the large itemsets of different levels. It starts

level-wise searching. For cross-level sequences, pruning can be achieved

by checking the ancestor-descendant relation, e.g. if 2** → 1** is pruned,

then 21* → 1**, 211 → 11* are pruned too. Tables 7 and 8 show the

sequences at levels 1, 2 and levels 1, 3 respectively.

Table 7 Candidate and Large 2-sequence at levels 1 and 2

1** 2** 11* 21* 23* 1** 0 3▲ 2▲ 2▲ 2** 0 1 11* 3▲ 0 2▲ 2▲ 21* 23*

Table 8 Candidate and Large 2-sequence at levels 1 to 3

1** 2** 11* 21* 23* 111 211 231 1** 0 3▲ 2▲ 2▲ 2▲ 2▲ 2** 0 1 11* 3▲ 0 2▲ 2▲ 2▲ 2▲ 21* 23* 111 3▲ 2▲ 2▲ 2▲ 2▲ 211 231

STEP 6: Find the maximal sequences by deleting those sequences that are

Large-1-sequence：<(1**)>, < (2**)>, <(11*)>, < (21*)>, < (23*)> <(111)>, < (211)> < (231)> Large-2-sequence：< (1**), (2**)>, < (1**), (21*)>, < (1**), (23*)> , < (1**), (211)>, < (1**), (231)>, <(11*), (2**)> , < (11*), (21*)>, < (11*), (23*)>, < (11*), (211)> , < (11*), (231)>, <(111), (2**)>, < (111), (21*)> , < (111), (23*)> ,< (111), (211)>, < (111), (231)>

In the following, we compare our algorithm with the GSP and the Apriori-Level

approaches. Table 9 shows the candidate and large sequences generated by the three

approaches, using the example in this section. It can be seen that Top-Down approach

generates fewer candidate sequences at both 1-sequence and 2-sequence phases.

Table 9 Comparison of generated sequences

K-sequence GSP Apriori-Level Top-Down

Candidate sequence 22 16 16 1 Large sequence 8 8 8 Candidate sequence 64 64 20 2 Large sequence 15 15 15 Candidate sequence 60 60 60 3 Large sequence 0 0 0

The complexity of finding maximal browsing sequences on a given level depends

on the number of large itemsets and sequences on that level. The complexities of

finding multiple-level web browsing sequences therefore are independent from each

other. Meaning the complexity only depends on the large itemsets and sequences

from its own level. However, the complexity of finding cross-level web browsing

sequences depends on not only the large itemsets and sequences of current level but

also all higher levels. For simplicity, assuming running time complexity for each

level is constant, O(T), and there are M levels. The total running time complexity for

finding multiple-level web browsing sequences will be O(MT). However, the total

running time complexity for finding cross-level web browsing sequences will be (1 +

2 + ... + M)T, i.e., O(M2T).

5. CONCLUSION

In this work, we have proposed a top-down level-wise web-mining algorithm that can

process web server logs to discover generalized web browsing patterns. The

inclusion of concept hierarchy (taxonomy) of web pages produces browsing patterns

of different granularity. This allows the views of users’ browsing behavior from

various levels of perspectives. In addition, we show that the proposed Town-Down

Apriori-Level approaches.

Although the proposed method works well in generalized web browsing patterns

mining, it is just a beginning. The proposed algorithm is a generate-and-test

approach that requires several database scans, depending on the size of large itmesets.

To improve the efficiency, algorithms based on data transformation approach need to

be considered and compared. More numerical simulations need to be carried out in

order to justify the efficiency of the different approaches.

5. ACKNOWLEDGEMENT

This work was partially supported by National Science Council of the Republic of

China, under grant number NSC-96-2213-E-390-003.

6. REFERENCES

1. Agrawal, R. and Srikant, R.: Mining Sequential Patterns, Proc. of the 11th

International Conference on Data Engineering (1995), 3-14.

2. Chen, N., Chen, A.: Discovery of Multiple-Level Sequential Patterns from Large

Database, Proc. of the International Symposium on Future Software Technology,

3. Chen, M.S., Park J.S. and Yu, P.S.: Efficient Data Mining for Path Traversal

Patterns, IEEE Transactions on Knowledge and Data Engineering, Vol. 10 (1998),

209-221.

