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Standard Room
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Rs. 4,225
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Room Overview
Standard Room
Mon, 06 Mar – Tue, 07 Mar (1 Night) | 1 Room | 1 Guest
Standard Room
(based on 4 reviews)
by mayankgauda on November 17, 2015
I visited so many times with friends & family, once upon time this place very one of the best attraction of Nashik but nowadays this hotel missing its charm so management needs to think about it; because still this place has great potential to recreate its previous charm. You can good food over here. Good Place for small get together & party.
by GunjanGupta11 on October 8, 2015
It is a nice and simple place with all the functional items in the room. Its not a luxury property. The staff is very polite and helpful. Food is very tasty and fresh. The place is full of greenery and is at a very peaceful location.
by chitratibrewal on October 5, 2015
we enjoyed a lot the property and stay . excellent ambiance and landscaping. Food is awesome. This is the best location to stay peacefully. Very peaceful ambiance. We receive good services. Excellent place for family and friends gathering.
by ParikshitPune on June 8, 2015
I was here as a guest for a weeding ceremony being held nearby. This place has been gifted with a great locaion - Right on the Nasik-Mumbai Road and they have maintained the premises very well. Pros: - Ample amount of car parking space - Well maintained greenery in the premises - Beautiful cottages Cons: - Bathrooms and rooms are clean but the WCs are not spotless. - ACc in some rooms are Window ACs with no control over temperature - No power back-up - Fan in my room had to be pushed after switching on each time for it to rotate - I asked for tea at 6:45 in the morning. I was told that the kitchen starts only after 7:30 am !!! The room rates are so high that they are not at all justifiable with the currently provided services. Though the cons exceed the pros, I believe all flaws are such that they could be fixed. If they are then this will make a great place to stay.
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Dr. Gregory Bland MD Patient Reviews
- Plastic Surgery Colorado Springs, CO
Overall Rating
22 Patient Reviews
- Wait Time 7 minutes
- Easy Appointments
- Promptness
- Friendly Staff
- Fair and Accurate Diagnosis
- Bedside Manner
- Spends Time With Patients
- Appropriate Followup
Showing 1 - 12 reviews
5.0 of 5
September 6th, 2016
Two thumbs up!
His pricing was the most reasonable compared to other surgeons for the same procedure. He was professional, caring, and considerate. And, he does great work!
5.0 of 5
August 22nd, 2016
Excellent Plastic Surgeon
I saw Dr. Bland into 2006, he put performed plastic surgery/augmentation on my breasts and I could not have been happier with the results!! He and his office staff were incredibly professional and kind !! They listened intently to questions and answer them with confidence !
1.0 of 5
May 9th, 2016
I am unhappy with my breast implant replacement. Implants were supposed to go under muscle and and the old capsules removed. He did not do this. I now have CC and have to have them redone. He did offer to fix the CC but I don't want to take a chance on the same thing happening again.
5.0 of 5
February 8th, 2016
Great Experience!
Dr. Bland and his staff were amazing! After speaking with Dr. Bland about the procedure I wanted to have, he presented me with all my options so I knew I was making the right decision for me. He did not try to pressure me into anything and was very reassuring that I had made a good decision. He answered all my questions and several of the staff contacted me after my surgery to make sure I was doing well. I would definitely recommend Dr. Bland to a friend or family member.
5.0 of 5
November 29th, 2015
Great physician and team!
Dr Bland explained the surgery thoroughly. I was very well prepared. Results exceeded my expectations. I am a nurse and an attorney and therefore am very critical of healthcare providers.
5.0 of 5
October 16th, 2015
I recommend Dr. Bland to everyone. He knows what he is talking about and made feel very comfortable that I had made the right choice by chosing him. His staff is amazing just like him.
5.0 of 5
March 4th, 2015
Great Experience
This is the third time I have Dr. Bland fix something. Great Doctor, easy to talk to and my surgery went great. I always look 100 percent the way we discussed, no outlandish expectations. I look natural and no one ever realizes that I have had plastic surgery to change something. I recommend Dr. Bland to anyone who wants to correct or change their look. Thank you and your staff for their expert care and the friendly atmosphere of Premier MediSpa.
1.0 of 5
January 25th, 2015
He Ruined my nose
Dr. Bland performed a rhinoplasty MANY years ago. He was recommended to me by my mom (a nurse). He left so much scar tissue that all consultations with plastic surgeons since have said there is nothing they can do. I hate my big disfigured nose!
5.0 of 5
September 23rd, 2014
I wouldn't go to anyone else! Dr Bland, his wife and entire staff are very professional, kind and caring. The aftercare is superior, as well as the ease of the procedure itself. Everything was explained well, I knew what to expect and how to contact them should I need to. Best experience!!!!!
5.0 of 5
February 9th, 2014
Best Team Around!!
I had the opportunity to research some options before having breast augmentation. DR. Bland and team were thr most knowledgeable and professional group of people that I have met within this speciality. Dr. Bland discussed placement options according to my anatomy. He identified that I had less orginial tissue in the bottom half of my breast and was able to make me appear fuller where I needed it. On average of all the doctors that I had a consultation with ( about 6 between Denver and COS) his rates were actually in the lower percent. Dr. Bland is also skilled in sub-fascial placement, he was the only doctor in my experience that was knowledgeable in this placement type. He did subfascial on me, so its not on top of the muscle ( where it could feel less natural and more of the implant) or under thr muscle ( where if u raise your arm you see the implant move). Looks more natural! Gerty (his wife) works alongside with him. Gerty is there to answer any questions at any time of the day or night as well as shes checking on you; calling to see how you are. Then he has Sam , shes great she walks through every step with you, is friendly and makes you feel at ease. Dr. Bland and team display a strong unit together, I am extremely pleased with my expierence with this staff. Thank You!!
5.0 of 5
September 19th, 2013
Dr. Bland and his staff were so nice, caring and comforting. I had to have surgery to correct issues from a previous surgery (unfortunately not performed by him initially). He made sure I understood everything regarding my procedure. He easy-going, sweet and thorough. He encourages immediate feedback to better himself. I am very confused by the comments made by the lady with the face lift??? Dr. Bland, Gerti and his staff are not like that. Two of my friends have also seen Dr. Bland and were very pleased as well. I did more than 18 months of research prior to meeting Dr. Bland and I am truly grateful I chose him.
5.0 of 5
July 30th, 2013
Dr. Bland, Gerti, and the entire staff are simply the best!!! Dr. Bland is professional, yet kind and gentle. He genuinely cares and exudes confidence and integrity. I feel so blessed to have found him and his staff. I have always been treated like royalty there and made to feel like family. Dr. Bland has far exceeded my expectations on all my procedures. He is a perfectionist that demands the best from himself and his staff. I truly have come to love and adore all of them at Premiere MediSpa and Center for Plastic Surgery. I think of them as my friends and my family. I would recommend Dr. Bland to everyone. Again, Dr. Bland and his entire staff are The Best!!!!!!! I am forever a fan and a frequent flyer! Warmly, Jodi P.S. To the person who wrote the negative review.......you clearly have Dr. Bland confused with someone else. A little sketchy that you waited 5 years to vent. Hmmm...After 5 years, your credibility is questionable at best. Just sayin'............
