Question
Machine Learning - Collaborative Filtering (Recommenders)

This module will discuss implementing collaborative filtering machine learning algorithms using the Mahout platform.

• Know when to use item-based and user-based collaborative filtering techniques.
• Employ common collaborative filtering algorithms.
• Optimize collaborative filtering algorithms for large datasets on Hadoop.

Owen, S., Anil, R., & Friedman, E. (2011). Mahout in action. Shelter island: Manning Publications. ISBN-10: 1935182684. ISBN-13: 978-1935182689

1. Discuss how you would improve upon pure item-based and pure user-based collaborative filtering.

2. You are to use collaborative filtering techniques to predict which political party voters who have not been polled will vote for in an upcoming election. We assume that we have a large data store of voters and many attributes about the voters. Attributes include age_group (with values of young, middle, old), gender, income_bracket (with values of under_50K, 50_150K, 150_300K, over_300K), marital_status, number_of_children, profession (with many different values), education_level (with values of no_high_school, high_school, bachelors, masters, doctor), number_of_automobiles, political_party, and state. Also assume that many voters have already been polled and the party they stated that they would vote for is also stored in the data store.

a) Design a schema for a structured cloud table such as Accumulo to represent this data.

b) Write pseudocode for determining similarity called VoterSimilarity() with signature:

UserSimilarity similarity = VoterSimilarity(voterA, voterB);

Assume that facts such as gender or state with totally different values either have a similarity value of 0 or 1. Assume that attributes that have values over a spectrum, such as age_group or education_level, have a value of 1 for an exact match; 0 for one end of the spectrum to the other such as young to old or no_high_school to doctor; or the fraction of difference for other measurements such as no_high_school to high_school is ¾, no_high_school to bachelors is ½, high_school to doctor is ¼, etc. To determine overall similarity between two voters, just add up the similarity scores for each of the attributes for each of the two voters and compare their overall scores.

c) Given a voter who has not been polled, write pseudocode to find all nearest neighbors of voters who have been polled that pass a certain threshold. The signature is:

Neighborhood neighborhood =
nearestNeighbors (threshold,
voterA /* not polled */,
allVoters /* all voters */);

Assume that you have access to the VoterSimilarity() method from the previous section.

d) Write pseudocode for selecting the how a voter will vote. A simple metric is to determine if the majority of the neighborhood were polled Democrat or Republican.