4. Chen, L., Sycara, K.: WebMate: A Personal Agent for Browsing and Searching,

The Second International Conference on Autonomous Agents, ACM (1998).

5. Cohen, E., Krishnamurthy B. and Rexford, J.: Efficient Algorithms for Predicting

Requests to Web Servers, The Eighteenth IEEE Annual Joint Conference on

Computer and Communications Societies, Vol. 1 (1999), 284-293.

6. Cooley, R., Mobasher B. and Srivastava, J.: Grouping Web Page References into

Transactions for Mining World Wide Web Browsing Patterns, Knowledge and

Data Engineering Exchange Workshop (1997), 2-9.

7. Cosala, R., Blockleel, H.: Web Mining Research: A Survey, ACM SIGKDD, Vol.

2, Issue 1 (2000),1-15.

8. Mannila H. and Toivonen, H.: Discovering Generalized Episodes Using Minimal

Occurrences, Proc. of the 2nd International Conference on Knowledge Discovery

and Data Mining (1996), 146-151.

9. Oates, T. et al.: A Family of Algorithms for Finding Temporal Structure in Data,

Proc. of the 6th International Workshop on AI and Statistics (1997), 371-378.

of the 5th International Conference on Knowledge-based Intelligent Information

Engineering Systems, Osaka, Japan (2001), 495-499.

11. Pal, S.K., Talwar, V. and Mitra, P.: Web Mining in Soft Computing Framework:

Relevance, State of the Art and Future Directions, IEEE Transactions on Neural

Network, 13(5) (2002), 1163-1177.

12. Pei, J., Han, J.W., Mortazavi-Asl, B., Pinto, H., Chen, Q., Dayal U. and Hsu,

M.C.: Prefixspan: Mining Sequential Patterns by Prefix-Projected Growth, Proc.

of the 17th IEEE International Conference on Data Engineering, Heidelberg,

Germany, (2001).

13. Piategsky-Shapiro, G.: Discovery, Analysis and Presentation of Strong Rules,

Knowledge Discovery in Databases, AAAI/MIT press (1991), 229-248.

14. Pinto, H.: Multiple-Dimensional Sequential Patterns Mining, University of Lethe

bridge, Alberta, Canada, Master Thesis, (2001).

15. Spliliopoulou, M., Faulstich, L.C.: WUM: A Web Utilization miner, Workshop

on the Web and Data Base (WEBKDD) (1998 ),109-115.

16. Srikant, R. and Agrawal, R.: Mining Sequential Patterns: Generalizations and

Performance Improvements, Proc. of the 5th International Conference on

Extending Database Technology (1996), 3-17.

Transaction Databases, Proc. of the 9th National Conference on Fuzzy Theory

and Its Application, Taiwan (2001), 624-628.

18. Wang, S.L., Lo, W.S., Hong, T.P.: Discovery of Cross-Level Sequential Patterns

from Transaction Databases, Proceedings of the 6th International Conference on

Knowledge-based Intelligent Information Engineering Systems (2002), 683-687.

19. Wang, S.L., Lo, W.S., Hong, T.P.: Mining of Generalized Web Browsing Patterns,

Proceedings of the 7th World Multi Conference on Systemics, Cybernetics, and

Informatics, Orlando, Florida, USA (2003), 267-271.

20. Yen, S.J. and Chen, A.L.P.: An Efficient Approach to Discovering Knowledge

from Large Databases, Proceedings of the 4th International Conference on

Parallel and Distributed Information Systems (1996), 8-18.

21. Zaki, M.J.: Efficient Enumeration of Frequent Sequences, Proc. of the 7th

International Conference on Information and knowledge Management,

Washington DC (1998), 68-75.

22. Zhang, M,. Kao, B., Yip, C.L. and Cheung, D.: A GSP-Based Efficient Algorithm

for Mining Frequent Sequences, Proc. of the IC-AI’2001, Las Vegas, Nevada,