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text:
Family Deported after Teen is Caught with Marijuana
By: Gerri L. Elder
An entire Tucson, Ariz., family has been deported after a high school student in the family was found with marijuana in his backpack at school.
When the teen boy was seen at school acting incoherently and appeared to be under the influence of drugs or alcohol, school officials searched his backpack. When they found that the ninth-grader had a small amount of marijuana, they called the police.
A police officer arrived at Catalina High Magnet School to investigate the situation. He called the student's parents to come to the high school and asked to see their driver's licenses when they arrived.
The student's parents allegedly told the police officer that they had been living in the United States illegally for six years with their two children. The couple has a 12-year-old son in addition to the ninth-grade student at Catalina High Magnet School.
Since the parents could not produce valid driver's licenses to show the police officer at the school, the Border Patrol was called. When Border Patrol agents arrived at the school they took the parents and the student into custody and then went to the 12-year-old child's school and picked him up.
The mother and her two sons were taken to the border of Mexico for a procedure known as voluntary return. The father was held for formal deportation because the agency had previously apprehended him a number of times. They apparently were never given the chance to consult with a criminal defense attorney.
Although the police officer faced scathing public criticism from immigration rights activists for the way the case was handled, and there was even a public protest by the students of the high school, police officials say that the case was handled correctly.
Since the ninth-grade boy had allegedly committed a crime, the police department policy allows officers to contact the Border Patrol when they suspect that a person is in the country illegally.
"We can't lose track of the fact that an administrator came across a juvenile who was violating the law, in possession of marijuana," Tucson Police Chief Robert Villasenor said. "That is a crime in this country, whether you are here illegally or not."
Immigration rights activists argue that allowing immigration authorities into the schools could create more mistrust and fear in the immigrant community.
Jennifer Allen, director of Tucson-based Border Action Network said, "Now you have people who are afraid to call the police when they have been robbed because they are afraid the police will come and instead of investigating the crime will ask them about their immigration status."
Chyrl Hill Lander, a spokeswoman for the Tucson Unified School District said she was unaware of other immigration-related arrests at Tucson area schools, and said the district would have preferred that police called the Border Patrol once they left the campus.
The policy of the Tucson Police Department is that if officers have already stopped a person on suspicion of committing a crime they may ask immigration agents to respond to determine if the person is in the country legally.
Villasenor said the Police Department doesn't want officers to become immigration officials, nor does he want to see crime victims or witnesses who are here illegally be too afraid to come forward because they might be deported. However, he says that federal immigration agents will be called when police officers believe they are required.
"While we don't want to put a chilling effect on anyone calling us, we are also obligated to do our job," Villasenor said.


text:
Amar ma'ruf nahi munkar
December 6, 2008 at 6:33 pm 14 comments
I've been meaning to speak about this for a long time coming but recent events have served to be the catalyst for finally penning this down.
"You are the best of peoples, evolved for mankind, enjoining what is right, forbidding what is wrong, and believing in Allah."
Surah al-'Imran 3:110
I really feel that there is something gravely wrong with the Muslim community in Singapore. (Maybe everywhere else but since I'm a living specimen of the Muslim community in Singapore, I shall speak for it.)
There are many, many lines in the Qur'an that speak of amar ma'ruf, nahi munkar, aka "Enjoin good, forbid evil". There are some camps that go all out to do this to the point of insulting and labelling others of kufr and other treacherous things. But for the most part, I think our community has failed in practicing what is oft-repeated in the Qur'an.
Based on my own experience when I was trying to change my ways of life, the very people that hindered me or mocked me were the Muslims themselves. Yes, I did have some who gave me encouragement but these were far & few in between. What I had to go through most often were snide comments, people calling me "Ustazah" (this hasn't stopped and each time it happens now, all I say is InsyaAllah heh), comments on my dressing, on my speech, on me suddenly being "so alim" and so many other nasty things. Most I let it pass but there were some that did hurt me at that time. I've forgiven them all now but my main point is, why?
And hey, you know what? This is actually a COMMON reaction to most people I've spoken to. Each time someone wants to change for the better, there are bound to be people (not one or two but many) who will say stuff like "Eleh, nak action alim konon" , "Sikit salah pun tak boleh ke? Allah paham la" [Even a small mistake is not allowed? Allah will understand la] and so many other really rubbish things. When one is trying to hold on tight to the Sunnah and trying to revive a sunnah in these last days, someone says "Jangan nak step Nabi". Astaghfirullah!
How hurtful their words, how inconsiderate people can be!
And then on the other end of the spectrum, I have to say that the Muslim community in Singapore actually encourages evil!
Don't believe me? Read through the next few lines and tell me you've never heard them before.
- During a family gathering, perhaps Eid, an uncle/aunty sees a youth, maybe 13-15 years of age and proceeds to ask "Ni mesti dah ada matair kan?" [Surely you have a girlfriend/boyfriend right?] Upon hearing a "no", they will say "Handsome/lawa macam gini takkan takde matair.." [You're so handsome/pretty, impossible that you don't have one.]
These words are actually mocking the youths. Already it is so difficult for youths to resist getting in a relationship at that tender age, these makcik pakcik just haaaaad to rub it in!
- Again, family gathering especially Eid. (Sorry I'm using examples from Eid, its just that this is when I see it happening the most.)
A young girl chooses to don a loose-fitting garment for Raya. A makcik (usually a makcik) will ask "Why wear this for Raya? All your other cousins are wearing kebaya and all. You look like you are drowning in it! You're so young, wear nice nice. You're making yourself look older! And you only wear celak? Where's your foundation and make-up? WHAT you don't wear make-up?! Come here, I put for you. Going visiting whole day, how can you go out of the house looking like THAT!"
Oh yeah, thanks makcik for the compliment!
I know that I could really come up with more examples. And mind you, these aren't things I made up in my mind. They are real words by real people.
Why stop someone from doing good or changing for the better? Just because you don't have the guts and the strength to leave your bad habits and bad deeds and attempt to please your Lord rather than your ego, that doesn't make it okay to make someone's struggle even harder than it already is!
I was really saddened by this, and it was amplified yesterday.
You see, yesterday I donned the niqab for the first time. My reason was simple, my Original Spiritual Comrade's husband was giving the Friday sermon and he chose to give the Prophet's last sermon. I wanted to hear him give it. BUT its makruh for a young lady to do the Friday prayers at the mosque because of the attention that she might attract. Its haram if she adorns herself. Therefore, I reasoned that since I really wanted to hear him give the khutbah, I'll come really early to the mosque and try be as invisible and unnoticeable as possible.
