Pop superstar Rihanna capped a celebrity-filled Coachella festival with a surprise appearance, as her sometime songwriter Sia took a sharply different approach by testing the possibilities of on-stage anonymity.

Rihanna turned up unannounced on stage during a headlining set of Calvin Harris, the British DJ behind a slew of electronic-infused smash hits. Sporting a camouflage cap, Rihanna went into her song ‘We Found Love,’ which was written by Harris, to the cheers of thousands of fans at the close of three days of revelry in the heat of the California desert.

Performing astride an imposing setup of flashing lights, Harris also brought in Big Sean and John Newman to sing their own hits recorded with him.

Taylor Swift, who is dating Harris and is one of the few stars even bigger than Rihanna, could be seen in the audience dancing along.

Swift’s presence is sure to fuel speculation that she could be a surprise guest next Sunday at Coachella, which runs for two consecutive weekends with the same lineups. Coachella has emerged into one of the world’s most lucrative music festivals and a destination for both partying youth and jet-set celebrities, with on-stage surprises a key part of the formula.

Amid the celebrity culture of Coachella, Sia - the Australian songwriter who wrote one of Rihanna’s biggest hits, ‘Diamonds’ - took the stage with the paradoxical goal of going unnoticed.

Sia, who has spoken of her unease since the breakthrough of her song ‘Chandelier,’ wore her now trademark half-black, half-platinum wig that covers her entire face other than her mouth and chin. Sia performed expressionless in a far corner of the stage, a giant bow over her wig, and handed over the visual representation of her music to a trio of dancers, one sporting a hairstyle uncannily like Sia’s wig.

Dancers put on contorted facial expressions, pulled their own noses and rammed their fingers into their mouths, with one performer simulating a heart attack as Sia sang her grim ‘Bird Set Free.’ For ‘Titanium,’ Sia’s hit with French DJ David Guetta featuring the signature lyric, ‘Fire away, fire away,’ two dancers donned masks of a panda and a donkey and alternatively beat each other and embraced.

Beyond the stars, Coachella has also built its reputation on selecting top indie and up-and-coming bands. Beach House, the dreamy pop duo from Baltimore, performed at Coachella for a third year but this time after achieving significant acclaim.

The band - which last year released two albums, ‘Depression Cherry’ and ‘Thank You Lucky Stars,’ within months of each other - returned to Coachella as a four-piece band with a bassist and drummer. Yet the music remains grounded in the melancholic chord progressions of keyboardist and singer Victoria Legrand and the band reinforced the imagery with a stage design that depicted a starry night, with Coachella’s palm trees lit up behind.

Legrand voiced delight in returning to the desert, calling the area ‘very loving, magical and mystical.’ Among the acts with the most palpable energy was Young Fathers, the experimental hip-hop trio from Scotland.

Then little known, Young Fathers won Britain’s prestigious Mercury Prize in 2014 and earlier this month came out with a second album, ‘White Men Are Black Men Too.’ Consisting of two artists of African descent and one who is white, Young Fathers brought a political edge to songs that merged rap with electroclash as the drummer pounded with such power that the platform shook.

Member Graham ‘G’ Hastings told the crowd that the band sought a world with ‘no borders, no flags’ and used profanity to denounce Republican presidential front-runner Donald Trump, who has campaigned against immigration. ‘We are Young Fathers, but we are all migrants. Everyone of you, everyone of us, whether you like it or not,’ Hastings said.

Other highlights included the cutting-edge saxophonist Kamasi Washington, who offered a rare jazz performance at Coachella. His ensemble included the double bassist Miles Mosley, whose heavy solo on his electrified instrument could fit into a metal song, and Battlecat, a hip-hop producer who scratched records and even turned his DJing into a jazz solo.

Washington, who gained a wider audience by playing on rapper Kendrick Lamar’s acclaimed ‘To Pimp a Butterfly’ album, said his sprawling ensemble came about because the musicians were all childhood friends in Los Angeles. ‘You might see that I got two drummers. That’s because I’ve got two homeboys who play drums,’ he joked.