Vote vote = PredictVote (voterA, neighborhood);
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1) Discuss how you would improve upon pure item-based and pure user-based collaborative filtering.
• Pure collaborative filtering leads to computing a similarity for every pair of items and putting the results into a giant matrix. The amount of calculation increases rapidly
• Distributed algorithm is the solution to this case.
• Case example: item-based collaborative filtering:
o We will apply co-occurrence matrix.
o Instead of computing the similarity between every pair of items, it’ll compute the number of times each pair of items occurs together in some user’s list of preferences, in order to fill out the matrix
o Co-occurrence is like similarity; the more two items turn up together, the more related or similar they probably are.
o Next, we compute user’s and recommendation vector using mapreduce
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      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheMissed (249μs)
      • Illuminate\Database\Events\StatementPrepared (1.18ms)
      • Illuminate\Database\Events\QueryExecuted (1.45ms)
      • eloquent.retrieved: App\Models\SubjectCat (88μs)
      • Illuminate\Cache\Events\KeyWritten (334μs)
      • Illuminate\Cache\Events\CacheHit (1.26ms)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • creating: site.layouts.app (388μs)
      • composing: site.layouts.app (18μs)
      • creating: components.canonical (451μs)
      • composing: components.canonical (74μs)
      • creating: components.open-graph (137μs)
      • composing: components.open-graph (49μs)
      • creating: site.headers.header (354μs)
      • composing: site.headers.header (64μs)
      • Illuminate\Cache\Events\CacheHit (1.39ms)
      • creating: components.footer (77μs)
      • composing: components.footer (69μs)
      • Illuminate\Cache\Events\CacheHit (730μs)
      • Illuminate\Cache\Events\CacheMissed (286μs)
      • Illuminate\Database\Events\StatementPrepared (766μs)
      • Illuminate\Database\Events\QueryExecuted (1.3ms)
      • eloquent.retrieved: App\Models\SubjectCat (80μs)
      • Illuminate\Cache\Events\KeyWritten (287μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (291μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • creating: components.forms.contact-us (248μs)
      • composing: components.forms.contact-us (130μs)
      • creating: components.forms.get-started (148μs)
      • composing: components.forms.get-started (48μs)
      • creating: components.forms.free-tool-download (89μs)
      • composing: components.forms.free-tool-download (41μs)
      • creating: components.forms.claim-free-worksheet (81μs)
      • composing: components.forms.claim-free-worksheet (39μs)
      • creating: components.forms.tutor-subscription-waitlist (189μs)
      • composing: components.forms.tutor-subscription-waitlist (47μs)
      • creating: components.forms.tutor-subscription-join (85μs)
      • composing: components.forms.tutor-subscription-join (39μs)
      • creating: components.forms.tutor-support (85μs)
      • composing: components.forms.tutor-support (41μs)
      • 311 x Illuminate\Cache\Events\CacheHit (14.2%)
        63.86ms
        20 x Illuminate\Database\Events\StatementPrepared (7.95%)
        35.75ms
        20 x Illuminate\Database\Events\QueryExecuted (5.34%)
        24.02ms
        11 x Illuminate\Cache\Events\CacheMissed (2.2%)
        9.89ms
        11 x Illuminate\Cache\Events\KeyWritten (1.75%)
        7.85ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.04%)
        4.69ms
        1 x Illuminate\Routing\Events\Routing (0.31%)
        1.38ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.26%)
        1.19ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.24%)
        1.07ms
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        543μs
        1 x creating: homework.show (0.11%)
        476μs
        1 x creating: components.canonical (0.1%)
        451μs
        1 x creating: site.layouts.app (0.09%)
        388μs
        1 x eloquent.booting: App\Models\SubjectCat (0.09%)
        383μs
        1 x creating: components.breadcrumbs (0.08%)
        365μs
        1 x creating: site.headers.header (0.08%)
        354μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        275μs
        1 x creating: components.forms.contact-us (0.06%)
        248μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        228μs
        1 x composing: homework.show (0.04%)
        201μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        193μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.04%)
        189μs
        1 x composing: components.breadcrumbs (0.04%)
        184μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        173μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        167μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        167μs
        1 x creating: components.forms.get-started (0.03%)
        148μs
        1 x creating: components.open-graph (0.03%)
        137μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        130μs
        1 x composing: components.forms.contact-us (0.03%)
        130μs
        1 x creating: components.forms.free-tool-download (0.02%)
        89μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        85μs
        1 x creating: components.forms.tutor-support (0.02%)
        85μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        81μs
        1 x creating: components.footer (0.02%)
        77μs
        1 x composing: components.canonical (0.02%)
        74μs
        1 x composing: components.footer (0.02%)
        69μs
        1 x composing: site.headers.header (0.01%)
        64μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        61μs
        1 x composing: components.open-graph (0.01%)
        49μs
        1 x composing: components.forms.get-started (0.01%)
        48μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        47μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        45μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        43μs
        1 x composing: components.forms.free-tool-download (0.01%)
        41μs
        1 x composing: components.forms.tutor-support (0.01%)
        41μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        39μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        39μs
        1 x composing: site.layouts.app (0%)
        18μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated44.22ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '42638' limit 1
        16.13mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 42638
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (512)
        1.18mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (42638)
        920μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.13mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 3
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 42638 and `subject` = 512 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        4.12mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 42638
        • 1: 512
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (512)
        1.11mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 42638 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.08mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 42638
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 42638 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        910μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 42638
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 42638 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        950μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 42638
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        3.95mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 3
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.18mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.31mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.21mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.24mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.9mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.52mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      6HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          aqQk5gelusrtr1HHsv06dFpxUm40nAx3T2JaBFyT
          utm_source
          direct
          redirectUrl
          /college-homework-library/Computer-Science/Machine-Learning/42638
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Computer-Scienc...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Computer-Science/Machine-Learning/42638
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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