After prayers, my Original Spiritual Comrade & I waited till the mosque was empty before we left. See, just like how Sayyidatina Aisya RA described the women who went to the mosque. "They came and left unnoticed." (Or atleast we tried.)
We then went for lunch and the whole day, I had the niqab on. I felt really comfortable in it so I didn't see the need for me to take it off just because prayers were over. However, certainly some people had problems with that. Along the way, I met a family friend. (Oh yes, the most amusing thing about yesterday was that 4 people recognized me. When I don't have the niqab on, nobody comes up to me to say Hi but when I do, everyone recognizes me! Must be the funky specs. ;p )
So anyway, we spoke for a bit and then parted ways. Barely 10mins later, I had a call from a very terrified-sounding mother. "Mee, I ask you a question. Just answer me by saying yes or no. Did you go out today with the niqab?"
Upon hearing my answer, she started whining and going Whyyyyyyyy and proceeded to be very dramatic and emotional. She went on to say "You see, apa you buat, semua orang tahu, abeh news sampai kat I." [You see, everything you do, everyone knows and the news will reach me.]
I was baffled, honestly. The way she was telling me off, it was as if someone caught me holding hands with a non-Mahram male! Ya Rabb!
It was 10mins, a mere 10mins since the time I parted ways with the previous lady and already she had contacted my mum to ask if I had started wearing the niqab. Honestly, so what if I did?!
When I got home, my mum sat me down to "get things clear" and told me that people think that I now have "buang dunya" [renounced the world]. It was very dramatic, as women always are *rolls eyes* and I just sat there wondering what grave sin I had done to deserve this much attention.
I was reflecting after that and I got really sad. When I was growing up, I had done so many un-Islamic things and none of that ever got to my parents. If they had only called my parents and informed them then, perhaps I could have saved myself a whole load of sins. But when it comes to something like wearing the niqab just to be invisible for a day, masyaAllah, the news spread like wildfire and I got a telling off for doing so. Sigh.
Why do we do this? Why do we allow haram acts to remain unmentioned and make a big hooha over something halal? Why highlight an act that will not incur the wrath of Allah and allow other Muslims to continue going on the path that will lead them to other than Jannah?
"Leave alone those who take their religion to be mere play and amusement, and are deceived by the life of this world. But proclaim (to them) this (truth): that every soul delivers itself to ruin by its own acts: it will find for itself no protector nor intercessor except Allah: if it offered every ransom, none will be accepted: such is (the end of) those who deliver themselves to ruin by their own acts: they will have for drink (only) boiling water, and for punishment, one most grievous: for they persisted in rejecting Allah."
Surah al-An'am 6:70
Allah is As-Sattar, the Most Beautiful Covering. That is one thing that Allah always reminds me. None of my bad deeds were mentioned by people because He didn't allow them to. No one told my parents about it because He allowed them to go unnoticed (if not unnoticed, then unmentioned). How many of my sins that I had done that He knows of but yet, covers them from people? MasyaAllah.. Allah, Allah..
I remember my Ustaz telling me about his life in Egypt years ago. He said if a lady was seen with a male that is not her mahram, the male would be confronted and made to explain to her parents or at least, her brother. He quoted other examples where he would confront someone who was not going to the mosque to pray when the Azan had just been heard.
I admired that so much. I mean, of course we do good deeds for Allah and we abstain from sin for Allah and not for the fact that people will see and talk. But masyaAllah, how much it would help if the Muslim community in Singapore does that! People persist in sin because they are not reminded of the sinfulness of such an act!
Its just amazing that the culture is such. Over here, you start praying a little longer or start wearing celak (especially for the males) and someone 'advises' you and says "Don't start becoming extremist." Whaaaaaat?
"Let there arise out of you a band of people inviting to all that is good, enjoining what is right, and forbidding what is wrong: they are the ones to attain felicity."
Surah al-'Imran 3:104
Yes, let there arise a band of us who will do this! Let us not allow our fellow brothers and sisters who are beginning to see the Light to suffer when they want to change for the better. Let us be good helpers and motivators and not ones who mock and make things harder for them. May Allah help us!
Before I end, here's a little something for all you wonderful souls who are in this struggle:
"O you who believe! Guard your own souls: if you follow (right) guidance, no hurt can come to you from those who stray. The goal of you all is to Allah: it is He that will show you the truth of all that you do."
Surah al-Maidah 5:105
I pray Allah helps the Muslim community to enjoin good and forbid evil, to not fear to speak the truth even if it hurts, to give us strength to spread His Word, to revive the Sunnah of the Prophet SAW even if its going to invite teasing and mocking from others, to give us strength to hold on to the rope of Allah and never let go. Amin ya Rabbal Alameen!
Entry filed under: Al-Qur'an, change, conversations, difficulty, dunya, good deed, myself, people, Prophet SAW, Qur'an, Sayyidatina Aisha RA.
14 Comments Add your own
it is, an experience isnt it :) to wear a niqab in public… hehe
Assalaamu'alaikum Kak I hope u know who I am ahaha…
Alhamdulillah, none of my relatives has ever asked me those questions, BUT my mum have been asked by one of her friends if I already had a boyfriend.
I don't get it actually. I don't think they aren't aware of Islam's stand on BGR. And if they see a couple, they would comment about them. These questions seriously contradict all that cuz they all ENCOURAGE BGR, don't you think?
How, how, HOW can we change this detrimental tradition? I highly doubt that only the SG Muslim community faces this somewhat hypocritical situation, I believe a lot of other Muslim communities worldwide face this too (:
Anyway, May Allah Bless you for being so brave! I have been musing about wearing the niqab for once, just to feel how women in niqab feel and yes, being invisible, and unrecognisable for once.
Well, I dunno if anyone's commented me behind my back whenever I wear the jubah to school, but there's been anyone, I forgive them (:
Wearing the jubah may seem extreme enough for some, especially if it's a young girl. I don't like wearing kebaya seh it's so darn flashy and TIGHT. I don't even like wearing baju kurung with flowery prints! Haha!
It's hard trying to become more religious, cuz I think people are afraid it will lead to extremism.
Ok, before this becomes a supplementary blog entry, I'll stop here haha!
Take care kak!
(I call my friends' older sisters kak, if you don't mind. A bit funny if my friend who is your younger bro's calling you kak and I don't haha. To me at least :D But if u object no hal xD)
Btw what's Original Spiritual Comrade? Sounds fascinating…
Therein lies the problem with the Malay/Muslim community. We forget the Hereafter and we want the dunya.
We're gradually becoming Westernized if we aren't already are.
Speaking of which, also an Eid example, there was a screening of Bujang Lapok – a classic Malay film reaching cult status. I happened to watch it in a relative's house – there were some uncomfortable scenes. Is it just me or is everyone else blind to the stark transgressions of God's Limits in such a film?
No boundaries between men & women. Singing together. Like duh? And we glorify such a film?!
Is it any wonder why we're in such a state?
If we forget God, don't expect God to remember us. If you want this worthless dunya, you can have all you want – but you'll never know whether you'd still be alive to enjoy it tomorrow.
Laugh all you want, you won't be laughing when you're buried 6 feet under.
Here lies the choice: dunya or akhirah?
We seriously need to return to our Lord and Cherisher.
May God help us in that.
May Allah prevent us from this.It's the opposite of Amar Ma'ruf nahi Munkar.
" The Hypocrites, men and women, (have an understanding) with each other: They enjoin evil, and forbid what is just, and are close with their hands. They have forgotten Allah. so He hath forgotten them. Verily the Hypocrites are rebellious and perverse. "
( سورة التوبة , At-Taubah, Chapter #9, Verse #67)
>>Watching the movie doesn't necessarily mean we endorse the trangressions thats being done in the movie.
I believe that's where the error comes in. If the elders who watch don't intervene in saying this is wrong, the younger generations will be confused.
Watching Western movies/dramas is a no-no but watching Bujang Lapok is okay.
It's precisely when the elders praise such a film, telling the young ones its a classic and such, that they will think: "So it's okay for men and women to sing together?"
Part of the dawah of Rasulullah (saw) was doing certain things and NOT doing certain things. If he didn't do something when he could do it, that means it's undesirable. So if we were to allow such movies to be portrayed and don't do anything to differentiate the right from wrong, the young ones will get influenced.
Truth is clear from falsehood.
Let them not be mixed.
>>They lived in a time different from our own. They will be judged according to what they know; we will be judged with a yardstick different from them.
Thank you for the reminder for I almost forgot about that.
May God guide us.
Salaam 'alaik..
Hm, I understand where you're coming from as I went through and experienced such phases as well..
The things that you brought up are real. But before we judge any of them, we must try understand why do they say such things and why they do the things the way they do.
Are they well-practicing muslims who purposely critisize other muslims or are they just muslims by birth who're still very ignorant of their own religion?
Seriously, if any of them had understood Islam well, they wouldn't go to such extremes.
Before we try argue with them what's right or wrong, telling them this or that is the way Islam has to be, that we have to do 'amr ma'ruf nahi munkar', there's something that's more important for them to understand. Which is the root of Islam, the Akidah. They should firstly understand, What is our purpose of life?
Allah explained our purpose of life in surah Adh-Dhariyat 51:56.. 'And I(Allah) created not the jinn and mankind except that they should worship Me (alone).'
We should understand that the concept of worship is not only in prayers or fasting or zakat or hajj but it encompasses whatever we do in this life that's according to Noble Qur'an and the way He recommends us to do it through the actions of Prophet Muhammad SAW (sunnah). This is Islam.
They should also understand the fact that we need Allah in our lives in everything that we do. If they can agree to this, only then, we can try explaining to them the secondary issues such as solat or why muslimahs have to cover themselves properly…We need to solat because we need Allah in our lives and if we have to don a certain dresscode while attending a formal function together with the president for example, it is even more compulsory to dress that way for Allah as that is the way He instructs us to.
It's important that we try to da'wah to them firstly through our own actions, then try to do it in a way that will want them to change themselves, bihikmah. Maybe even ponder, hm, how would Rasulullah SAW approach this matter?
It's easier said than done of course. But we have to try. Lessen the critisizing, try to understand more and after that work on the solutions.
Thier words may be hurtful and mindless to us not to them, but i'm sure they're mostly spoken out of ignorance.
As the words from stephan r covey's, habit 5 and what da'ies such as Hassan al-Banna normally practice "Seek to understand.. than be understood"
And Allah SWT knows best.
[…] Ameera writes beautifully, she almost always makes me cry reading her posts. And I truly share my sentiments on this post. […]
Asalamualaikum Ameera,
I understand your predicament especially so with all the Makcik/pakcik. Truthfully, I dread family gatherings especially Eid (like how you have quoted so many times. :P ) but each time this snide remarks are made, I reaffirm myself that I don't do this to get into anyone's good books nor am I "step nak macam Nabi".
All these people do not know the true love for Islam. I guess they are Muslims by birth. But believer by choice? Wallah hualam. So I hope you won't feel so – I don't know the right word – disgruntled by all these passing comments.
Cos afterall, whatever we do or we don't do has all been planned by Allah and as a blessed slaved to the Almighty, we should always be reminded of His graciousness.
And thanks for posting this up. It kinda remind me that I'm not alone during this harrowing family gathering.
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A suburban Chicago man who stayed in a Joliet, Ill. motel room with his dead girlfriend's corpse for two days, while buying alcohol with her money, was sentenced to one and a half years in prison Wednesday.
Derek Tanke, 43, pleaded guilty to using his girlfriend's ATM card to buy a bottle of vodka two days after Nancy Johnson, 54, passed away at the Bel-Air Motel room they had been sharing, Joliet Patch reports. Tanke was convicted of concealing a death and unlawful credit card use.
Tanke had been arrested six times previously for beating Johnson.
He reportedly told police that he punched the woman in the face several times days before she died, but the Chicago Sun-Times reports that Johnston had several medical problems and died of cirrhosis of the liver, a cause unrelated to the assault. Tanke was homeless when Johnston died in February, according to court records.
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I like what you like
- Tyrone Farmer
- 1 years ago
- Views:
1 Chapter 2: Collaborative filtering I like what you like We are going to start our exploration of data mining by looking at recommendation systems. Recommendation systems are everywhere from Amazon:
2 to last.fm recommending music or concerts: In the Amazon example, above, Amazon combines two bits of information to make a recommendation. The first is that I viewed The Lotus Sutra translated by Gene Reeves; the second, that customers who viewed that translation of the Lotus Sutra also viewed several other translations. The recommendation method we are looking at in this chapter is called collaborative filtering. It's called collaborative because it makes recommendations based on other people in effect, people collaborate to come up with recommendations. It works like this. Suppose the task is to recommend a book to you. I search among other users of the site to find one that is similar to you in the books she enjoys. Once I find that similar person I can see what she likes and recommend those books to you perhaps Paolo Bacigalupi's The Windup Girl. 2-2
3 COLLABORATIVE FILTERING How do I find someone who is similar? So the first step is to find someone who is similar. Here's the simple 2D (dimensional) explanation. Suppose users rate books on a 5 star system zero stars means the book is terrible, 5 stars means the book is great. Because I said we are looking at the simple 2D case, we restrict our ratings to two books: Neal Stephenson's Snow Crash and the Steig Larsson's The Girl with the Dragon Tattoo. First, here's a table showing 3 users who rated these books Snow Crash Amy 5 5 Bill 2 5 Jim 1 4 Girl with the Dragon Tattoo I would like to recommend a book to the mysterious Ms. X who rated Snow Crash 4 stars and The Girl with the Dragon Tattoo 2 stars. The first task is to find the person who is most similar, or closest, to Ms. X. I do this by computing distance. 2-3
4 Manhattan Distance The easiest distance measure to compute is what is called Manhattan Distance or cab driver distance. In the 2D case, each person is represented by an (x, y) point. I will add a subscript to the x and y to refer to different people. So (x1, y1) might be Amy and (x2, y2) might be the elusive Ms. X. Manhattan Distance is then calculated by x1 - x2 + y1 - y2 (so the absolute value of the difference between the x values plus the absolute value of the difference between the y values). So the Manhattan Distance for Amy and Ms. X is 4: Computing the distance between Ms. X and all three people gives us: Distance from Ms. X Amy 4 Bill 5 Jim 5 2-4
5 COLLABORATIVE FILTERING Amy is the closest match. We can look in her history and see, for example, that she gave five stars to Paolo Bacigalupi's The Windup Girl and we would recommend that book to Ms. X. Euclidean Distance One benefit of Manhattan Distance is that it is fast to compute. If we are Facebook and are trying to find who among one million users is most similar to little Danny from Kalamazoo, fast is good. Pythagorean Theorem You may recall the Pythagorean Theorem from your distant educational past. Here, instead of finding the Manhattan Distance between Amy and Ms. X (which was 4) we are going to figure out the straight line, as-the-crow-flies, distance 2-5
6 The Pythagorean Theorem tells us how to compute that distance. a c c = p a 2 + b 2 b This straight-line, as-the-crow-flies distance we are calling Euclidean Distance. The formula is p (x1 x 2 ) 2 +(y 1 y 2 ) 2 Recall that x1 is how well person 1 liked Dragon Tattoo and x2 is how well person 2 liked it; y1 is how well person 1 liked Snow Crash and y2 is how well person 2 liked it. Amy rated both Snow Crash and Dragon Tattoo a 5; The elusive Ms. X rated Dragon Tattoo a 2 and Snow Crash a 4. So the Euclidean distance between p (5 2)2 +(5 4) 2 = p = p 10 = 3.16 Computing the rest of the distances we get Distance from Ms. X Amy 3.16 Bill 3.61 Jim
7 COLLABORATIVE FILTERING N-dimensional thinking Let's branch out slightly from just looking at rating two books (and hence 2D) to looking at something slightly more complex. Suppose we work for an online streaming music service and we want to make the experience more compelling by recommending bands. Let's say users can rate bands on a star system 1-5 stars and they can give half star ratings (for example, you can give a band 2.5 stars). The following chart shows 8 users and their ratings of eight bands. Angelica Bill Chan Dan Hailey Jordyn Sam Veronica Blues Traveler Broken Bells Deadmau Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend The hyphens in the table indicate that a user didn't rate that particular band. For now we are going to compute the distance based on the number of bands they both reviewed. So, for example, when computing the distance between Angelica and Bill, we will use the ratings for Blues Traveler, Broken Bells, Phoenix, Slightly Stoopid, and Vampire Weekend. So the Manhattan Distance would be: 2-7
8 Angelica Bill Difference Blues Traveler Broken Bells Deadmau5-4 Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend Manhattan Distance: 9 The Manhattan Distance row, the last row of the table, is simply the sum of the differences: ( ). Computing the Euclidean Distance is similar. We only use the bands they both reviewed: Angelica Bill Difference Difference 2 Blues Traveler Broken Bells Deadmau5-4 Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend Sum of squares 18.5 Euclidean Distance
9 COLLABORATIVE FILTERING To parse that out a bit more: Euclidean = (3.5 2) 2 +(2 3.5) 2 + (5 2) 2 + ( ) 2 + (2 3) 2 = ( 1.5) ( 2) 2 + ( 1) 2 = = 18.5 = 4.3 Got it? Try an example on your own
10 Angelica Bill Chan Dan Hailey Jordyn Sam Veronica Blues Traveler Broken Bells Deadmau Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend s sharpen your pencil Compute the Euclidean Distance between Hailey and Veronica. Compute the Euclidean Distance between Hailey and Jordyn 2-10
11 COLLABORATIVE FILTERING s sharpen your pencil - solution Compute the Euclidean Distance between Hailey and Veronica. = p (4 5) 2 +(4 3) 2 = p 1+1= p 2=1.414 Compute the Euclidean Distance between Hailey and Jordyn = p (4 4.5) 2 +(1 4) 2 +(4 5) 2 +(4 4) 2 +(1 4) 2 = p ( 0.5) 2 +( 3) 2 +( 1) 2 + (0) 2 +( 3) 2 = p = p = A flaw It looks like we discovered a flaw with using these distance measures. When we computed the distance between Hailey and Veronica, we noticed they only rated two bands in common (Norah Jones and The Strokes), whereas when we computed the distance between Hailey and Jordyn, we noticed they rated five bands in common. This seems to skew our distance measurement, since the Hailey-Veronica distance is in 2 dimensions while the Hailey-Jordyn 2-11
12 distance is in 5 dimensions. Manhattan Distance and Euclidean Distance work best when there are no missing values. Dealing with missing values is an active area of scholarly research. Later in the book we will talk about how to deal with this problem. For now just be aware of the flaw as we continue our first exploration into building a recommendation system. A generalization We can generalize Manhattan Distance and Euclidean Distance to what is called the Minkowski Distance Metric: When n d(x, y) = ( x k y k r ) k=1 r = 1: The formula is Manhattan Distance. r = 2: The formula is Euclidean Distance r = : Supremum Distance 1 r h Arghhhh Math! When you see formulas like this in a book you have several options. One option is to see the formula-- brain neurons fire that say math formula--and then you quickly skip over it to the next English bit. I have to admit that I was once a skipper. The other option is to see the formula, pause, and dissect it. 2-12
13 COLLABORATIVE FILTERING Many times you ll find the formula quite understandable. Let s dissect it now. When r = 1 the formula reduces to Manhattan Distance: d(x, y) = x k y k n k=1 So for the music example we have been using throughout the chapter, x and y represent two people and d(x, y) represents the distance between them. n is the number of bands they both rated (both x and y rated that band). We ve done that calculation a few pages back: Angelica Bill Difference Blues Traveler Broken Bells Deadmau5-4 Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend Manhattan Distance: 9 That difference column represents the absolute value of the difference and we sum those up to get 9. When r = 2, we get the Euclidean distance: d(x, y) = (x k y k ) 2 n k=1 2-13
14 Here s the scoop! The greater the r, the more a large difference in one dimension will influence the total difference. Representing the data in Python (finally some coding) There are several ways of representing the data in the table above using Python. I am going to use Python's dictionary (also called an associative array or hash table): Remember, All the code for the book is available at 2-14
15 COLLABORATIVE FILTERING users = {"Angelica": {"Blues Traveler": 3.5, "Broken Bells": 2.0,!! "Norah Jones": 4.5, "Phoenix": 5.0,! "Slightly Stoopid": 1.5, "The Strokes": 2.5, "Vampire Weekend": 2.0}, "Bill": {"Blues Traveler": 2.0, "Broken Bells": 3.5, "Deadmau5": 4.0, "Phoenix": 2.0, "Slightly Stoopid": 3.5, "Vampire Weekend": 3.0}, "Chan": {"Blues Traveler": 5.0, "Broken Bells": 1.0, "Deadmau5": 1.0, "Norah Jones": 3.0, "Phoenix": 5, "Slightly Stoopid": 1.0}, "Dan": {"Blues Traveler": 3.0, "Broken Bells": 4.0, "Deadmau5": 4.5, "Phoenix": 3.0, "Slightly Stoopid": 4.5, "The Strokes": 4.0, "Vampire Weekend": 2.0}, "Hailey": {"Broken Bells": 4.0, "Deadmau5": 1.0, "Norah Jones": 4.0, "The Strokes": 4.0, "Vampire Weekend": 1.0}, "Jordyn": {"Broken Bells": 4.5, "Deadmau5": 4.0, "Norah Jones": 5.0, "Phoenix": 5.0, "Slightly Stoopid": 4.5, "The Strokes": 4.0, "Vampire Weekend": 4.0}, "Sam": {"Blues Traveler": 5.0, "Broken Bells": 2.0, "Norah Jones": 3.0, "Phoenix": 5.0, "Slightly Stoopid": 4.0, "The Strokes": 5.0}, "Veronica": {"Blues Traveler": 3.0, "Norah Jones": 5.0, "Phoenix": 4.0, "Slightly Stoopid": 2.5, "The Strokes": 3.0}} We can get the ratings of a particular user as follows: >>> users["veronica"] {"Blues Traveler": 3.0, "Norah Jones": 5.0, "Phoenix": 4.0, "Slightly Stoopid": 2.5, "The Strokes": 3.0} >>> 2-15
16 The code to compute Manhattan distance I'd like to write a function that computes the Manhattan distance as follows: def manhattan(rating1, rating2): """Computes the Manhattan distance. Both rating1 and rating2 are dictionaries of the form {'The Strokes': 3.0, 'Slightly Stoopid': """ distance = 0 for key in rating1: if key in rating2: distance += abs(rating1[key] - rating2[key]) return distance To test the function: >>> manhattan(users['hailey'], users['veronica']) 2.0 >>> manhattan(users['hailey'], users['jordyn']) 7.5 >>> Now a function to find the closest person (actually this returns a sorted list with the closest person first): def computenearestneighbor(username, users): """creates a sorted list of users based on their distance to username""" distances = [] for user in users: if user!= username: distance = manhattan(users[user], users[username]) distances.append((distance, user)) # sort based on distance -- closest first distances.sort() return distances 2-16
17 COLLABORATIVE FILTERING And just a quick test of that function: >>> computenearestneighbor("hailey", users) [(2.0, ''Veronica'), (4.0, 'Chan'),(4.0, 'Sam'), (4.5, 'Dan'), (5.0, 'Angelica'), (5.5, 'Bill'), (7.5, 'Jordyn')] Finally, we are going to put this all together to make recommendations. Let's say I want to make recommendations for Hailey. I find her nearest neighbor Veronica in this case. I will then find bands that Veronica has rated but Hailey has not. Also, I will assume that Hailey would have rated the bands the same as (or at least very similar to) Veronica. For example, Hailey has not rated the great band Phoenix. Veronica has rated Phoenix a '4' so we will assume Hailey is likely to enjoy the band as well. Here is my function to make recommendations. def recommend(username, users): """Give list of recommendations""" # first find nearest neighbor nearest = computenearestneighbor(username, users)[0][1] recommendations = [] # now find bands neighbor rated that user didn't neighborratings = users[nearest] userratings = users[username] for artist in neighborratings: if not artist in userratings: recommendations.append((artist, neighborratings[artist])) # using the fn sorted for variety - sort is more efficient return sorted(recommendations, key=lambda artisttuple: artisttuple[1], reverse = True) And now to make recommendations for Hailey: >>> recommend('hailey', users) [('Phoenix', 4.0), ('Blues Traveler', 3.0), ('Slightly Stoopid', 2.5)] That fits with our expectations. As we saw above, Hailey's nearest neighbor was Veronica and Veronica gave Phoenix a '4'. Let's try a few more: >>> recommend('chan', users) 2-17
18 [('The Strokes', 4.0), ('Vampire Weekend', 1.0)] >>> recommend('sam', users) [('Deadmau5', 1.0)] We think Chan will like The Strokes and also predict that Sam will not like Deadmau5. >>> recommend('angelica', users) [] Hmm. For Angelica we got back an empty set meaning we have no recommendations for her. Let us see what went wrong: >>> computenearestneighbor('angelica', users) [(3.5, 'Veronica'), (4.5, 'Chan'), (5.0, 'Hailey'), (8.0, 'Sam'), (9.0, 'Bill'), (9.0, 'Dan'), (9.5, 'Jordyn')] Angelica's nearest neighbor is Veronica. When we look at their ratings: Angelica Bill Chan Dan Hailey Jordyn Sam Veronica Blues Traveler Broken Bells Deadmau Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend We see that Angelica rated every band that Veronica did. We have no new ratings, so no recommendations. Shortly, we will see how to improve the system to avoid these cases. 2-18
19 COLLABORATIVE FILTERING s exercise 1) Implement the Minkowski Distance function. 2) Alter the computenearestneighbor function to use Minkowski Distance. 2-19
20 s exercise - solution 1) Implement the Minkowski Distance function. def minkowski(rating1, rating2, r): """Computes the Minkowski distance. Both rating1 and rating2 are dictionaries of the form {'The Strokes': 3.0, 'Slightly Stoopid': 2.5}""" distance = 0 commonratings = False for key in rating1: if key in rating2: distance += pow(abs(rating1[key] - rating2[key]), r) commonratings = True if commonratings: return pow(distance, 1/r) else: return 0 #Indicates no ratings in common 2) Alter the computenearestneighbor function to use Minkowski Distance. just need to alter the distance = line to distance = minkowski(users[user], users[username], 2) (the 2 as the r argument implements Euclidean) 2-20
21 COLLABORATIVE FILTERING Blame the users Let's take a look at the user ratings in a bit more detail. We see that users have very different behaviors when it comes to rating bands Bill seems to avoid the extremes. His ratings range from 2 to 4 Jordyn seems to like everthing. Her ratings range from 4 to 5. Angelica Bill Chan Dan Hailey Jordyn Sam Veronica Blues Traveler Broken Bells Deadmau Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend Hailey is a binary person giving either 1s or 4s to bands. 2-21
22 So how do we compare, for example, Hailey to Jordan? Does Hailey's '4' mean the same as Jordyn's '4' or Jordyn's '5'? I would guess it is more like Jordyn's '5'. This variability can create problems with a recommendation system. I absolutely love Broken Bells! They re tight! I give them a Broken Bells is ok. I d give them a 4.
23 COLLABORATIVE FILTERING Pearson Correlation Coefficient One way to fix this problem is to use the Pearson Correlation Coefficient. First, the general idea. Consider the following data (not from the data set above): Blues Traveler Norah Jones Phoenix The Strokes Weird Al Clara Robert This is an example of what is called 'grade inflation' in the data mining community. Clara's lowest rating is 4 all her rating are between 4 and 5. If we are to graph this chart it would look like 5 Blues Traveler Phoenix 4.5 The Strokes Norah Clara Weird Al Robert Straight line = Perfect Agreement!!! 2-23
24 Clara The fact that this is a straight line indicates a perfect agreement between Clara and Robert. Both rated Phoenix as the best band, Blues Traveler next, Norah Jones after that, and so on. As Clara and Robert agree less, the less the data points reside on a straight line: Pretty Good Agreement: Weird Al Norah Jones 4 The Strokes Blues Traveler Phoenix Clara Robert Not So Good Agreement: 5 Weird Al 4.5 Norah Jones The Strokes Phoenix 3 Blues Traveler Robert 2-24
25 COLLABORATIVE FILTERING So chart-wise, perfect agreement is indicated by a straight line. The Pearson Correlation Coefficient is a measure of correlation between two variables (in this specific case the correlation between Angelica and Bill). It ranges between -1 and 1 inclusive. 1 indicates perfect agreement. -1 indicates perfect disagreement. To give you a general feel for this, the chart above with the straight line has a Pearson of 1, the chart above that I labelled pretty good agreement has a Pearson of 0.91, and the not so good agreement chart has a Pearson of 0.81 So we can use this to find the individual who is most similar to the person we are interested in. The formula for the Pearson Correlation Coefficient is r = n i=1 (x i x)(y i y) n (x i x) 2 n (y i y) 2 i=1 i=1 h Arghhhh Math Again! Here's a personal confession. I have a Bachelor of Fine Arts degree in music. While I have taken courses in ballet, modern dance, and costume design, I did not have a single math course as an undergrad. Before that, I attended an all boys trade high school where I took courses in plumbing and automobile repair, but no courses in math other than the basics. Either due to this background or some innate wiring in my brain, when I read a book that has formulas like the one above, I tend to skip over the formulas and continue with the text below them. If you are like me I would urge you to fight 2-25
26 that urge and actually look at the formula. Many formulas that on a quick glimpse look complex are actually understandable by mere mortals. Other than perhaps looking complex, the problem with the formula above is that the algorithm to implement it would require multiple passes through the data. Fortunately for us algorithmic people, there is an alternative formula, which is an approximation of Pearson: r = n i=1 x i y i n 2 x i=1 i ( x i=1 i )2 n n n i=1 x i n n i=1 n y i=1 i n y 2 i ( y i=1 i )2 n (Remember what I said two paragraphs above about not skipping over formulas) This formula, in addition to looking initially horribly complex is, more importantly, numerically unstable meaning that what might be a small error is amplified by this reformulation. The big plus is that we can implement it using a single-pass algorithm, which we will get to shortly. First, let s dissect this formula and work through the example we saw a few pages back: Blues Traveler Norah Jones Phoenix The Strokes Weird Al Clara Robert To start with, let us compute 2-26
27 COLLABORATIVE FILTERING n i=1 x i y i Which is in the first expression in the numerator. Here the x and y represent Clara and Robert. Blues Traveler Norah Jones Phoenix The Strokes Weird Al Clara Robert For each band we are going to multiple Clara s and Robert s rating together and sum the results: (4.75 4) + (4.5 3) + (5 5) + (4.25 2) + (4 1) = = 70 Sweet! Now let s compute the rest of the numerator: n x i=1 i n n y i=1 i 2-27
28 So the n i=1 x i is the sum of Clara s ratings, which is The sum of Robert s is 15 and they rated 5 bands: = 67.5 So the numerator in the formula on page 26 is = 2.5 Now let s dissect the denominator. First, n i=1 x 2 i ( x i=1 i )2 n n Blues Traveler Norah Jones Phoenix The Strokes Weird Al Clara Robert = (4.75) 2 + (4.5) 2 + (5) 2 + (4.25) 2 + (4) 2 = n 2 x i=1 i 2-28
29 COLLABORATIVE FILTERING We ve already computed the sum of Clara s ratings, which is Square that and we get We divide that by the number of co-rated bands (5) and we get Putting that together: =.625 = Next we do the same computation for Robert: n n y 2 i ( y i=1 i )2 = = i=1 n Putting this altogether we get: r = ( ) = = 1.00 So 1 means there was perfect agreement between Clara and Robert! Take a break before moving on!! 2-29
30 s exercise Before going to the next page, implement the algorithm in Python. You should get the following results. >>> pearson(users['angelica'], users['bill']) >>> pearson(users['angelica'], users['hailey']) >>> pearson(users['angelica'], users['jordyn']) >>> For this implementation you will need 2 Python functions sqrt (square root) and power operator ** which raises its left argument to the power of its right argument: >>> from math import sqrt >>> sqrt(9) 3.0 >>> 3**
31 COLLABORATIVE FILTERING s exercise - solution Here is my implementation of Pearson def pearson(rating1, rating2): sum_xy = 0 sum_x = 0 sum_y = 0 sum_x2 = 0 sum_y2 = 0 n = 0 for key in rating1: if key in rating2: n += 1 x = rating1[key] y = rating2[key] sum_xy += x * y sum_x += x sum_y += y sum_x2 += x**2 sum_y2 += y**2 # if no ratings in common return 0 if n == 0: return 0 # now compute denominator denominator = sqrt(sum_x2 - (sum_x**2) / n) * sqrt(sum_y2 - (sum_y**2) / n) if denominator == 0: return 0 else: return (sum_xy - (sum_x * sum_y) / n) / denominator 2-31
32 One last formula Cosine Similarity I would like to present one last formula, which is very popular in text mining but also used in collaborative filtering cosine similarity. To see when we might use this formula, let s say I change my example slightly. We will keep track of the number of times a person played a particular song track and use that information to base our recommendations on. number of plays The Decemberists The King is Dead Radiohead The King of Limbs Katy Perry E.T. Ann Ben Sally Just by eye-balling the above chart (and by using any of the distance formulas mentioned above) we can see that Sally is more similar in listening habits to Ann than Ben is. So what is the problem? I have around four thousand tracks in itunes. Here is a snapshot of the top few ordered by number of plays: 2-32
33 COLLABORATIVE FILTERING So my top track is Moonlight Sonata by Marcus Miller with 25 plays. Chances are that you have played that track zero times. In fact, chances are good that you have not played any of my top tracks. In addition, there are over 15 million tracks in itunes and I have only four thousand. So the data for a single person is sparse since it has relatively few non-zero attributes (plays of a track). When we compare two people by using the number of plays of the 15 million tracks, mostly they will have shared zeros in common. However, we do not want to use these shared zeros when we are computing similarity. A similar case can be made when we are comparing text documents using words. Suppose we liked a certain book, say Tom Corbett Space Cadet: The Space Pioneers by Carey Rockwell and we want to find a similar book. One possible way is to use word frequency. The attributes will be individual words and the values of those attributes will be the frequency of those words in the book. So 6.13% of the words in The Space Pioneers are occurrences of the word the, 0.89% are the word Tom, 0.25% of the words are space. I can compute the similarity of this book to others by using these word frequencies. However, the same problem related to sparseness of data occurs here. There are 6,629 unique words in The Space Pioneers and there are a bit over one million unique words in English. So if our attributes are English words, there will be relatively few non-zero attributes for The Space Pioneers or any other book. Again, any measure of similarity should not depend on the shared-zero values. 2-33
34 Cosine similarity ignores 0-0 matches. It is defined as cos(x, y) = x y x y where indicates the dot product and x indicates the length of the vector x. The length of a vector is n 2 x i=1 i Let s give this a try with the perfect agreement example used above: Blues Traveler Norah Jones Phoenix The Strokes Weird Al Clara Robert The two vectors are: x = (4.75, 4.5,5, 4.25, 4) y = (4,3,5,2,1) then x = = = y = = 55 = The dot product is 2-34
35 COLLABORATIVE FILTERING x y = (4.75 4) + (4.5 3) + (5 5) + (4.25 2) + (4 1) = 70 And the cosine similarity is cos(x, y) = = = The cosine similarity rating ranges from 1 indicated perfect similarity to -1 indicate perfect negative similarity. So represents very good agreement. s sharpen your pencil Compute the Cosine Similarity between Angelica and Veronica (from our dataset). (Consider dashes equal to zero) Blues Traveler Broken Bells Deadmau 5 Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend Angelica Veronica
36 s sharpen your pencil - solution Compute the Cosine Similarity between Angelica and Veronica (from our dataset). Blues Traveler Broken Bells Deadmau 5 Norah Jones Phoenix Slightly Stoopid The Strokes Vampire Weekend Angelica Veronica x = (3.5,2,0, 4.5,5,1.5,2.5,2) y = (3,0,0,5, 4,2.5, 3,0) x = = 74 = y = = = The dot product is x y = (3.5 3) + (2 0) + (0 0) + (4.5 5) + (5 4) + ( ) + (2.5 3) + (2 0) = Cosine Similarity is cos(x, y) = = =
37 COLLABORATIVE FILTERING Which similarity measure to use? We will be exploring this question throughout the book. For now, here are a few helpful hints: If the data is subject to grade-inflation (different users may be using different scales) use Pearson. If your data is dense (almost all attributes have nonzero values) and the magnitude of the attribute values is important, use distance measures such as Euclidean or Manhattan. Good job, guys, nailed it! If the data is sparse consider using Cosine Similarity. 2-37
38 So, if the data is dense (nearly all attributes have non-zero values) then Manhattan and Euclidean are reasonable to use. What happens if the data is not dense? Consider an expanded music rating system and three people, all of which have rated 100 songs on our site: Jake: hardcore fan of Co untry Linda and Eric: love, love, love 60s rock! Linda and Eric enjoy the same kind of music. In fact, among their ratings, they have 20 songs in common and the difference in their ratings of those 20 songs (on a scale of 1 to 5) averages only 0.5!! The Manhattan Distance between them would be 20 x.5 = 10. The Euclidean Distance would be: d = (.5)2 20 = = 5 =
39 COLLABORATIVE FILTERING Linda and Jake have rated only one song in common: Chris Cagle s What a Beautiful Day. Linda thought it was okay and rated it a 3, Jake thought it was awesome and gave it a 5. So the Manhattan Distance between Jake and Linda is 2 and the Euclidean Distance is d = (3 5) 2 = 4 = 2 So both the Manhattan and Euclidean Distances show that Jake is a closer match to Linda than Eric is. So in this case both distance measures produce poor results. Hey, I have an idea that might fix this problem. Right now, people rate tunes on a scale of 1 to 5. How about for the tunes people don t rate I will assume the rating is 0. That way we solve the problem of sparse data as every object has a value for every attribute! Good idea, but that doesn t work either. To see why we need to bring in a few more characters into our little drama: Cooper and Kelsey. Jake, Cooper and Kelsey have amazingly similar musical tastes. Jake has rated 25 songs on our site. 2-39
40 Cooper has rated 26 songs, and 25 of them are the same songs Jake rated. They love the same kind of music and the average distance in their ratings is only 0.25!! Kelsey loves both music and our site and has rated 150 songs. 25 of those songs are the same as the ones Cooper and Jake rated. Like Cooper, the average distance in her ratings and Jake s is only 0.25!! Our gut feeling is that Cooper and Kelsey are equally close matches to Jake. Cooper Now consider our modified Manhattan and Euclidean distance formulas where we assign a 0 for every song the person didn t rate. With this scheme, Cooper is a much closer match to Jake than Kelsey is. Why? Kelsey 2-40
41 COLLABORATIVE FILTERING To answer why, let us look at a the following simplified example (again, a 0 means that person did not rate that song): Song: Jake Cooper Kelsey Again, looking at the songs they mutually rated (songs 4, 5, and 6), Cooper and Kelsey seem like equally close matches for Jake. However, Manhattan Distance using those zero values tells a different story: d Cooper,Jake = (4 0) + (5 4.5) + (5 5) ) = = 5 d Kelsey,Jake = (5 0) + (4 0) + (4 0) + (5 4.5) + (5 5) + (5 4.5) + (5 0) +(5 0) + (4 0) + (4 0) = = 32 The problem is that these zero values tend to dominate any measure of distance. So the solution of adding zeros is no better than the original distance formulas. One workaround people have used is to compute in some sense an average distance where one computes the distance by using songs they rated in common divided that by the number of songs they rated in common. Again, Manhattan and Euclidean work spectacularly well on dense data, but if the data is sparse it may be better to use Cosine Similarity. 2-41
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